Delaunay Triangulation Research Papers

Primitives for the Manipulation of General Subdivisions and Computation of Voronoi Diagrams

1985, ACM Transactions on Graphics

The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then... more

descriptionView Paper arrow_downwardDownload

Madill, A., Flowers, P., Frost, N., & Locke, A. (2018). A meta-methodology to enhance pluralist qualitative research: One man’s use of socio-sexual media and midlife adjustment to HIV. Psychology & Health, 33(10), 1209-1228.

by Anna Madill

doi.org/10.1080/08870446.2018.1475670

Aim: Our aim is to offer and illustrates a novel meta-methodology to enhance the rigour of method selection and understanding of results in pluralist qualitative research (PQR). Method: To do so, we make innovative use of Braun and... more

descriptionView Paper arrow_downwardDownload

Automated building generalization based on urban morphology and Gestalt theory

by Tinghua Ai

2004, International Journal of …

Building generalization is a difficult operation due to the complexity of the spatial distribution of buildings and for reasons of spatial recognition. In this study, building generalization is decomposed into two steps, i.e. building... more

Table 1. Possible operations for the generalization of buildings. 2.1. ANALYSIS Of possible operations jor Dullaing generalization In a digital environment, the generalization process has been decomposed into many operations (McMaster and Shea 1992), such as simplification, aggregation, combinations, collapse, etc. In particular, considering building features only, the following seem to form a subset of operations, ie. aggregation, collapse, displacement, exaggeration, selective omission, simplification and_ typification. The meanings of these operations are derived from the work by McMaster and Shea, with occasional modifications. Table 1 illustrates such operations.

Figure 1. Hierarchical structure of cities (after Patricios 2002). (a) Enclave, (b) block, (c) superblock and (d) neighbourhood.

Table2. Graphic illustrations of Gestalt factors.

Figure3. Two kinds of direct alignments. (a) Extension alignment and (b) parallel alignment.

Figure 8. Generalization of grouped buildings to various scales. (a) For 1:25000 scale, by typification, (b) for 1:50000 scale, by typification and aggregation, (c) for 1:100000 scale, by aggregation operation, and (d) for 1:250000 scale, by aggregation operation. #*. eS ee To demonstrate the method discussed in previous sections, an example is presented for purposes of evaluation. Indeed, the evaluation of generalization results is a very difficult issue. The adequacy of a generalization result is dependent on various factors such as the algorithms and constrain algorithms and o perations. The emphasis here is on the use s used to select the of urban morphology and Gestalt theory for the formation of constraints for grouping buildings in urban areas. Therefore, groupings and (2 two parameters should be considered, i.e. ( ) the adequacy of the the adequacy of the decision automatically to make a particular generalization operation (e.g. aggregation). In other words, how good an agegregation/or ty pification algorithm is will not be discussed here. The original dataset is from a developed city on the mainland of China. The

Table4. Evaluation of the example. Tr gene mor his paper has presented a met phology for the global organization hod for building groupings and then ralizations. The method makes use of the concepts developed in urban of the building groups and the formation of hierarchies. The neighbourhood model in urban morphology provides global constraints for guiding the global parti who e by means of roads (and/or rivers), neig hbourhoods are formed. Local cons and ioning of buildings set on the map as a by which enclaves, blocks, superblocks or raints are formed from Gestalt principles provide the criteria for the further grouping of enclaves, blocks, superblocks or neighbourhoods. After the grouping, some useful information, such as the sum of the building area, mean separation and standard deviation of the separations, is attached to each group. By making use of the attached information, an appropriate operation is selected to generalize a building group.

descriptionView Paper arrow_downwardDownload

Minicolumnar abnormalities in autism

by Helmut Heinsen

2006, Acta Neuropathologica

Autism is characterized by qualitative abnormalities in behavior and higher order cognitive functions. Minicolumnar irregularities observed in autism provide a neurologically sound localization to observed clinical and anatomical... more

descriptionView Paper arrow_downwardDownload

A fingerprint matching using minutiae triangulation

by Sushmita Chauhan

2004, Biometric Authentication

We present a new technique for fingerprint minutiae matching. The proposed method connects minutiae using a Delaunay triangulation and analyzes the relative position and orientation of each minutia with respect to its neighbors obtained... more

descriptionView Paper arrow_downwardDownload

Dissolved organic fluorophores in southeastern US coastal waters: correction method for eliminating Rayleigh and Raman scattering peaks in excitation–emission matrices

by Wade Sheldon

2004, Marine Chemistry

Fluorescence-based observations provide useful, sensitive information concerning the nature and distribution of colored dissolved organic matter (CDOM) in coastal and freshwater environments. The excitation -emission matrix (EEM)... more

Fluorescence-based observations provide useful, sensitive information concerning the nature and distribution of colored dissolved organic matter (CDOM) in coastal and freshwater environments. The excitation -emission matrix (EEM) technique has become widely used for evaluating sources and sinks of CDOM. Water scattering peaks, however, can create problems for quantitative analysis and display of the EEMs, especially for samples with low CDOM concentrations. Here we report a new method for eliminating Rayleigh and Raman scatter peaks from EEMs during post-processing of the data in MATLABR. An algorithm was developed to excise scatter peaks (i.e. peak emission F 10 -15 nm at each excitation wavelength) from the scan data and replace the excised values using three-dimensional interpolation of the remaining data (Delaunay triangulation method). The interpolated surface was constrained to pass through the non-excised values so that only data in excised portions were replaced. Tests of the algorithm in non-scatter regions indicate expected deviations of 0 -4% for interpolated regions of DOM fluorescence peaks (i.e. difference between measured and interpolated intensity after removal/interpolation), which is within machine error for the primary observations. This new scattering correction method is shown to provide much improved results in the quantitative analysis of EEMs compared to the conventional blanksubtraction procedure. The method is used to process EEMs and fluorescence quantum yields for water samples obtained along a salinity transect in a river located on the coast of the southeastern United States. Results of this analysis demonstrate observed shifts in EEM peak positions along most of the transect cannot be accounted for by a simple model that computes EEMs as a function of salinity assuming that the dominant driver of EEM spectral change is mixing between riverine and marine waters within the estuary. Other results show that fluorescence apparent quantum yields (AQYs) increased with increasing salinity and pH in the estuary and that the highest quantum yields are observed on excitation by 350 -380-nm light. Modeling results and the observed EEM spectral changes indicate that photoreactions had an important effect on the fluorescent dissolved organic matter (FDOM) optical properties in the estuary. The increase in fluorescence quantum yields with increasing salinity and pH in the estuary likely were caused by reactions involving magnesium or hydroxide ions that reduced fluorescence quenching by chelated iron and possibly other paramagnetic ions. The results of the study indicate that 0304-4203/$ -see front matter D Marine Chemistry 89 (2004) 15 -36 EEM analysis with careful scatter correction can provide a powerful tool for evaluating pathways for carbon cycling in estuaries. D

Fig. 1. Emission spectra of a water sample from the Satilla Estuary in the southeastern United States. The spectra are shown as line plots with the scatter-corrected scan overlain on the uncorrected scan to illustrate the peak removal and interpolation. The corrected scans are shaded. (A) Excitation at 300 nm; (B) excitation at 350 nm.

Fig. 2. Contour plots of the EEM of a Satilla water sample shown before and after scatter removal. freshwater reach (Gao and Zepp, 1998; Alber and Sheldon, 1999; Cai et al., 2000; Moran et al., 2000). The Satilla Estuary is about 30—40 km long and it enters the Atlantic Ocean in southern Georgia, USA about 40 km north of the Georgia—Florida border. Extensive tidal marshes flank the Satilla River and The Satilla River is a highly colored river with high dissolved organic carbon (25-30 mg | '), low pH (<6) and high iron content (up to 12 «1M) in its

Fig. 3. Comparison of scatter-corrected contour plots of EEMs from the high-salinity end-member (A) and the riverine end-member (B) of the Satilla Estuary. The letters A, T, M and C refer to typical positions for EEM peaks in freshwaters and seawater (see text) that have been identified by Coble (1996). To illustrate the variability of the fluorophores in the end and estuary, the EEMs of the salt-water and freshwater -members of the Satilla Estuary during a dry period low tide, in August 1998, are compared in Fig. 3 (contour view). Features in these data are consistent wit h the presence of two primary groups of fluoro- phores, as has been reported for other estuaries (Mop- per De and Schultz, 1993; de Souza-Sierra et al., 1997; Castillo, 1998; Del Castillo et al., 1999, 2000): (1) a “humic” fluorescence with emission band at 425-— 460 nm and excitation bands at <250 and at 295-330 nm; (2) protein fluorescence with emission band at 310-350 nm and excitation at 275 nm. The protein luminescence was significant only in the samples with high salinity during this study. In Fig. 3 and other figures in this paper, we have labeled four character- istic FDOM peak positions that were previously iden- tified by Coble (1996). These regions included a primary fluorescence peak from dissolved humic sub- stances (Peak A), a secondary humic substances peak characteristic of terrestrially derived DOM (Peak C), a secondary humic substances peak characteristic of marine-derived DOM (Peak M), and a peak attribut- able to fluorescence from aromatic amino acids, pri- marily tryptophan and/or tyrosine (Peak T). To illustrate the impact of the selective excision/interpo- lation scatter removal technique on quantitative anal- ysis of EEM data, we have compared this new

Fig. 4. Apparent quantum yields for scatter-corrected fluorescence of water samples from the Satilla Estuary as a function of salinity and excitation wavelength. Quinine sulfate was used as the reference standard. Excitation data for 290, 320, 350, 380, and 410 nm are shown.

Fig. 5. DOC-normalized fluorescence (excitation at 350 nm) versus salinity in the Satilla Estuary and a saltwater sample obtained 6 km east 0! the mouth of the estuary in the South Atlantic Bight. quantum yield with increasing salinity was largely offset by a decrease in the specific absorption coeffi- cient, i.e. the DOC-normalized absorption coefficient. The FDOM in the saltwater end member fluoresced more efficiently than the estuarine FDOM, but, none- theless, the fluorescence to DOC ratio of the saltwater Blough and Green, 1995). The DOC normalized fluorescence intensity at 450 nm (with excitation at 350 nm) was comparatively constant throughout the estuary with the exception of a drop-off in the saltwater end-member (Fig. 5). This result stems from the fact that within the estuary, the increase in fluorescence

Fig. 6. Wavelengths of emission (closed circles) and excitation (open circles) for long-wavelength (humic) peaks vs. salinity in scatter-corrected EEMs for water samples obtained from the Satilla Estuary compared to emission (closed triangles) and excitation (open triangles) wavelengths for humic emission peaks of EEMs modeled using simple mixing model and EEM end-members for the estuary. ee ee ee ee ee ee ee ee eee ee ee ee Changes in the emission and excitation maxima at the long-wavelength, “humic”? EEM peak (C/M re- gion of the EEM) versus salinity exhibited hypso- chromic shifts that were qualitatively similar to those reported by others (de Souza-Sierra et al., 1997; Del Castillo et al., 2000) (Fig. 6). However, the shift in the maxima to shorter wavelengths occurred at lower salinities than previously reported for other estuaries (de Souza-Sierra et al., 1997; Del Castillo et al., 2000) (Fig. 6). For example, at a salinity of 18, the emission maximum had already blue shifted by about 20 nm compared to the freshwater end member of the estu- ary, whereas Del Castillo et al. (2000) and de Souza- Sierra et al. (1997) reported much smaller shifts at this mid-range salinity. The observed shift in the Satilla Estuary EEMs versus salinity was also considerably larger than that predicted by a simple mixing model used in our MATLAB ® routines (Fig. 6). This simple model, which was similar to that described previously (Del Castillo et al., 1999, 2000), involved the simu- lated mixing of weighted EEMs of the riverine and Other factors besides simple mixing that could explain the observed FDOM spectral and quantum yield changes in the estuary include: (1) changes in physico-chemical parameters during seawater/fresh- water mixing that influence fluorescence efficiencies; (2) inputs from water sources along the estuary that have different fluorescence signatures than the riverine

Fig. 7. Comparison of EEM (contour plot) for a laboratory experiment in which Satilla riverine end-member was mixed with high-salinity end- member (dilution factor was 10.4; final salinity of mixture was 31.3) and EEM simulated using the mixing model based on the end-member EEMs and an assumed salinity of 31.3. (A) EEM for laboratory mixture; (B) EEM for modeled mixture. the saltwater FDOM, and the corrected EEM was compared to the simulated using the mixing model based on the end-member EEMs and an assumed salinity of 31.3 (Fig. 7). The EEM of the laboratory mixture exhibited a bimodal peak in the humic region (at excitation 340 nm/emission 446 nm and excitation 314 nm/emission 436 nm) that differed significantly from that of the modeled EEM (one peak with maximum at excitation 324 nm; emission 450 nm). Although others (de Souza-Sierra et al., 1997; Del Castillo et al., 2000) reported that EEM changes that occurred on mixing some estuarine water samples with open ocean water or artificial seawater could be explained by simple physical mixing, this was not the case with the Satilla Estuary water sample (Fig. 7). Physico-chemical parameters that change during sea- water/fresh water mixing, such as pH and tempera- ture, can affect fluorescence intensity to varying extents (Zepp and Schlotzhauer, 1981; Laane, 1982; Willey, 1984). As with many estuaries in the south- eastern US, the pH in the Satilla Estuary increases from pH 5-6 at the freshwater end up to pH 8 at the coast. Other possibly relevant parameters include a pronounced drop in iron concentrations from the Fluorescence intensity, corrected for dilution, can increase sharply as seawater is mixed with river water in laboratory experiments (Willey and Atkinson, 1982; Willey, 1984; de Souza-Sierra et al., 1997; Esteves et al., 1999), due in part to ionic interactions involving magnesium (Willey, 1984) and possibly to increases in pH (Zepp and Schlotzhauer, 1981; Kouassi et al., 1990; Green and Blough, 1994). This response is thought to result in nonlinear fluorescence plots for low salinity regions of some estuaries, and subsequent overestimation of FDOM at salinities beyond where this interaction occurs. We observed an increase in apparent fluorescence quantum yield with increasing salinity in the region close to the riverine end of the Satilla Estuary (Fig. 4). To learn more about the nature of this change, we diluted the freshwater end member of the Satilla Estuary with its high-salinity end-member (10.4:1 ratio of ocean water to Satilla water, final salinity 31.3). The EEM was then corrected using our MATLAB® software by removing the fluorescence emission derived from

Comparison of three-dimensional surface integration results for an undiluted low-fluorescence sample from the South Atlantic Bight (SAB) and a 11-fold dilution of a Satilla River sample (Satilla) Algorithm indicates scatter removal by selective excision and Delaunay interpolation and blank subtract indicates scatter reduction by subtraction of a Nanopure® deionized water blank prior to correction for grating configuration and quinine sulfate calibration. Satilla results were not corrected for dilution. Polygon limits and descriptions were based on Coble (1996).

descriptionView Paper arrow_downwardDownload

Geographic Patterns of (Genetic, Morphologic, Linguistic) Variation: How Barriers Can Be Detected by Using Monmonier's Algorithm

by Evelyne Heyer

2004, Human Biology

When sampling locations are known, the association between genetic and geographic distances can be tested by spatial autocorrelation or regression methods. These tests give some clues to the possible shape of the genetic landscape.... more

descriptionView Paper arrow_downwardDownload

Parallel 3D Delaunay Triangulation

by Roberto Scopigno

1993, Computer Graphics Forum

The paper deals with the parallelization of Delaunay triangulation algorithms, giving more emphasis to pratical issues and implementation than to theoretical complexity. Two parallel implementations are presented. The first one is built... more

descriptionView Paper arrow_downwardDownload

A REVIEW ON DELAUNAY TRIANGULATION WITH APPLICATION ON COMPUTER VISION

by Simena Dinas

Delaunay Triangulation is formed by a net of triangles that guarantee one property: the circumcircle of each triangle contains only the vertices of the triangle; then, there are not any point of other triangle inside the circum-circle;... more

Figure 1: a) Set of Points P. b) Delaunay Triangulation of P. c) Convex Hull of P d) Circumcircles of the Delaunay Triangulation of P. e) Circumcircles and Circumcentres of the Delaunay Triangulation of P f) Voronoi Diagram and Delaunay Triangulation of P Voronoi Diagrams is represented in figure 1f. Radial Sweep has four steps [HD06]; [MW82]: i) to choose the centroid in a set of points P, then, linking togethe e centroid point with every point in P. ii) Sort and order the points by orientation and distance (except the centroid), then 1k them all together in star-shape without crossing, iii) to add triangles to form a convex shape (convex hull), joi gether the points inside and outside. A triangulation is created, but it may or may not be a Delaunay Triangulation ) Finally, is required to arrange the points focused on their angles in order to produce a correct triangulation. For the se points P shown in figure 1a a Delaunay Triangulation is created in figure 1b. A convex hull for P is depicted in yure 1c. Whereas figure 1d depicts the circumcircles, figure 1e shows the centers for each circumcircles. Finally, th oronoi Diagrams is represented in figure 1f.

Figure 3: a) Delaunay Triangles b) Non-Delaunay Triangles c) Bad Angles in a Delaunay Triangulation. d) Good Angles in a Delaunay Triangulation. e) No-Unique Delaunay Triangulation f) No-Unique Delaunay Tetrahedralization for every triangle, the circumcircle encloses three points. Boundary: The external edges of a Delaunay Triangulation DT (P), make the Convex-hull for P. The Loca

Sequence of insertion of a point p in a Delaunay Triangulation. In figure 4a: the initial Delaunay Triangulation of the set of eight points. In fgure 4b: a new point p is inserted in To let P? be a set of points in R’ then to let T* be a Triangulation of P*, T? is a Delaunay Triangulation of P*, DT’ (P’) if and only if for every triangle of T’, the circumcircle does not contain any other points of P? (see figures 4a, Ab, 4c, 4d and 4e). Delaunay Tetrahedralization is based on extending Delaunay Triangulation to three dimensions. To let P* be a set of points in R® then to let T° be a Tetrahedralization of P*, T’ is a Delaunay Tetrahedralization of P®, DT? (P°) if and only if for every tetrahedron of T°, the circumsphere contains no other points of P®.

Figure 5: a) The Lena Picture. b) Corner Extraction of Lena Picture c) Delaunay Triangulation by Using Cloud of Points from Lena Picture order to depict an easily identifiable triangulation. The features extracted were comers or interesting points from the image. Preliminary results on Delaunay Triangulation include implementation and tests. In order to show the Delaunay In general terms, the Delaunay Triangulation can be proved with a cloud of points; however, data can be hardly

Figure 6: a) This Figure Shows an Image Called Tsukuba b) This Figure Represents the Tsukuba Cloud of Points Extracted from the Image c) This Figure Represents the Tsukuba Triangulation by Means of the Cloud of Points Extracted from the Image d) The Tsukuba Picture Superimposes with the Triangulation of the Figure 6c

Delaunay Triangulation and Tetrahedralization Tests Jelaunay Triangulation orientation and inCircle tests: To calculate a Delaunay Triangulation, a circumcircle test Delaunay Triangulation is shown in figure 4e. Some steps have been ignored.

descriptionView Paper arrow_downwardDownload

Automatic reconstruction of surfaces and scalar fields from 3D scans

by Chandrajit Bajaj

1995, Proceedings of the 22nd annual conference on Computer graphics and interactive techniques - SIGGRAPH '95

We present an efficient and uniform approach for the automatic reconstruction of surfaces of CAD (computer aided design) models and scalar fields defined on them, from an unorganized collection of scanned point data. A possible... more

descriptionView Paper arrow_downwardDownload

Composite Structured Mesh Generation with Automatic Domain Decomposition in Complex Geometries

by K.W. Chau

2013, Composite Structured Mesh Generation with Automatic Domain Decomposition in Complex Geometries

This paper presents a novel automatic domain decomposition method to generate quality composite structured meshes in complex domains with arbitrary shapes, in which quality structured mesh generation still remains a challenge. The... more

mesh nodes are classified into three types: internal nodes, boundary nodes, and external nodes. The first two types are active nodes on which computations are carried out, while the external nodes are inactive and only used to maintain the global structure of the mesh. Fig. 1 shows meshes generated in an L-shaped domain with and without “blank-off’ technique. As shown in Fig. la, the dashed lines consist of external mesh nodes. The mesh without “blank- off’ technique (see Fig. 1b) has fewer nodes (4x11) than mesh with “blank-off’ technique (7x11, Fig. la), but its mesh orthogonality is much worse than that with “blank-off’ technique. This “blank-off’ technique is very suitable for multi-block mesh generation in the sense that each blocked-mesh contains only active nodes and all inactive nodes will be automatically excluded. Fig. lc shows a multi-block scheme incorporated with “blank-off’ technique. As can be seen, two blocks can be used for mesh generation with “blank-off’ technique in this L- shaped domain in order to maintain the maximum mesh orthogonality.

(b) Domain B:5 interface lines in solid lines; Interface lines BA and BH sharing one effective concave point B

Assembling is actually a re-numbering process to make the global indices of mesh nodes in each block satisfy a structured mesh. In this study, to simplify the assembling process, assembling always occurs between two structured meshes at one time, which means assembling can occur either between two neighboring blocks B; and B,, denoted by B+8,=8,,,, or between an assembled mesh and a neighboring block B, denoted by B,,+B,=B This assembling I+m+n * process is an iteration process described as follows:

2.5 Discussions Comparing Fig. 10a without refinement to Figs. 10b, c and d with refinements, it has shown tha refinement for the initial input boundary produced more virtual edges connecting to the inserted fla points, and thus more choices of the SVE for the effective concave points. Although it may yield more blocks, the shape of blocks may be more regular. On the other hand, refinement can also reduce the uncertainties of the IDT for the inpu boundary which may contain flat points or other points ineffective to geometry controls. 2.5.1 Parameters

the idea of the current study. It is expected to be more difficult to apply the present algorithm because of the natural complexities of 3D problems.

descriptionView Paper arrow_downwardDownload

A multi-modal approach for face modeling and recognition

by Mohammad Mahoor

2007

of a dissertation at the University of Miami. Dissertation supervised by Dr. Mohamed Abdel-Mottaleb. No. of pages in text. (169)

Figure 5.2: A set of 1-D log-Gabor filters seen in logarithmic and linear frequency scales.

Figure 1.1: Annual biometric industry revenues for the years 2007-2012 [8]

Figure 1.2: The percent of biometric market by technology in 2006 [8].

Figure 1.3: The general block diagram of our system for multi-modal face recognition based on 3-D ARG models.

Figure 1.4: The general block diagram of our system for multi-modal face recognition based on ridge images and 2-D ARG models.

Figure 1.5: Comparison between the three categories of algorithms for 3-D face recog- nition, performance of the system versus complexity.

1.3.2 A Unified Approach for 2-D/3-D Face Recognition

Figure 2.3: The graph representation of faces used in elastic bunch graph matching [163].(a)Elastic graph representation. (b)Bunch graph.

Figure 3.1: Template matching: (a) Template range image (b) A sample filtered facial range image (c) Detected area of the face in the sample range image.

Figure 3.3: Three feature points labeling: (a) Gaussian curvature on a patch around the nose and eyes (b) Result of thresholding the Gaussian curvature image(c) Final result of feature points labeling

Figure 3.4: 2-D and 3-D range views of an individual: 2-D gray scale images, 3-D range images at 1/4 of the original resolution (both from scanner’s point of view) and a rotated version of 3-D range image [115].

Table 3.1: Performance Comparison Between the Two Methods and the Manually Labeled Features Based on the Average MSE (pixels) Over All 70 Subjects.

Figure 3.7: Extracted facial features sample images from UM database, where stan- dard method outperforms our method, (0) Improved ASM, (*) Standard ASM. The MSE (pixels) of the enhanced to standard ASM for the images are (a) [34.64, 24.87] and (b) [14.02, 9.55).

Figure 4.1: Block diagram of our system for 3-D face recognition from range data. and 3-D facial features labeling were presented in Chapter three.

Figure 4.2: Sample of ridge image extracted for different subjects.

Table 4.2: Results of first-ranked recognition rate on the Gavab face database using range data.

Figure 4.4: CMC curves for frontal neutral images in Gavab database based on ridge images matched using the ICP and Hausdorff distance techniques.

Figure 4.5: ROC curves for frontal neutral images in Gavab database based on ridge images matched using the ICP and Hausdorff distance techniques.

Figure 4.7: CMC curve for 370 subjects in the FRGC V2.0 database based on ridge images matched with the ICP and Hausdorff techniques.

Figure 4.8: ROC curve for the neutral faces versus neutral in FRGC2.0 database (total of 2365 facial images for 432 individual subjects); ICP technique is used for matching the ridge images.

Figure 4.9: ROC I: the data are within the semesters. ROC II: the data are within the year. ROC III: the images are between the semesters.

Figure 5.3: Two pairs of log-Gabor wavelets, odd-symmetric and even-symmetric (all tuned to the same frequency, wo = 1, but having bandwidths of 1 and 3 octaves respectively. )

Figure 5.4: Angular component at angle = 0 and sigma = 1.5.

Figure 5.6: The mutual relation between the nodes.

Figure 5.7: Extracted landmark points. 57 landmark points (white color) are ex- tracted by the ASM method and the 52 landmark points (blue color) are added by aligning a standard template to the facial points.

Figure 5.8: Maps that show number of the selected (a) 2-D and (a) 3-D attributes at each node of the ARG model.

Figure 5.9: Results of feature selection for 3-D and 2-D attributes in the ARG model.

Figure 5.10: Neutral 3-D model used to estimate and normalize the pose of a deformed 3-D model. The refernce model is at angles (pitch, yaw, roll) = (0,0,0).

Figure 5.11: 3-D textured model (a) before normalization and (b) after normalization.

Figure 5.12: Fusion can be accomplished at various levels in a biometric system [140].

Figure 5.13: Dual threshold scenarios and uncertainty in a verification mode.

Figure 5.15: Cumulative Match Characteristic curves using the ARG modeling and two different fusion techniques on the UM database.

Figure 5.16: Results of rank-one identification using the ARG modeling and two different fusion techniques on the UM database and the results of other matching techniques applied to the UM database.

Figure 5.18: Imposing uncertainty and then applying DS rule of combination to fuse the three match scores resulted from ARG modeling (the UM face database), the Equal Error Rate was improved by 1.5%.

Figure 5.19: Analyzing the robustness of the ARG model in face recognition with respect to added noise in location of the nodes. Results of rank-one identification are represented for 2-D attributes, 3-D attributes, mutual relations, and multi-modal fusion with respect to various values of o of the Gaussian noise.

Figure 5.20: CMC curves. (a)for 2-D, 3-D, Mutual relations features, and fusion using DS rule and weighted sum rule for the neutral images versus neutral in FRGC V2.0 data-set; (b) the details in (a).

Figure 5.21: Results of rank-one identification using the 2-D ARG modeling, 3-D ridge images, and two different fusion techniques on the FRGC database.

Figure 5.22: ROC curves for 2-D, 3-D, Mutual relations features, and fusion using DS rule and weighted sum rule for the neutral images versus neutral in FRGC V2.0 data-set.

To find the parameters of the 2-D affine transformation, we need at least three cor- by the model coordinate system. extracted feature points in the image coordinate system with the points represented

Figure A.1: Detecting the center of the mouth and the eyes as the salient features for initialization.

Table C.1: Sequential Floating Forward Selection algorithm for feature selection |139

Table 1.1: Typical applications of face. .2.1 Applications of Face Recognition

Table 1.2: Variations in facial appearance Inter-person and intra-person variations.

Table 2.1: Facial features extraction techniques.

Table 2.2: Classification of 2-D face recognition techniques [179]. that there exist significant statistical redundancies in natural images [142]. For |

Table 4.5: Verification rates (%) at 0.1% FAR for the ROC I, II, and III of the neutral v.s. neutral images.

descriptionView Paper arrow_downwardDownload

An <formula formulatype="inline"><tex Notation="TeX">$\bm{O(n\log n)}$</tex></formula> Shortest Path Algorithm Based on Delaunay Triangulation

by Gene Jan

2000, IEEE/ASME Transactions on Mechatronics

In Euclidean and/or λ-geometry planes with obstacles, the shortest path problem involves determining the shortest path between a source and a destination. There are three different approaches to solve this problem in the Euclidean plane:... more

descriptionView Paper arrow_downwardDownload

Publikasi_ThesisS2

by Pius Anggoro

Fungsi pembangkit mesh adaptif, meshqt2d, telah berhasil dikembangkan dengan menggunakan bahasa pemrograman matematik MATLAB®. Keluaran program pembangkit mesh ini secara umum adalah file yang berisi data distribusi nodal dan data... more

descriptionView Paper arrow_downwardDownload

AN ENHANCED ALGORITHM FOR SURFACE RECONSTRUCTION FROM A CLOUD OF POINTS

by Ashraf Hussein

In this paper, a comparative study is performed between the most eminent computational geometry based surface reconstruction algorithms. These algorithms are the Crust, the Power Crust, the Tight Cocone and the Ball Pivoting algorithm.... more

-Surface accumulation and assembling: Finally, the initial mesh and the small meshes (of the holes) are all accumulated to form the object surface. The new small meshes are “pasted” to the initial mesh. 4, Implementation and Results

(e) original surface (f) sample points (7108 points) Figure 2. The Stanford models. (a), (b) Bunny. (c), (d) Dragon. (e), (f) Happy.

Figure 7. The output meshes of the four algorithms when applied on the noisy 1889 Stanford Bunny. Figure 7 shows the reconstructed meshes after applying the four algorithms on the noisy Bunny. Generally, each algorithm output retains the same expected features (the Crust output is not a manifold, the Power Crust the number of holes in each mesh. The BPA appeared in (figure 7(d)) ou and tout is dense, etc), but the noise effect the Crust (figure 7(a)) outputs have the largest number of holes, but the BPA holes are slightly wider. The Tigh number of (figure 7(b) , du built at the ears. t Cocone output (figure 7(c)) has the less holes, followed by the Power Crust output t the Tight Cocone mesh is not correctly

SMA egg NF MEE AEN YM Aen ee. Figure 6. The output meshes of the four algorithms when applied on 1889 Stanford Bunny.

The new hybrid system was tested on a 28060 points sample of an incomplete Bunny model. The model is shown in figure 8. The code used for the RBF part is available in [24]. The cloud of points contains many undersampled regions and represents a good example of a misregistered data set. The BPA was applied using p = 0.5. Figure 9(a, b) shows that the reconstructed surface after applying the BPA (phase one) contains many holes in different places (the back, the tail, the head ... etc) with different sizes. Figure 9(c, d) also shows how the holes disappeared after applying the additional phases of the system. The output surface is 29967 points in size.

AG] ViMu vice Aye Me Figure 8. Incomplete Bunny sample points (28060 points). 4.5 Accuracy Assessment

Figure 10. Bunny with hole at the back. The circle surrounds the hole. Table 6. error statistics with different neighborhood radii

Figure 11. Relation between mean value of the error and the neighborhood radius

Table 2. Regression test results of time curves Table 3. Regression test results of memory curves

The output size of the mes f the model shape, has time and memory. In algorithms construct, regardless o the same linear behavior of the figure 5, where output size is plo this fact is proved. As the Power C triangular and its vertices are not plot points, it is not appropriate to tted rus hes that the four against input size, t output mesh is not the original input its size with the meshes sizes of the other three algorithms. Otherwise, the number of vertices and the output size of the Power Crust output meshes are written separate y in table 5.

Figure 6 shows the reconstructed meshes of the 1889 Bunny model after applying the different algorithms on it. The Crust output (figure 6(a)) is good but it is not a manifold. The BPA output (figure 6(d)) shows a problem at the right ear end and another one at the left ear. Besides being watertight, the Power Crust output (figure 6(b)) may be the best of the four, except that the mesh is very dense and not triangular. The Tight Cocone output (figure 6(c)) is also watertight, but shows a problem at the left ear end (a triangle is not connected to the rest of the ear).

Table 4. Regression test results of mesh size curves

descriptionView Paper arrow_downwardDownload

Efficient computation of clipped Voronoi diagram for mesh generation

by Yang Liu

2013, Computer-Aided Design

The Voronoi diagram is a fundamental geometric structure widely used in various fields, especially in computer graphics and geometry computing. For a set of points in a compact domain (i.e. a bounded and closed 2D region or a 3D volume),... more

The Voronoi diagram is a fundamental geometric structure widely used in various fields, especially in computer graphics and geometry computing. For a set of points in a compact domain (i.e. a bounded and closed 2D region or a 3D volume), some Voronoi cells of their Voronoi diagram are infinite or partially outside of the domain, but in practice only the parts of the cells inside the domain are needed, as when computing the centroidal Voronoi tessellation. Such a Voronoi diagram confined to a compact domain is called a clipped Voronoi diagram. We present an efficient algorithm to compute the clipped Voronoi diagram for a set of sites with respect to a compact 2D region or a 3D volume. We also apply the proposed method to optimal mesh generation based on the centroidal Voronoi tessellation. 5 biology and so on. 6 Suppose that a set of sites in a compact domain in 7 R d is given. Each site is associated with a Voronoi 8 cell containing all the points in R d closer to the site 9 than to any other sites; these cells constitute the 10 Voronoi diagram of the set of sites. Voronoi cells of 11 those sites on the convex hull are infinite, and some 12 of Voronoi cells may be partially outside of the spec-13 ified domain. However, in many applications one 14 usually needs only the parts of Voronoi cells inside 15 the specific domain. That is, the Voronoi diagram 16 restricted to the given domain, which is defined as 17 the intersection of the Voronoi diagram and the do-18 main, and is therefore called the clipped Voronoi 19 diagram [1]. The corresponding Voronoi cells are 20 called the clipped Voronoi cells (see Figure 1). 21 Computing the clipped Voronoi diagram in a con-22 42 remeshing framework to 2D/3D mesh generation. 43 To minimize the CVT energy function, one needs to 44 compute the clipped Voronoi diagram in the input 45 domain for function evaluation and gradient com-46 putation (see Section 2). 47 In this paper, we shall present practical algo-48 rithms for computing clipped Voronoi diagrams 49 based on several simple operations. The main idea 50 intersection of Voronoi diagram and the domain di-52 rectly, we first detect the Voronoi cells that have in-53 tersections with domain boundary and then apply 54 computation for those cells only. We use a simple 55 and efficient algorithm based on connectivity propa-56 gation for detecting the cells that intersect with the 57 domain boundary (i.e., polygons in 2D and mesh 58 surfaces in 3D, respectively). We also utilize the 59 presented techniques for mesh generation as appli-60 cations. The contributions of this paper include : 61 • introduce new methods for computing the 62 clipped Voronoi diagram in 2D regions (Sec-63 tion 3) and 3D volumes (Section 4); 64 • present practical algorithms for 2D/3D mesh 65 generation based on the presented clipped 66 Voronoi diagram computation techniques (Sec-67 tion 5).

Figure 1: Examples of clipped Voronoi diagram in a circle (a) and a cylinder (b). The clipped Voronoi cells on the boundary are shaded.

Figure 2: Illustration of main steps for computing clipped Voronoi diagram in 2D. (a) Delaunay triangulation, (b) 2D Voronoi diagram, (c) detect boundary sites, (d) compute clipped Voronoi diagram.

Figure 5: 2D CVT-based meshing. (a) The clipped Voronoi diagram of initial sites; (b) the result of CV with p = 1; (c) the result of constrained optimization. Notice that boundary seeds are constrained on th border; (d) the final uniform 2D meshing.

Figure 3: Illustration of clipped Voronoi diagram computation of 500 sites in a torus. (a) Surface RVD of 227 boundary sites, (b) Clipped Voronoi diagram.

Figure 4: Illustration of the propagation process. The green points are the vertices of input boundary mesh and the white points are the sites. The yellow points in (b) are the vertices of RVD.

Figure 6: Illustration of the CVT-based tetrahedral meshing algorithm. The wireframe is the boundary of the input mesh. (a) The clipped Voronoi diagram of the initial sites (the boundary Voronoi cells are shaded); (b) the result of the unconstrained CVT with p = 1; (c) the result of the constrained optimization. Notice that boundary seeds are constrained on the surface S; (d) the final isotropic tetrahedral meshing result.

Figure 7: Results of clipped Voronoi diagram computation.

Figure 8: Comparison of the propagation-based surface RVD computation with the kd-tree-based approach.

Figure 9: The timing curve of the clipped Voronoi diagram computation against the number of sites on Bone model.

Figure 10: Clipped Voronoi diagram of a sphere. The sites are the vertices of the sphere. (a) The surface RVD, (b) the clipped Voronoi diagram.

Figure 12: CVT-based 2D mesh generation of a ring. Figure 11: Clipped Voronoi diagram of a cube. Red points represent the sites. (a) The input domain, (b) the surface RVD, (c) the clipped Voronoi dia- gram.

Figure 13: CVT-based 2D mesh generation. The boundary vertices of the input domain are used as constraints.

Figure 15: Comparison of the meshing qualities of the sphere with the Delaunay refinement approach implemented in CGAL [4].

Figure 16: Comparison with the octree based ap- proach [27]. The resulting tetrahedral mesh has 200k tetrahedra.

Figure 17: Approximation error of gargoyle model: 50K vertices, 256K tetrahedra, mean/max Haus- dorff distance: 0.045%/0.37%. Our approach pro- duces smaller approximation error compared with [30] (mean error: 0.053%) using the same number of vertices.

descriptionView Paper arrow_downwardDownload

A Multimodal Approach for Face Modeling and Recognition

by Mohammad Mahoor

2000, IEEE Transactions on Information Forensics and Security

of a dissertation at the University of Miami. Dissertation supervised by Dr. Mohamed Abdel-Mottaleb. No. of pages in text. (169)

descriptionView Paper arrow_downwardDownload

Fingerprint verification using computational geometry

by DYNA Revista and

This paper presents a robust minutiae based method for fingerprint verification. The proposed method uses Delaunay Triangulation to represent minutiae as nodes of a connected graph composed of triangles. The minimum angle over all... more

descriptionView Paper arrow_downwardDownload

Exploiting Voronoi Diagram Properties In Face Segmentation and Feature Extraction

by Abbas Cheddad and

2008, Pattern Recognition

Segmentation of human faces from still images is a research field of rapidly increasing interest. Although the field encounters several challenges, this paper seeks to present a novel face segmentation and facial feature extraction... more

Fig. 13. An image from WWW, our ellipse and circle model superimposed on the detected face. (a) Eyes detected and (b) Geometrical distance measurement generating seven unique points. Table 5

Fig. 1. The GUI of the proposed system: (1) the currently loaded image, (2) an optional check box to store the process with its information in an external file (HTML) as shown in Fig. 24 in the Appendix, the generated file can be viewed or deleted by clicking the “View” drop-down menu, (3) elapsed time for face detection measured in seconds, (4) image complement segmentation, (5) direct image segmentation, (6) segmented face displayed as a blob and (7) the settings panel.

Fig. 2. (Left) Delaunay triangulation of seven dot patterns (black) and their VD (thick lines in blue). (right) This naturally created Voronoi diagrams on these rocks might have been the inspiration behind the discovery of VD.

Fig. 3. Delaunay construction. pgr defines a Delaunay triangle when the centre (S) of the circle circumscribed to pqr is a Voronoi vertex.

Fig. 4 and 5. 4. Gray-level frequency (getting global maxima). 5. Exposing local minima.

Fig. 6. Delaunay triangulation generated from points of the histogram shown in Fig 4 and 5. end for

Fig. 7. Application of the algorithm on a scene of nature, as it is clear our method can be extended to segmentation of non-face images. Top to bottom: original image, direct image segmentation (DS), image complement segmentation (CS) and the corresponding colour mapping of DS.

Fig. 8. Comparison of image segmentation using the K-means and of our method. (a) Original images; (b) (left column) output of K-means segmentation with Gauss law, (middle column) output of K-means segmentation with Rayleigh law and (Right column) face region; (c) (left column) the proposed image complement segmentation, (middle column) direct segmentation and (right column) face region.

Fig. 9. Applying distance transformation to separate the face when it is merged with the background. (a) Original image, (b) Voronoi-based image segmentation, (c) face boundary merged with the background, (d) the distance transformation of (c) with an appropriate threshold, and (e) the final segmented face.

Fig. 11. Face repairing. (a) Original BioID image, (b) image segmented into homoge- nous regions, (c) face blob detected but the left eye region is missing, and (d) face boundary repaired thanks to the convex hull. Fig. 10. Test results of face segmentation on Set 3 (BioID). (Columns left to right) Original images, Voronoi based image segmentation and segmented faces. attractive:

Given the sequence of coordinates of Delaunay triangles (e.g., possible feature points), the pseudo-code described beneath follows:

Fig. 12. Clustering concept based on Delaunay Triangulations.

Fig. 14. The proposed ellipse and circle for mouth and nose detection.

Fig. 15. The process of mouth detection. (a) The two possible mouth regions, (b) the two possible nose regions, (c) detected nose and (d) detected mouth, the neare: location to the nose of the two possibilities.

Fig. 16. An example of the test set from the BioID database. Fig. 17. Segmented faces corresponding to the set shown in Fig. 16.

Fig. 18. Automatic location of eyes shown as red cross signs. Faces are copped and zoomed manually to enhance the visualization

Fig. 19. Eye regions extracted. Note that the applied DisT gives each face feature its representative.

Fig. 20. Eyes detected shown as red crosses. (a) Sample from the BioID database, (b) sample from our CCD camera and (c) samples from the WWW.

Fig. 21. Feature extraction. Top two rows refer to ORL database while the bottom one refers to our CCD database.

Fig. 22. Mouth and nose probable locations. (a) Geometrical distance measurement generating seven unique points, (b) distance transform applied on the seven poin (c) extracted probable mouth regions and (d) extracted probable nose regions.

Fig. 23. A general block diagram of the proposed system.

Fig. 26. Delaunay graph: (left) model face image; (middle) skin synthesized image; (right) selected facial regions and Delaunay graph [37]. Fig. 25. Face (skin) skeleton and face shape refinement: (a) a binarized face image; (b) initial skeleton; (c) skeleton after artifacts removing; (d) components in the face after artifacts removing. The S-triangles in each component have the same colour [35].

Fig. 24. The HTML report generated by triggering the check box appearing in Fig. 1.

Fig. 27. Our system’s rotation invariance: (left box) features extraction before rotation and (right box) rotating the face model image by 45° counter-clockwise. Note, eve! though the rotation was approximately corrected (0 = —42.5926) but the features were extracted perfectly.

Fig. 28. Our system’s adaptation to scale changes. Face size (25 x 37).

Fig. 29. Our system’s adaptation to scale changes. Face size (65 x 88).

descriptionView Paper arrow_downwardDownload

Triangulation for Surface Modelling

by Ali Alesheikh

Surface reconstruction by means of triangulation of point data leads to computational complex optimization problems. Delaunay triangulation is a common method for domain triangulation. There are other algorithms for triangulating a point... more

descriptionView Paper arrow_downwardDownload

Quasi-3D modeling of airborne TEM data by spatially constrained inversion

by ANDERS VEST CHRISTIANSEN and

2008, GEOPHYSICS

We present a new methodology, spatially constrained inversion ͑SCI͒, that produces quasi-3D conductivity modeling of electromagnetic ͑EM͒ data using a 1D forward solution. Spatial constraints are set between the model parameters of... more

descriptionView Paper arrow_downwardDownload

Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization

by Jorge Nocedal

1997, ACM Transactions on Mathematical Software

In this article, software for the numerical approximation of double integrals over a variety of regions is described. The software was written in Cϩϩ. Classes for a large number of shapes are provided. A global adaptive integration... more

Fig. 1. Finite regions available in Cubpack++. regions, we refer to the Cubpack++ User’s Manual [Cools et al. 1994]. At this point, we only want to mention that the regions are specified by the user by giving the points or distances indicated in the figures. The transformations applied to nonprimitive regions appear in Table II. 5. PRIMITIVE REGIONS

Fig. 2. Infinite regions available in Cubpack+ +. The region is that part of the plane marked with X and bounded by the solid lines; lines with an arrow have to be extended to infinity. 5.2 The Parallelogram C,

Fig. 3. Used subdivisions of a triangle, a parallelogram, and a circle. An active circle is dissected into a circle and four polar rectangles, as in Figure 3, such that all five subregions are of equal area. If this kind of subdivision has occurred too many times, then the active circle is divided into four polar rectangles such that all four subregions are of equal area.

After calling Integrate you can access the integral and error on each part of a collection, i.e., you know Roof.Integral( ) as well as Walls.Integral( ), etc.

Table I. Elementary Transformations transformation to obtain another virgin region of different shape (we call this strategy “passing the buck”) or the application of a basic cubature formula with error estimate (see Section 5). In the case of active regions, processing at present means subdivision, although in principle it might mean the application of a more accurate cubature formula. The region or regions obtained by processing an active region are called its “descen- dants.”

descriptionView Paper arrow_downwardDownload

A contact domain method for large deformation frictional contact problems. Part 1: Theoretical basis

by J. Cante

2009, Computer Methods in Applied Mechanics and Engineering

In the first part of this work, the theoretical basis of a frictional contact domain method for two-dimensional large deformation problems is presented. Most of the existing contact formulations impose the contact constraints on the... more

descriptionView Paper arrow_downwardDownload

Primal/Dual Mesh with Application to Triangular/Simplex Mesh and Delaunay/Voronoi

by Humayun Irshad

This document describes an extension of ITK to handle both primal and dual meshes simultaneously. This paper describe in particular the data structure, an extension of itk::QuadEdgeMesh, a filter to compute and add to the the structure... more

Figure 9: Primal to dual mesh with inside hole

The genus of a surface is related to the Euler characteristic x. For an orientable surface such as a spher (genus 0) or torus (genus 1), the relationship is

Figure 2: Triangulation and Simplex Mesh and a tetrahedron of non-zero volume is a 3-simplex mesh. Formally, a k-Simplex Mesh (kSM) of R? is defined as a pair (V(M), N(M)) [1] where:

Figure 3: Examples of Dual Meshes. (We also sampled the border points.)

Figure 4: a) A 1-Simplex mesh and its dual; b) A 2-Simplex mesh and its dual triangulation; c) same as (b). The dual of the triangulation boundary is considered to extract the simplex mesh.

Table 2: Summaries of changes in new data structure

We perform last test on non-planer mesh. A spherical triangulation mesh can be seen in figure 11(a), generated simplex (dual) mesh along with triangulation (primal) mesh can be seen in figure 1 1(b) and finally, simplex (dual) mesh generated with new adaptor can be seen in figure 11(c).

existing data structure by adding two reference pair; primal point to dual cell and primal cell to dual point as shown below. With this design, no look up table is required to maintain the primal and dual references. So it is very efficient approach but not compatible with respect to previous code and test cases.

descriptionView Paper arrow_downwardDownload

Efficient and good Delaunay meshes from random points

by Scott Mitchell

2011, Computer-Aided Design

We present a Conforming Delaunay Triangulation (CDT) algorithm based on maximal Poisson disk sampling. Points are unbiased, meaning the probability of introducing a vertex in a disk-free subregion is proportional to its area, except in a... more

descriptionView Paper arrow_downwardDownload

Text region extraction in a document image based on the Delaunay tessellation

by yi xiao

2003, Pattern Recognition

In this paper, Delaunay triangulation is applied for the extraction of text areas in a document image. By representing the location of connected components in a document image with their centroids, the page structure is described as a set... more

Fig. 1. Connected components in a text region. Each connected component is bound by a rectangular box.

Fig. 2. Delaunay triangulation for the point set V = { py, po, P3> P4, ps} ina plane. B( pi, p2, p3) is the circumscribing circle of Delaunay triangle A p; po p3. B(p1, p2, p3) does not contain any other points pq, ps.

Fig. 3. Delaunay triangulation on the connected component cen- troids. Character “t” (a connected component in the middle) has 5 neighbours: e, f, h, n, c. They are linked to “t” by Delaunay edges. Character “th” has 5 neighbours: e, p, t, i, c.

Fig. 4. The correctly classified foreground (filled) and background triangles in a document image.

Fig. 5. Pool triangles caused by wider inter-word gap. (a) A doc- ument image, and (b) its Delaunay triangulation.

Fig. 7. LS histogram for image from Fig. 4. J, = 52, /, = 65. Fig. 6. Thread triangles are indicated with filled triangles. They are formed by single text lines, titles, and some random points in the image.

Fig. 8. The « histogram h;(«) of each edge-connected foreground triangle area Ti in Fig. 4, i= 1,2,...,8.

Fig. 10. Generation of text body boundaries and single text lines. (a) The binary image page. (b) Partition the foreground (filled triangles) and background triangles. (c) Pend the “holes” in text regions by marking pool triangles as foreground triangles. Text areas are connected foreground triangles (filled triangles) with r > rj. (d) Find the thread triangles (filled triangles). (e¢) Cluster thread triangles (filled triangles), filter out irregular shaped thread triangles. (f) The text body boundaries consist of adjacent sides of background triangles and text area triangles. The single text lines are shortest sides of regular thread triangles.

Fig. 13. Comparison of different methods. (a) The binarized textual image. (b) Kise et al.’s method. Each head line in S7 (“CADA Data”, “Enterprise WAN”) is divided into two regions. Words in one line of the reference list are fragmented in Sg. (c) Antonacopoulos’ method. The vertical and horizontal smearing value is 8 and 7 respectively. The second head line in S7 is split into two blocks. The image in S7 is merged with a text region. (d) The proposed method. All the single text lines are partitioned into individual lines. The title °>CADA Data” is classified into one cluster in collinearity test. The same is to the title “Enterprise WAN”.

Regularity ratio for the connected foreground triangle groups in Fig. 4

Processing time of typical document images

Mo: Kise et al.’s method,M3: the proposed methoc *Delaunay triangulation/Voronoi diagram. Border following method [4]. °Plane sweep method [4]. 4Contour tricing method [19]. €Conventional incremental method [5]. Comparison of processing time for the two methods Table 3

MI: Antonacopoulos’ method, M2: Kise et al.’s method, M3: the proposed method. Segmentation results for wide inter-word document images Table 4

descriptionView Paper arrow_downwardDownload

A faster circle-sweep Delaunay triangulation algorithm

by Ahmad Biniaz

2011, Advances in Engineering Software

This paper presents a new way to compute the Delaunay triangulation of a planar set $P$ of $n$ points, using sweep-circle technique combined with the standard recursive edge-flipping. The algorithm sweeps the plane by an increasing circle... more

Fig. 6. The next unused vertex vg is taken from the input list. Projection of 1g hits the edge (v3, v7) of frontier (a), walking to the left side started (b), walking on the left follower site (c), end of left-side walking (d).

Fig. 7. The basin. Generation of tiny triangles (a), Projection of v; on the frontier (b), right-side and right-side follower neighbors of 1; (c), detecting the basin (d), bottom vertex, left and right borders of basin (e), and removing basin (f).

Fig. 8. Conversion of the frontier to the convex hull. Scanning the frontier for missed triangles (a), frontier is now coinciding with the convex hull, and triangulation is completed (b).

Fig. 1. Points are numbered according to their priorities. The frontier is (1, 4, 6, 3, 5, 2,1). The next Delaunay triangle is A635.

Fig. 2. The advancing front edges in dashed lines and the lover convex hull edges in dot lines: vertical projection of the next site hits the advancing front (a), new triangle is constructed and legalized, advancing front is updated, walking to the left and right (b), and walk in right-side direction is stopped (c).

Fig. 3. The validated Delaunay edges in full-lines and the non-validated edges in dashed lines. The sites are numbered according to their distance from O. Front is (1, 9, 1, 7, 4, 6, 2, 5, 3, 8, 1). The ultimate points associated to frontal triples (6, 2, 5) and (8, 1,9) are shown.

Fig. 4. The main idea of the sweep-circle algorithm. The sites are numbered according to their distances from O. Projection of v;¢ hits the edge (v,,, vg) of the frontier (a), new triangle is generated (b) and legalized (c).

Fig. 9. Each vertex of the frontier points to the rightmost triangle being defined by that vertex. The frontier data structure must support O(1) time access to a triangle from a neighboring triangle. Almost all commonly used data structures storing planar triangulations support this opera- tion: DCEL (Doubly Connected Edge List) or simply a linked list

Fig. 10. Implementation of the frontier: A hash-table on a circular double linked list. Fig. 11. The influence of parameter k on spent CPU time in triangulation phase. Dashed lines for Zalik, and solid lines for sweep-circle.

Fig. 5. Two possible configurations for initial frontier. The sites are numbered according to their distances from O.

We analyzed the relation between spent CPU time and the num- ber of entries into the hash-table, h, which is related to k. Fig. 11 compares the spent CPU time of our sweep-circle and Zalik’ sweep-line algorithms according to parameter k, while triangulat- ing different set of points at uniform distribution. The same result: also obtained by triangulating non-uniform distributions such as Gaussian and grid datasets. It shows that the value of k has a great affect on the running time of both algorithms. If k is too small or toc large, the running time of the algorithms increased. So, it is impor- tant to select an appropriate value for k.

Fig. 12. Number of searches per site while triangulating 100 000 (a), 500 000 (b), and 1 000 000 (c) uniformly distributed points for different values of k. Total searches (table searches + list-searches) are marked in k = \/n, ~/n.

Since k = y/n, thus h = 1+ |n/k| = O(n//n) = O(Wn?). But for dif- ferent distributions a different number of points lie on the frontier and at each iteration of the algorithm the precise value of f; depends on the arrangement of the points already passed. The frontier has a wavy shape and does not coincide with the convex hull, thus, it has more vertices than convex hull of swept points. So, the size of fron- tier is bigger than O(v/7) using Fact 1. To estimate the average size of frontier we perform an experiment. The algorithm was tested on four different distributions of points with sizes ranging from 2!° to 27° sites. Fig. 13 shows the size of frontier for each distribution. To estimate each curve by a formula, we used regression analysis and estimated each curve with some different terms. The greatest term was V7” for all datasets, but the other terms (which has no af- fect in complexity analysis and their sign is not important) was sta- ted by big-O notation. By removing the less important terms the size of frontier for each dataset is f; = ov?) on average. Thus

Fig. 14. Various point distributions: uniform (a), Gaussian (b), points arranged in clusters (c), and points arranged in tilted grid (d).

Fig. 15. Typical run times needed for sweep-circle (a), and Zalik (b) algorithms.

Fig. 16. Points covering boundary of objects.

Fig. 17. Cost of Fortune. Number of tests per site needed to maintain the heap and the splay tree.

Algorithm 1. Sweep-circle Delauany triangulation algorithm

Spent CPU time (s) within Zalik and sweep-circle while triangulating point sets with uniform distributions.

Strange run times (in second) of algorithms when triangulating 1 000 000 points arranged in k degree tilted 1000 x 1000 square grids. Table 2

Spent CPU time (s) for boundary point sets.

Comparison of heuristics for detecting basins (the number of legalized triangles).

Performance of the hash table and linked lists (k= 100 for Zalik, and k = 3/n for sweep-circle), which defined as the number of searches per site.

Number of in-circle tests and legalized edges per site, and their spent CPU time.

Number of in-circle tests per site for sweep-circle and Dwyer.

descriptionView Paper arrow_downwardDownload

Structure Preserving Binary Image Morphing using Delaunay Triangulation

by Abbas Cheddad

2017, Pattern Recognition Letters

Mathematical morphology has been of a great significance to several scientific fields. Dilation, as one of the fundamental operations, has been very much reliant on the common methods based on the set theory and on using specific shaped... more

descriptionView Paper arrow_downwardDownload

An efficient algorithm for fingerprint matching

by Marina Gavrilova

2006, 18th International Conference on Pattern Recognition (ICPR'06)

This paper proposes novel topology-based algorithms for fingerprint matching. Three major aspects of fingerprint matching are considered: local matching, tolerance to deformation and global matching. The approach improves both the... more

descriptionView Paper arrow_downwardDownload

Tetrahedral mesh generation based on node insertion in crystal lattice arrangements and advancing-front-Delaunay triangulation

by Raul Radovitzky

2000, Computer Methods in Applied Mechanics and Engineering

A method of unstructured tetrahedral-mesh generation for general three-dimensional domains is presented. A c o n ventional boundary representation is adopted as the basis for the description of solids with evolving geometry and topology.... more

Figure 2: Example of the meshing of edges 3.1 Meshing of edges Triangulations of one-dimensional objects such as edges may conveniently be under- stood as discrete solutions of the eikonal equation:

Figure 4: Node insertion on a discretized surface

Figure 5: Surface remeshing. Snapshot of the advancing front algorithm in progress

The octree approach is not in itself an element generation technique. Elements are generated in the terminal octants by a variety of methods including: the use of templates and template matching between octants followed by element removal schemes [64]; and Delaunay triangulation on an octant-by-octant basis followed by a procedure to ensure octant compatibility [56]. The most critical issues in these approaches concern the compatibility between the boundary of the domain and the octree and the compatibility between octants. The former compatibility requirement may restrict the complexity of the domains that can be successfully meshed or may lead to meshes with poor quality at the boundary.

where R and p are the radii of the circumscribed and inscribed spheres, respectively. The quality of a tetrahedron is in inverse proportion to its aspect ratio. Other al- ternative tetrahedron quality measures are discussed elsewhere [45, 29]. A plausible measure of the quality of a triangulation 7 may be derived from the consideration of the standard interpolation error estimate (e. g., [12]):

possible arrangement of spheres. The size of the unit cell is a. Fig. 8 shows the Delaunay triangulation of the FCC unit cell, which consists of a total of 24 elements, 8 of which are equilateral, with an aspect ratio 0 = 1 and a size h = 0.356a, and the remaining 16 have a low aspect ratio 0 = (2+ V3)/3 ~ 1.24 and a size h = 0.408a. All the elements in the Delaunay mesh of the FCC unit cell have the same volume V = a®/24. Fig. 8 also highlights the two types of elements encountered in the Delaunay triangulation of the FCC unit cell. Representative elements of each type are defined by the nodal sets:

‘igure 8: Delaunay mesh of an FCC unit cell. Representative tetrahedra of each type o=lando= 2tv5 ~ 1.24) are highlighted.

Figure 9: Degeneracies present in a Delaunay triangulation of the FCC unit cell: The six face centered nodes lie in the same circumsphere leading to mesh non-uniqueness and potential slivers

By periodicity, the preceding observations carry over ipso facto to uniform meshes. An example of an FCC lattice covering a cube is shown in Fig. 10. A careful Delaunay triangulation of this lattice exhibits no slivers and contains two classes of tetrahedra, such as already identified in the triangulation of one FCC cell, of aspect ratios 0 = 1 and o = (2+ V3)/3 ~ 1.24.

Figure 11: Example of a Schénhardt (impossible to mesh) polyhedron

Figure 14: Advancing front Delaunay: Initial search region

descriptionView Paper arrow_downwardDownload

MAST-2D diffusive model for flood prediction on domains with triangular Delaunay unstructured meshes

by Marco Sinagra

2011, Advances in Water Resources

A new methodology for the solution of the 2D diffusive shallow water equations over Delaunay unstructured triangular meshes is presented. Before developing the new algorithm, the following question is addressed: it is worth developing and... more

descriptionView Paper arrow_downwardDownload

Learning Topology with the Generative Gaussian Graph and the EM Algorithm

by Michael Aupetit

Given a set of points and a set of prototypes representing them, how to create a graph of the prototypes whose topology accounts for that of the points? This problem had not yet been explored in the framework of statistical learning... more

descriptionView Paper arrow_downwardDownload

Combinatorial optimization in geometry

by Igor Rivin

2003, Advances in Applied Mathematics

In this paper we extend and unify the results of [20] and . As a consequence, the results of are generalized from the framework of ideal polyhedra in H 3 to that of singular Euclidean structures on surfaces, possibly with an infinite... more

descriptionView Paper arrow_downwardDownload

Delaunay mesh generation governed by metric specifications. Part II. applications

by paul george

1997

This paper proposes a Delaunay-type mesh generation algorithm governed by a metric map. The classical method is briefly established and then the different steps it involves are extended. It will be shown that the proposed method applies... more

Regeneration of the constrained edges H. Borouchaki et al. / Finite Elements in Analysis and Design 25 (1997) 61-83

Fig. 4. Unit circle, anisotropic case. Uihede, SEILOCE PULULIONE UTE SOY TL The problem under consideration is: how to interpolate a metric on a segment from the metrics of its endpoints? or how to define a function that permits to interpolate (in terms of size) in a monotonuous and continuous way from one ellipse, say .4, to another ellipse, say 2? In the isotropic case, the solution is obvious. Indeed, if the first metric is defined by AJ, and the second by pI, the desired size for the first is hy = 1/2 and for the other h, = 1 /./u , thus an interpolation function, in a case of an arithmetical progression (in terms of size), is defined by

H. Borouchaki et al./ Finite Elements in Analysis and Design 25 (1997) 61-83

Fig. 6. Interpolation curves (h in terms of £).

H. Borouchaki et al./ Finite Elements in Analysis and Design 25 (1997) 61-83 Fig. 11. Geometrical progression (iso). Fig. 10. Arithmetical progression (iso).

descriptionView Paper arrow_downwardDownload

Bregman Voronoi diagrams: Properties, algorithms and applications

by Frank Nielsen

2007, Arxiv preprint arXiv:0709.2196

The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others. We may define... more

descriptionView Paper arrow_downwardDownload

On Nonobtuse Simplicial Partitions

by Sergey Korotov

2009, SIAM Review

This paper surveys some results on acute and nonobtuse simplices and associated spatial partitions. These partitions are relevant in numerical mathematics, including piecewise polynomial approximation theory and the finite element method.... more

descriptionView Paper arrow_downwardDownload

Constrained Delaunay triangulation for multiresolution surface description

by Enrico Puppo

1988, [1988 Proceedings] 9th International Conference on Pattern Recognition

The problem of building a constrained Delaunay triangulation (CDT) at different levels of resolution is considered for hierarchical description of topographic surfaces. The surface is approximated at each level by a network of planar... more

descriptionView Paper arrow_downwardDownload

Properties of n-dimensional triangulations

by Charles Lawson

1986, Computer Aided Geometric Design

This paper establishes a number of mathematical results relevant to the problem of constructing a triangulation, i.e., a simplical tessellation of the convex hull of an arbitrary finite set of points in n-space.

3. Triangulations of sets of n + 2 points SASS Ey we One might expect the general n-dimensional case to be much more complicated than the 2D case. Although there is more complexity in the higher-dimensional cases, there are, fortunately, two very useful properties that persist. It remains true that a given set of n+ 2 points in R” admits of at most two different triangulations by n-dimensional simplices. Furthermore, if the n+ 2 points do not all lie on a common n-sphere, one of the possible triangulations is uniquely selected by the sphere test that will be described shortly. These facts will be established in the following two sections.

These are examples of the following general principle: If a point set A has parameters (09, 91, 6.) with o, # 0, the subset #* consisting of the points indexed in S, and S, will lie in an (n — o,)-dimensional linear manifold and have a (0, o,, o,) configuration. (Note that these two related configurations are in the same row in Table 1.) Any triangulation of # is related to a triangulation of #* by the fact that any simplex in a triangulation of F is the convex hull of the union of a simplex in a triangulation of A* with the points of P\F*.

As an example consider Case 2 of Fig. 1 with S, = {1,3} and S, = {2, 4}. To apply the sphere test we may choose any one of the four points and ask whether it is inside or outside the open ball circumscribing the other three points. Fig. 3 illustrates the four possible ways of applying the test for this example. We find p, € B,, p,;© B;, p, € B,, and p, ¢ B,. Thus any one of these tests results in the selection of 7, = {t,, t,} as the preferred triangulation. The crucial fact that the result of the sphere test is unique independent of the choice of the test point is established by the following theorem.

A pair of n-simplices, ¢; and ¢;, sharing a common (n — 1)-dimensional facet 1;; will be said to satisfy the local sphere test if the vertex of ¢; not in 1¢;; is outside the open ball B, circumscribing 1;. By Theorem 3, this is equivalent to the requirement that the vertex of f; not in f,, is outside the open ball B; circumscribing 1,;.

Table 1. Characterizing parameters for all of the significantly different configurations of n + 2 points in R” for n =1, 2 3, and 4.

descriptionView Paper arrow_downwardDownload

Simulation of static and dynamic wrinkles of skin

by Nadia Magnenat-thalmann

1996, Proceedings Computer Animation '96

Wrinkles are an extremely important contribution for enhancing the realism of human figure models. In this paper, we present an approach to generate static and dynamic wrinkles on human skin. For the static model, we consider micro and... more

descriptionView Paper arrow_downwardDownload

Quality Induced Fingerprint Identification using Extended Feature Set

by mayank vatsa

2008

Automatic fingerprint identification systems use level-1 and level-2 features for fingerprint identification. However, forensic examiners utilize inherent level-3 details along with level-2 features. Existing level-3 feature extraction... more

descriptionView Paper arrow_downwardDownload

Multimodal speech data acquisition with the use of EMA, fast-speed video cameras and a dedicated microphone array

by Robert Wielgat and

2016, 2016 MIXDES - 23rd International Conference Mixed Design of Integrated Circuits and Systems

Electromagnetic Articulography (EMA) is one of the methods of examining tongue movements. This technique is usually supported by audio recordings and may be supplemented by video data in order to analyze external articulator movements. In... more

descriptionView Paper arrow_downwardDownload

Rapid scene reconstruction on mobile phones from panoramic images

by Clemens Arth

2011, 2011 10th IEEE International Symposium on Mixed and Augmented Reality

Rapid 3D reconstruction of environments has become an active research topic due to the importance of 3D models in a huge number of applications, be it in Augmented Reality (AR), architecture or other commercial areas. In this paper we... more

descriptionView Paper arrow_downwardDownload

SPATIALLY CONSTRAINED INVERSION FOR QUASI 3-D MODELLING OF AEM DATA

by Kurt Sørensen

2007

SUMMARY The spatially constrained inversion (SCI) produces quasi- 3D modelling of geoelectrical and EM data of varying spatial density, using a 1D forward solution. Information migrate horizontally through spatial constraints and allow... more

descriptionView Paper arrow_downwardDownload

Algorithm 875

by Steven Benson

2008, ACM Transactions on Mathematical Software

Delaunay refinement is a widely used method for the construction of guaranteed quality triangular and tetrahedral meshes. We present the algorithm and the software for the parallel constrained Delaunay mesh generation. Our approach is... more

descriptionView Paper arrow_downwardDownload

The drainage network extraction from contour lines for contour line generalization

by Tinghua Ai

2007, ISPRS Journal of Photogrammetry and Remote Sensing

Unlike the simplification of independent line features, the generalization of terrain contour is to handle the "line group", which describes the geomorphologic characteristics, such as the terrain valley and ridge. In decision level, the... more

descriptionView Paper arrow_downwardDownload

Variational delaunay approach to the generation of tetrahedral finite element meshes

by Petr Krysl

1999

We describe an algorithm which generates tetrahedral decomposition of a general solid body, whose surface is given as a collection of triangular facets. The principal idea is to modify the constraints in such a way as to make them appear... more

descriptionView Paper arrow_downwardDownload

Parallel Delaunay mesh generation kernel

by Demian Nave

2003, International Journal for Numerical …

We present the results of an evaluation study on the re-structuring of a latency-bound mesh generation algorithm into a latency-tolerant parallel kernel. We use concurrency at a ÿne-grain level to tolerate long, variable, and... more

Figure 1. Point insertion and element creation steps of the BW algorithm; initial and final meshes at each iteration shown at the leftmost and the rightmost columns, respectively.

Figure 2. (Left) Submeshes of a triangulation and their inter-submesh interfaces. (Right) Cavity ex- pansion over more than one submesh. The tetrahedra t € M, and t* € M) are non-Delaunay w.r.t. point P€Mo; thus the cavity Cp is an interface cavity. Dashed lines show the inter-submesh interfaces.

Figure 3. Left: Time diagram that depicts two overlapping cavities expanding concurrently while a remote request is serviced from the submesh M@ for the expansion of the cavity AFBCA. Right: A new cavity ABCDEA is expanding concurrently in the submesh M,. The two cavities share an element (shaded triangle ABC) and thus one of the cavities will free its elements (role-over or setback) and will expand at some point later.

Figure 4. Time diagram of two adjacent cavities that expand concurrently. While the cavity AFGHBCA of the point P; is expanding on one processor, the cavity ACEIA completes its expansion (on another processor) unaware of the new point P; which violates the Delaunay criterion (shaded circle on the right).

Figure 5. Breakdown in percentages of overheads occurred by a parallel mesh gener- ator based on the SMGP implementation of the LTBW kernel, for 16 nodes on an SP machine and three different mesh sizes.

Figure 6. Quality of the mesh measured in terms of angles.

Figure 7. Breakdown in percentages of cavity computation occurred by a paral- lel mesh generator based on the LTBW kernel, for one and two million element meshes of the Tee geometry on 16 nodes of a CoW.

Table I. Breakdown of the total execution time (in seconds) using the traditional approach on a 16 processor SP.

Table II. Total execution time (in seconds) for the sequential and traditional approach as well as the parallel mesh generation using the LTBW, its SMGP implementation, and the SMGP implementation post-processed by ParMetis for further improving the quality of the partitions on a 16 processor SP.

Table III. Quality of submeshes measured in terms of the maximum surface-to-volume ratio (S/V) and imbalance on a 16 node SP. Table IV. Breakdown of the number of successfully completed cavities for the processor which is the least effective (first row) and most effective (last row) in tolerating latency for generating 16M element mesh for the Cube-in-Cube geometry on a 32 node (Sparc) CoW.

Table V. Total run time for the processor with the worst latency tolerance. Also total time spend in expanding and triangulating cavities (meshing time), total time spent in expanding and triangulating cavities in the presence of active interface cavities i.e. meshing time in presence of active cavities (Act. Cavs), the number in parenthesis depict the time spend in meshing interface cavities, total setback time and percentage of latency the LTBW kernel utilizes effectively on a 32 node CoW for meshing the Cube-in-Cube geometry with 8 and 16 million elements. All times are in seconds. element mesh. This implies that the LTBW kernel during the time that waits for the com- pletion of remote service requests, it completes more than 60% of the mesh refinement. The rest of the mesh refinement takes place while there are no active interface cavities present (see third and fourth columns of Table IV).

Table VI. Total run time, imbalance time due to variable and unpredictable nature of the BW kernel, and communication overhead (receive side) for the processor with least useful polling (first four rows) and maximum useful polling (last four rows). All times are in seconds, and were generated on a 32 node (Sparc) CoW.

descriptionView Paper arrow_downwardDownload

Depth-color image registration for 3D surface texture construction using kinect camera system

by Ramazan Aygun

2014, Ieee Southeastcon 2014

Today some camera systems provide various opportunities to the scientists in computer vision since they capture color and depth images of a scene simultaneously. This paper presents a new 3D model construction and surface texture mapping... more

descriptionView Paper arrow_downwardDownload

Log In

Delaunay Triangulation

Related Topics