Topology preservation

Recently, feature maps have been applied to various problem domains. The success of some of these applications critically depends on whether feature maps are topologically ordered. In this paper, we propose a novel measure for quantifying the neighborhood preserving property of feature maps. Two data sets were tested to illustrate the performance of the proposed method.

This paper presents a model-based object recognition approach that uses a hierarchical Gabor wavelet representation. The key idea is to use magnitude, phase and frequency measures of Gabor wavelet representation in an innovative flexible matching approach that can provide robust recognition. A Gabor grid, a topology-preserving map, eficiently encodes both signal energy and structural information of an object in a sparse multi-resolution representation. The Gabor grid subsamples the Gabor wavelet decomposition of an object model and is deformed to allow the indexed object model match with the image data. Flexible matching between the model and the image minimizes a cost function based on local similarity and geometric distortion of the Gabor grid. Grid erosion and repairing is performed whenever a collapsed grid, due to object occlusion, is detected. The results on infrared imagery are presented, where objects undergo rotation, translation, scale, occlusion and aspect variations under changing environmental conditions.

This paper presents a model-based object recognition approach that uses a hierarchical Gabor wavelet representation. The key idea is to use magnitude, phase and frequency measures of Gabor wavelet representation in an innovative flexible matching approach that can provide robust recognition. A Gabor grid, a topology-preserving map, eficiently encodes both signal energy and structural information of an object in a sparse multi-resolution representation. The Gabor grid subsamples the Gabor wavelet decomposition of an object model and is deformed to allow the indexed object model match with the image data. Flexible matching between the model and the image minimizes a cost function based on local similarity and geometric distortion of the Gabor grid. Grid erosion and repairing is performed whenever a collapsed grid, due to object occlusion, is detected. The results on infrared imagery are presented, where objects undergo rotation, translation, scale, occlusion and aspect variations under changing environmental conditions.

In addition to the source coding VQ artifacts, which usually introduce visible distortions in the form of block effect and staircase noise along the edges, the VQ indexes encoded bit stream is vulnerable to transmission errors resulting in a visually annoying artifact having an impulse block noise in the reconstructed images. In this paper, we propose to combine the compression and the transmission methods. We use the Self Organization Feature Map (SOFM) neural network for vector image coding. An important characteristic of this approach is the topology preserving property of the SOFM. This means that the designed codebook is an ordered codebook in essence and that no more effort is needed to order the generated codewords. A fuzzy- based post processing system is included at the receiver end in order to increase the robustness to multipath noisy channels.

In this paper we show that the (co)chain complex associated with a decomposition of the computational domain, commonly called a mesh in computational science and engineering, can be represented by a block-bidiagonal matrix that we call the Hasse matrix. Moreover, we show that topology-preserving mesh refinements, produced by the action of (the simplest) Euler operators, can be reduced to multi-linear transformations of the Hasse matrix representing the complex. Our main result is a new representation of the (co)chain complex underlying field computations, a representation that provides new insights into the transformations induced by local mesh refinements. This paper is a further contribution towards bridging the subject of computer representations for solid and physical modeling-which flourished borderline between computer graphics, engineering mechanics and computer science with its own methods and data structures-under the general cover of linear algebra and algebraic topology. The main advantage of such an approach is that topology, geometry and physics may coexist in one and the same formalized framework, concurring together to define, represent and simulate the behavior of the model. Our approach is based on first principles and is general in that it applies to most representational domains that can be characterized as cell complexes, without any restrictions on their type, dimension, codimension, orientability, manifoldness, connectedness. Contrary to what might appear at first sight, the theoretical complexity of the present approach is not greater than that of current methods, provided that sparse-matrix techniques with double element access (by rows and by columns) are employed. Last but not least, our tensorbased approach is a significant step forward in achieving close integration of geometrical representations and physics-based simulations, i.e., in the concurrent modeling of shape and behavior.

Artificial neural networks techniques have been successfully applied in vector quantization (VQ) encoding. The objective of VQ is to statistically preserve the topological relationships existing in a data set and to project the data to a lattice of lower dimensions, for visualization, compression, storage, or transmission purposes. However, one of the major drawbacks in the application of artificial neural networks is the difficulty to properly specify the structure of the lattice that best preserves the topology of the data. To overcome this problem, in this paper we introduce merging algorithms for machine-fusion, boostingfusion-based and hybrid-fusion ensembles of SOM, NG and GSOM networks. In these ensembles not the output signals of the base learners are combined, but their architectures are properly merged. We empirically show the quality and robustness of the topological representation of our proposed algorithm using both synthetic and real benchmarks datasets.

The pervasive use and exchange of digital content led to increased efforts in the research community for efficient approaches to protect intellectual property rights. While watermarking techniques have been used extensively for raster image format, watermarking approaches for the vector map format have been largely inspired from existing image watermarking techniques, without due consideration to the suitability of these techniques for this different data format. A key requirement of any watermarking approach of vector data is the preservation of the topological quality of the watermarked data. This is sometimes referred to as the invisibility of the watermark. For vector map data, the topological quality and invisibility are fundamentally different, but currently submerged

Dans cet article, nous proposons un algorithme d'alignement dense d'images en 3D qui permet d'estimer la transformation Euclidienne entre des paires de poses de caméras à partir des intensités des pixels. En utilisant la représentation des images dans l'espace d'échelle, l'originalité de l'approche proposée consiste en l'adaptation automatique du paramètre d'échelle au sein de chaque niveau d'une pyramide d'images multirésolutions. Ceci est accompli au travers de l'optimisation continue de l'échelle ainsi que la pose de la caméra, simultanément. L'approche proposée permet d'améliorer de manière significative la robustesse de l'algorithme d'alignement d'images aux larges mouvements entre images. Des expérimentations variées sur l'ensemble de données TUM RGB-D montrent que l'algorithme proposé surpasse l'approche classique basée pyramides à niveaux d'échelle fixes.

This work describes a neural network based architecture that represents and estimates object motion in videos. This architecture addresses multiple computer vision tasks such as image segmentation, object representation or characterization, motion analysis and tracking. The use of a neural network architecture allows for the simultaneous estimation of global and local motion and the representation of deformable objects. This architecture also avoids the problem of finding corresponding features while tracking moving objects. Due to the parallel nature of neural networks, the architecture has been implemented on GPUs that allows the system to meet a set of requirements such as: time constraints management, robustness, high processing speed and re-configurability. Experiments are presented that demonstrate the validity of our architecture to solve problems of mobile agents tracking and motion analysis.

This paper aims to address the ability of self-organizing neural network models to manage real-time applications. Specifically, we introduce a Graphics Processing Unit (GPU) implementation with Compute Unified Device Architecture (CUDA) of the Growing Neural Gas (GNG) network. The Growing Neural Gas network with its attributes of growth, flexibility, rapid adaptation, and excellent quality representation of the input space makes it a suitable model for real time applications. In contrast to existing algorithms the proposed GPU implementation allow the acceleration keeping good quality of representation. Comparative experiments using iterative, parallel and hybrid implementation are carried out to demonstrate the effectiveness of CUDA implementation in representing linear and non-linear input spaces under time restrictions.

This paper presents a robust approach to nonrigid modelling and tracking. The contour of the object is described by an active growing neural gas (A-GNG) network which allows the model to re-deform locally. The approach is novel in that the nodes of the network are described by their geometrical position, the underlying local feature structure of the image, and the distance vector between the modal image and any successive images. A second contribution is the correspondence of the nodes which is measured through the calculation of the topographic product, a topology preserving objective function which quantifies the neighbourhood preservation before and after the mapping. As a result, we can achieve the automatic modelling and tracking of objects without using any annotated training sets. Experimental results have shown the superiority of our proposed method over the original growing neural gas (GNG) network.

The Self-Organizing Map (SOM) is a popular unsupervised neural network able to provide effective clustering and data visualization for data represented in multidimensional input spaces. In this paper we describe Fast Learning SOM (FLSOM) which adopts a learning algorithm that improves the performance of the standard SOM with respect to the convergence time in the training phase. We show that FLSOM also improves the quality of the map by providing better clustering quality and topology preservation of multidimensional input data. Several tests have been carried out on different multidimensional datasets, which demonstrate better performances of the algorithm in comparison with the original SOM.

This paper aims to address the ability of self-organizing neural network models to manage video and image processing in real-time. The Growing Neural Gas networks (GNG) with its attributes of growth, flexibility, rapid adaptation, and excellent quality representation of the input space makes it a suitable model for real time applications. A number of applications are presented that includes: image compression, hand and medical image contours representation, surveillance systems, hand gesture recognition systems or 3D data reconstruction.

In addition to the source coding VQ artifacts, which usually introduce visible distortions in the form of block effect and staircase noise along the edges, the VQ indexes encoded bit stream is vulnerable to transmission errors resulting in a visually annoying artifact having an impulse block noise in the reconstructed images. In this paper, we propose to combine the compression and the transmission methods. We use the Self Organization Feature Map (SOFM) neural network for vector image coding. An important characteristic of this approach is the topology preserving property of the SOFM. This means that the designed codebook is an ordered codebook in essence and that no more effort is needed to order the generated codewords. A fuzzy- based post processing system is included at the receiver end in order to increase the robustness to multipath noisy channels.

In this work, we propose the use of the Neural Gas (NG), a neural network that uses an unsupervised competitive hebbian learning (CHL), to develop a reverse engineering process. This is a simple and accurate method to reconstruct objects from the point cloud obtained from overlapped multiple views using low cost sensors. In contrast to other methods that may need several stages that include downsampling, noise filtering and many other tasks, the NG automatically obtains the 3D model of the scanned objects. To demonstrate the validity of our proposal we tested our method with several models and performed a study of the neural network parameterization calculating the quality of representation and also comparing results with other neural methods like Growing Neural Gas and Kohonen maps or clasical

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights  An original computational approach for cluster analysis is proposed.  The method consists of two phases, which are based on Self-Organizing Map.  Topology-preserving and connectivity functions are used in the clustering process.  The method is proved using three benchmark datasets and a real biological dataset.  Automation in parameterization results in a user-friendly methodology.

Self-organizing map (SOM) is a neural network model widely used in high dimensional data visualization processes. A trained SOM provides a simplified data model as well as a projection of the multidimensional input data into a bi-dimensional plane that reflects the relationships involving the training patters. Visualization methods based in SOM explore different characteristics related to the data learned by the network. It is necessary to find methods to determine the goodness of a trained network in order to evaluate the quality of the high dimensional data visualizations generated using the SOM simplified model. The degree of topology preservation is the most common concept used to implement this measure. Several qualitative and quantitative methods have been proposed for measuring the degree of SOM topology preservation, in particular using Kohonen model. In this work, two measuring topology preservation methods for Growing Cell Structures (GCS) model are proposed: the topographic function and the topology preserving map.

The Self-Organizing Map (SOM) is a neural network model that performs an ordered projection of a high dimensional input space in a low-dimensional topological structure. The process in which such mapping is formed is defined by the SOM algorithm, which is a competitive, unsupervised and nonparametric method, since it does not make any assumption about the input data distribution. The feature maps provided by this algorithm have been successfully applied for vector quantization, clustering and high dimensional data visualization processes. However, the initialization of the network topology and the selection of the SOM training parameters are two difficult tasks caused by the unknown distribution of the input signals. A misconfiguration of these parameters can generate a feature map of low-quality, so it is necessary to have some measure of the degree of adaptation of the SOM network to the input data model. The topology preservation is the most common concept used to implement this measure. Several qualitative and quantitative methods have been proposed for measuring the degree of SOM topology preservation, particularly using Kohonen's model. In this work, two methods for measuring the topology preservation of the Growing Cell Structures (GCSs) model are proposed: the topographic function and the topology preserving map.

Non-linear rank-order-based filtering of color images is difficult to implement; the multivariate nature of colors does not allow the introduction of a mathematicallycorrect and topology-preserving ordering relation. The most widely investigated approach is based on the use of reduced ordering relations introduced according to different scalars. We propose pseudo-morphologic and median operators based on reduced ordering of colors, with respect to scalars computed as geometrical shape invariants of a triangle representation of colors. The same color representation allows the introduction of a luminance invariant inter-color distance, used with good results in distance-based color filters.

Self-organizing maps (SOM) are widely used for their topology preservation property: neighboring input vectors are quantified (or classified) either on the same location or on neighbor ones on a predefined grid. SOM are also widely used for their more classical vector quantization property. We show in this paper that using SOM instead of the more classical Simple Competitive Learning (SCL) algorithm drastically increases the speed of convergence of the vector quantization process. This fact is demonstrated through extensive simulations on artificial and real examples, with specific SOM (fixed and decreasing neighborhoods) and SCL algorithms.

Making results reliable is one of the major concerns in artificial neural networks research. It is often argued that Self-Organizing Maps are less sensitive than other neural paradigms to problems related to convergence, local minima, etc. This paper introduces objective statistical measures that can be used to assess the stability of the results of SOM, both on the distortion and on the topology preservation points of views.

Statistical re-sampling techniques have been used extensively and successfully in the machine learning approaches for generations of classifier and predictor ensembles. It has been frequently shown that combining so called unstable predictors has a stabilizing effect on and improves the performance of the prediction system generated in this way. In this paper we use the resampling techniques in the context of a topology preserving map which can be used for scale invariant classification, taking into account the fact that it models the residual after feedback with a family of distributions and finds filters which make the residuals most likely under this model. This model is applied to artificial data sets and compared with a similar version based on the Self Organising Map (SOM).

In a previous paper [1] we showed that a 3D object can be digitized without changing the topology if the object is r-regular and if the reconstruction method fulfills certain requirements. In this paper we give two important examples for such reconstruction methods. First, we introduce Majority Interpolation, an algorithm to interpolate sampling points at doubled resolution such that topological ambiguities are resolved. Second, we show how the well-known Marching Cubes algorithm has to be modified such that it is topology preserving. This is the first approach of digitizing 3D objects which guarantees topology preservation for voxel-based or polygonal surface-based reconstructions.

In a previous paper [1] we showed that a 3D object can be digitized without changing the topology if the object is r-regular and if the reconstruction method fulfills certain requirements. In this paper we give two important examples for such reconstruction methods. First, we introduce Majority Interpolation, an algorithm to interpolate sampling points at doubled resolution such that topological ambiguities are resolved. Second, we show how the well-known Marching Cubes algorithm has to be modified such that it is topology preserving. This is the first approach of digitizing 3D objects which guarantees topology preservation for voxel-based or polygonal surface-based reconstructions.

Topology is a fundamental property of shapes in pictures. Since the input for any image analysis algorithm is a digital image, which does not need to have the same topological characteristics as the imaged real world, it is important to know, which shapes can be digitized without topological changes. Most existing approaches do not take into account the unavoidable blurring in real image acquisition systems or use extremely simplified and thus unrealistic models of digitization with blurring. In case of the mostly used square grids we show which binary images can be digitized topologically correctly after blurring with an arbitrary non-negative radially symmetric point spread function, which is an important step forward to real digitization.

In this paper we derive a sampling theorem, which is the first one to guarantee topology preservation during digitization of 3D objects. This new theorem is applicable to several reconstruction methods, e.g. a unionof-balls reconstruction and the trilinear interpolation.

The well-known marching cubes algorithm is modified to apply to the face-centered cubic (fcc) grid. Thus, the local configurations that are considered when extracting the local surface patches are not cubic anymore. This paper presents three different partitionings of the fcc grid to be used for the local configurations. The three candidates are evaluated theoretically and experimentally and compared with the original marching cubes algorithm. It is proved that the reconstructed surface is topologically equivalent to the surface of the original object when the surface of the original object that is digitized is smooth and a sufficiently dense fcc grid is used.

In order to make image analysis methods more reliable it is important to analyse to what extend shape information is preserved during image digitization. Most existing approaches to this problem consider topology preservation and are restricted to ideal binary images. We extend these results in two ways. First, we characterize the set of binary images which can be correctly digitized by both regular and irregular sampling grids, such that not only topology is preserved but also the Hausdorff distance between the original image and the reconstruction is bounded. Second, we prove an analogous theorem for gray scale images that arise from blurring of binary images with a certain filter type. These results are steps towards a theory of shape digitization applicable to real optical systems.

We define strong r-similarity and the morphing distance to bound geometric distortions between shapes of equal topology. We then derive a necessary and sufficient condition for a set and its digitizations to be r-similar, regardless of the sampling grid. We also extend these results to certain gray scale images. Our findings are steps towards a theory of shape digitization for real optical systems.

Virtual Coordinate Systems (VCS) characterize each node in a network by its hop distances to a subset of nodes called anchors. Performance of VCS based algorithms is highly sensitive to number of anchors and their placement. Extreme Node Search (ENS), a novel and efficient anchor placement scheme, is proposed that demonstrates significantly improved performance over state-of-the-art. ENS starts with two randomly placed anchors and then uses a Directional Virtual Coordinate (DVC) transformation, which restores the lost directionality in traditional VCS, to identify anchor candidates in a completely distributed manner. A vector-based representation is proposed for the DVC domain, which is then used to introduce the concept of angles between virtual directions in the transformed domain. Ability to specify cardinal directions and use angles is a radical change from the traditional VC system approaches. By selecting two anchor pairs with near orthogonal directional coordinates under the DVC transformation, a novel Topology Preserving Map (TPM) generation scheme is developed. This new TPM generation scheme requires significantly less computations than the existing PCA based method. Use of ENS significantly enhances the PCA based TPM generation as well. Simulation results for representative WSNs indicate that the ENS based anchor sets significantly improve performance of all prominent VC based routing schemes. For instance, Directional Virtual Coordinate Routing, when combined with ENS anchor placement strategy, outperforms even the geographic Greedy Perimeter Stateless Routing scheme that relies on exact physical node coordinates.

A novel scheme is presented that allows individual nodes in sensor networks to achieve network/topology-awareness by listening to regular packets associated with applications. Nodes, initially oblivious to network topology and their position within the network, gradually infer information required to evaluate their own Virtual Coordinates (VCs). A Singular Value Decomposition based transformation allows each node to convert the VCs of nodes, gleaned from the source or destination address field of packets, to corresponding Topological Coordinates (TCs). Eventually each node generates a topology map of the network, thus becoming aware of its own location and those of other nodes. Effectiveness of self-learning scheme, in terms of convergence of different stages, and gradual development of network awareness at nodes are illustrated. While many applications of network awareness within nodes can be foreseen, we illustrate how performance of routing can improve dramatically over time as network awareness develops within a node.

This paper tackles the problem of computing topological invariants of geometric objects in a robust manner, using only point cloud data sampled from the object. It is now widely recognised that this kind of topological analysis can give qualitative information about data sets which is not readily available by other means. In particular, it can be an aid to visualisation of high dimensional data. Standard simplicial complexes for approximating the topological type of the underlying space (such asČech, Rips, or α-shape) produce simplicial complexes whose vertex set has the same size as the underlying set of point cloud data. Such constructions are sometimes still tractable, but are wasteful (of computing resources) since the homotopy types of the underlying objects are generally realisable on much smaller vertex sets. We obtain smaller complexes by choosing a set of 'landmark' points from our data set, and then constructing a "witness complex" on this set using ideas motivated by the usual Delaunay complex in Euclidean space. The key idea is that the remaining (non-landmark) data points are used as witnesses to the existence of edges or simplices spanned by combinations of landmark points. Our construction generalises the topology-preserving graphs of Martinetz and Schulten [MS94] in two directions. First, it produces a simplicial complex rather than a graph. Secondly it actually produces a nested family of simplicial complexes, which represent the data at different feature scales, suitable for calculating persistent homology [ELZ00, ZC04]. We find that in addition to the complexes being smaller, they also provide (in a precise sense) a better picture of the homology, with less noise, than the full scale constructions using all the data points. We illustrate the use of these complexes in qualitatively analyzing a data set of 3 × 3 pixel patches studied by David Mumford et al [LPM03].

The modification of conforming hexahedral meshes is difficult to perform since their structure does not allow easy local refinement or un-refinement such that the modification does not go through the boundary. In this paper we prove that the set of hex flipping transformations of Bern et al. (2002) [1] is the only possible local modification on a geometrical hex mesh of valence less than five i.e., with less than five edges per vertex. We propose a new basis of transformations that can generate sequences of local modifications on hex meshes of valence less than six. For quadrilateral meshes, we show the equivalence between modifying locally the number of quads on a mesh and the number of its internal vertices.

The batch version of soft topology-preserving map producing retinotopy and ocular dominance in visual cortex is proven to be reduced to the elastic net. This verifies numerous results of numerical simulations described in the literature demonstrating similarities of neural patterns produced by lateral and elastic synaptic interactions.

Soft topology-preserving mapping with ÿxed lateral interactions has been applied for the formation of retinotopy and ocular dominance. The learning is based on controlled deformation of the energy landscape modelled by deterministic annealing, which can be more realistic metaphor than changing the lateral interaction range.

Computation of persistent homology of simplicial representations such as the Rips and the Cěch complexes do not efficiently scale to large point clouds. It is, therefore, meaningful to devise approximate representations and evaluate the trade-off between their efficiency and effectiveness. The lazy witness complex economically defines such a representation using only a few selected points, called landmarks. Topological data analysis traditionally considers a point cloud in a Euclidean space. In many situations, however, data is available in the form of a weighted graph. A graph along with the geodesic distance defines a metric space. This metric space of a graph is amenable to topological data analysis. We discuss the computation of persistent homologies on a weighted graph. We present a lazy witness complex approach leveraging the notion of-net that we adapt to weighted graphs and their geodesic distance to select landmarks. We show that the value of the parameter of the-net provides control on the trade-off between choice and number of landmarks and the quality of the approximate simplicial representation. We present three algorithms for constructing an-net of a graph. We comparatively and empirically evaluate the efficiency and effectiveness of the choice of landmarks that they induce for the topological data analysis of different real-world graphs.

Mesh simplification has received tremendous attention over the past years. Most of the previous works deal with a proper choice of error measures to guide the simplification. Preserving the topological characteristics of the mesh and possibly of data attached to the mesh is a more recent topic, the present paper is about. We introduce a new topology preserving simplification algorithm for triangular meshes, possibly non-manifold, with embedded polylines. In this context embedded means that the edges of the polylines are also edges of the mesh. The paper introduces a robust test to detect if the collapse of an edge in the mesh modifies either the topology of the mesh or the topology of the embedded polylines. This validity test is derived using combinatorial topology results. More precisely we define a so-called extended complex from the input mesh and the embedded polylines. We show that if an edge collapse of the mesh preserves the topology of this extended complex, then it also preserves both the topology of the mesh and the embedded polylines. Our validity test can be used for any 2-complex mesh, including non-manifold triangular meshes. It can be combined with any previously introduced error measure. Implementation of this validity test is described. We demonstrate the power and versatility of our method with scientific data sets from neuroscience, geology and CAD/CAM models from mechanical engineering.

An octree-based mesh generation method is proposed to create reasonable-quality, geometry-adapted unstructured hexahedral meshes automatically from triangulated surface models without any sharp geometrical features. A new, easy-to-implement, easy-to-understand set of refinement templates is developed to perform local mesh refinement efficiently even for concave refinement domains without creating hanging nodes. A buffer layer is inserted on an octree core mesh to improve the mesh quality significantly. Laplacian-like smoothing, angle-based smoothing and local optimization-based untangling methods are used with certain restrictions to further improve the mesh quality. Several examples are shown to demonstrate the capability of our hexahedral mesh generation method for complex geometries.

The class of geometric deformable models, also known as level sets, has brought tremendous impact on medical imagery due to its capability of topology preservation and fast shape recovery. Ultrasonic heart images are often characterized by high level of speckle noise causing erroneous detection of cavities. We propose a new stopping term for computing level sets in order to robustly detect the heart cavities in echocardiographic images. Robustness is ensured by the use of the coefficient of variation. Experimental results show significant improvement, especially for images acquired with low frequencies.

This paper describes an algorithm to extract adaptive and quality quadrilateral/hexahedral meshes directly from volumetric data. First, a bottom-up surface topology preserving octree-based algorithm is applied to select a starting octree level. Then the dual contouring method is used to extract a preliminary uniform quad/hex mesh, which is decomposed into finer quads/hexes adaptively without introducing any hanging nodes. The positions of all boundary vertices are recalculated to approximate the boundary surface more accurately. Mesh adaptivity can be controlled by a feature sensitive error function, the regions that users are interested in, or finite element calculation results. Finally, a relaxation based technique is deployed to improve mesh quality. Several demonstration examples are provided from a wide variety of application domains. Some extracted meshes have been extensively used in finite element simulations.

This paper presents a model-based object recognition approach that uses a Gabor wavelet representation. The key idea is to use magnitude, phase, and frequency measures of the Gabor wavelet representation in an innovative flexible matching approach that can provide robust recognition. The Gabor grid, a topology-preserving map, efficiently encodes both signal energy and structural information of an object in a sparse multiresolution representation. The Gabor grid subsamples the Gabor wavelet decomposition of an object model and is deformed to allow the indexed object model match with similar representation obtained using image data. Flexible matching between the model and the image minimizes a cost function based on local similarity and geometric distortion of the Gabor grid. Grid erosion and repairing is performed whenever a collapsed grid, due to object occlusion, is detected. The results on infrared imagery are presented, where objects undergo rotation, translation, scale, occlusion, and aspect variations under changing environmental conditions. I. INTRODUCTION M ODEL-BASED object recognition in real-world outdoor situations is difficult because a robust algorithm has to consider multiple factors such as: i) object contrast, signature, scale, and aspect variations; ii) noise and spurious low resolution sensor data; and iii) high clutter, partial object occlusion, and articulation. Current approaches use shape primitives, silhouettes and contours, colors, and invariant object features for matching. The performance of these methods is acceptable when objects are well defined, have high contrast, and are at close ranges. However, the recognition results generated by these approaches do not gracefully degrade and produce high false alarms when competitive clutter and object shape distortion are present in the input data [4], [6]. To improve the recognition performance under multiscenarios and varying environmental conditions, model of sensors, atmosphere, and background clutter are helpful in addition to the geometric model of an object. Using only a minimum set of object models and sensor model, multiscale Gabor wavelet representation of objects and a flexible matching mechanism described in this paper can potentially help to improve the recognition performance under real-world situations. The use of Gabor wavelet representation to recognize threedimensional (3-D) objects is motivated by the fact that as compared to popular edge-based representations, it is a rich multiresolution representation with sound theoretical basis and Manuscript

The pervasive use and exchange of digital content led to increased efforts in the research community for efficient approaches to protect intellectual property rights. While watermarking techniques have been used extensively for raster image format, watermarking approaches for the vector map format have been largely inspired from existing image watermarking techniques, without due consideration to the suitability of these techniques for this different data format. A key requirement of any watermarking approach of vector data is the preservation of the topological quality of the watermarked data. This is sometimes referred to as the invisibility of the watermark. For vector map data, the topological quality and invisibility are fundamentally different, but currently submerged

This work describes a neural network based architecture that represents and estimates object motion in videos. This architecture addresses multiple computer vision tasks such as image segmentation, object representation or characterization, motion analysis and tracking. The use of a neural network architecture allows for the simultaneous estimation of global and local motion and the representation of deformable objects. This architecture also avoids the problem of finding corresponding features while tracking moving objects. Due to the parallel nature of neural networks, the architecture has been implemented on GPUs that allows the system to meet a set of requirements such as: time constraints management, robustness, high processing speed and re-configurability. Experiments are presented that demonstrate the validity of our architecture to solve problems of mobile agents tracking and motion analysis.

This paper aims to address the ability of self-organizing neural network models to manage video and image processing in real-time. The Growing Neural Gas networks (GNG) with its attributes of growth, flexibility, rapid adaptation, and excellent quality representation of the input space makes it a suitable model for real time applications. A number of applications are presented that includes: image compression, hand and medical image contours representation, surveillance systems, hand gesture recognition systems or 3D data reconstruction.

This article surveys important concepts related to pyramidal architecture, hierarchical processing and multi-resolution techniques in imaging context. Types of processes including bottom-up and top-down related to such hierarchical structures are explained. Relationships consisting of intra-level and inter-level communication networks are discussed. We investigate regular and irregular pyramidal structures. This includes binpyramid; quad-pyramid (and overlapped quad-pyramid); dual-pyramid; hexagonalpyramid; adaptive pyramid and disparity pyramid.

Topology preservation during training of Self-Organizing maps is a key issue to obtain a good quality model in process monitoring. In this paper, different existing indexes for topology preservation measurement are exposed and also an index proposed in a previous work is improved. The index is based on the smooth trajectory of the current process state projected over the output space under non abrupt changes of the values of the process variables.

Agglomerated multigrid methods for unstructured grids are studied critically for solving a model diffusion equation on highly-stretched grids typical of practical viscous simulations, following a previous work focused on isotropic grids. Different primal elements, including prismatic and tetrahedral elements in three dimensions, are considered. The components of an efficient node-centered full-coarsening multigrid scheme are identified and assessed using quantitative analysis methods. Fast grid-independent convergence is demonstrated for mixed-element grids composed of tetrahedral elements in the isotropic regions and prismatic elements in the highly-stretched regions. Implicit lines natural to advancing-layer/ advancing-front grid generation techniques are essential elements of both relaxation and agglomeration. On agglomerated grids, consistent average-least-square discretizations augmented with edge-directional gradients to increase h-ellipticity of the operator are used. Simpler (edge-terms-only) coarse-grid discretizations are also studied and shown to produce grid-dependent convergence-only effective on grids with minimal skewing.

Self-organizing maps have long been used for data visualization and clustering. When using the standard SOM training method, it is well-known that an appropriate choice of the final adaptation radius is crucial for obtaining topology-preserving maps. Similar considerations apply to other training schemes. Consequently, various heuristics have been suggested to assist the user in selecting the most appropriate map in each case. With regard to the standard algorithm, equiprobabilistic maps have been argued to provide a more "faithful" fit to the data, although the overfitting problem still remains. Interestingly, certain equiprobabilistic maps also provide generative mixture densities. The purpose of this paper is to explore the potential of the equiprobabilistic map idea as a means to reach plausible predictive densities (capable of avoiding the previous difficulties). A new monitorization idea is introduced, and a few examples are used to illustrate the scope of the approach.

Simultaneous Localization And Mapping (SLAM) is a fundamental problem in mobile robotics. While point-based SLAM methods provide accurate camera localization, the generated maps lack semantic information. On the other hand, state of the art object detection methods provide rich information about entities present in the scene from a single image. This work marries the two and proposes a method for representing generic objects as quadrics which allows object detections to be seamlessly integrated in a SLAM framework. For scene coverage, additional dominant planar structures are modeled as infinite planes. Experiments show that the proposed points-planes-quadrics representation can easily incorporate Manhattan and object affordance constraints, greatly improving camera localization and leading to semantically meaningful maps. The performance of our SLAM system is demonstrated in https://youtu.be/dR-rB9keF8M.