Elcvia Electronic Letters on Computer Vision and Image Analysis, 2007
Differential equations is an essential tool for describing the nature of the physical universe an... more Differential equations is an essential tool for describing the nature of the physical universe and naturally also an essential part of models for computer graphics and vision. Some examples are: light rays, which follow the shortest path, and are conveniently described using the ...
OpenTissue is a multidisciplinary, open source programming toolkit for physics-based simulation, ... more OpenTissue is a multidisciplinary, open source programming toolkit for physics-based simulation, collision detection, scientific visualization, and medical imaging. The toolkit was initiated in 2001, is driven by academia, and is used by several universities. It implements several cutting edge simulators using cutting edge programming techniques. OpenTissue is available under Windows and Linux, and it implements almost all algorithms presented in the accompanying book, Erleben et al. Physics-Based Animation, Charles River Media, 2005. This presentation will give an overview of OpenTissue: what it can do, how it is done, and where the toolkit is going
The estimation of the covariance matrix is an initial step in many multivariate statistical metho... more The estimation of the covariance matrix is an initial step in many multivariate statistical methods such as principal components analysis and factor analysis, but in many practical applications the dimensionality of the sample space is large compared to the number of samples, and the usual maximum likelihood estimate is poor. Typically, improvements are obtained by modelling or regularization. From a practical point of view, these methods are often computationally heavy and rely on approximations. As a fast substitute, we propose an easily calculable maximum a posteriori (MAP) estimator based on a new class of prior distributions generalizing the inverse Wishart prior, discuss its properties, and demonstrate the estimator on simulated and real data.
Kerawit Somchaipeng(1,2), Jon Sporring(2), Sven Kreiborg(1), and Peter Johansen(2) ... (1)3D-Lab,... more Kerawit Somchaipeng(1,2), Jon Sporring(2), Sven Kreiborg(1), and Peter Johansen(2) ... (1)3D-Lab, School of Dentistry, Dept. of Pediatric Dentistry, University of Copenhagen,Nørre Alle 20, DK-2200, Copenhagen N, Denmark ... (2)Dept. of Computer Science, University ...
Automatic segmentation is performed using watersheds of the gradient magnitude and compression te... more Automatic segmentation is performed using watersheds of the gradient magnitude and compression techniques. Linear Scale-Space is used to discover the neighbourhood structure and catchment basins are locally merged with Minimum Description Length. The algorithm can form a basis for a large range of automatic segmentation algorithms based on watersheds, scale-spaces, and compression.
Communications in Computer and Information Science, 2007
Density estimation employed in multi-pass global illumination algorithms give cause to a trade-of... more Density estimation employed in multi-pass global illumination algorithms give cause to a trade-off problem between bias and noise. The problem is seen most evident as blurring of strong illumination features. In particular this blurring erodes fine structures and sharp lines prominent in caustics. To address this problem we introduce a novel photon mapping algorithm based on nonlinear anisotropic diffusion. Our algorithm adapts according to the structure of the photon map such that smoothing occurs along edges and structures and not across. In this way we preserve the important illumination features, while eliminating noise. We call our method diffusion based photon mapping.
We consider ray bundles emanating from a source such as a camera or light source. We derive the f... more We consider ray bundles emanating from a source such as a camera or light source. We derive the full spatial and temporal structure to first order of the intersection of ray bundles with scene geometry, where scene geometry given as any implicit function. Further, we present the full details of 2 often used geometrical representations. The first order structure may be used as the linear approximation of the change of photons as the camera, objects, and light source change as function of space and time. Our work generalises previous work on ray differentials and photon differentials .
In this paper, we propose a multi-scale, multi-kernel shape, compactly supported kernel bundle fr... more In this paper, we propose a multi-scale, multi-kernel shape, compactly supported kernel bundle framework for stationary velocity field-based image registration (Wendland kernel bundle stationary velocity field, wKB-SVF). We exploit the possibility of directly choosing kernels to construct a reproducing kernel Hilbert space (RKHS) instead of imposing it from a differential operator. The proposed framework allows us to minimize computational cost without sacrificing the theoretical foundations of SVF-based diffeomorphic registration. In order to recover deformations occurring at different scales, we use compactly supported Wendland kernels at multiple scales and orders to parameterize the velocity fields, and the framework allows simultaneous optimization over all scales. The performance of wKB-SVF is extensively compared to the 14 non-rigid registration algorithms presented in a recent comparison paper. On both MGH10 and CUMC12 datasets, the accuracy of wKB-SVF is improved when compared to other registration algorithms. In a disease-specific application for intra-subject registration, atrophy scores estimated using the proposed registration scheme separates the diagnostic groups of Alzheimer's and normal controls better than the state-of-the-art segmentation technique. Experimental results show that wKB-SVF is a robust, flexible registration framework that allows theoretically well-founded and computationally efficient multi-scale representation of deformations and is equally well-suited for both inter- and intra-subject image registration.
A scale space approach is taken for building Bounding Volume Hierarchies (BVHs) for collision det... more A scale space approach is taken for building Bounding Volume Hierarchies (BVHs) for collision detection. A spherical bounding volume is generated at each node of the BVH using estimates of the mass distribution. Traditional top-down methods approximates the surface of an object in a coarse to fine manner, by recursively increasing resolution by some factor, e.g. 2. The method presented in this article analyzes the mass distribution of a solid object using a well founded scale-space based on the Diffusion Equation: the Gaussian Scale-Space. In the Gaussian scale-space, the deep structure of extremal mass points is naturally binary, and the linking process is therefore simple. The main contribution of this article is a novel approach for constructing BVHs using Multi-Scale Singularity Trees (MSSTs) for collision detection. The BVH-building algorithm extends the field with a new method based on volumetric shape rather than statistics of the surface geometry or geometrical constructs such as medial surfaces.
Bogusław Cyganek, Combined detector of locally-oriented structures and corners in images based on... more Bogusław Cyganek, Combined detector of locally-oriented structures and corners in images based on a scale-space tensor representation of local neighborhoods of pixels, Proceedings of the 2003 international conference on Computational science: PartII, June 02-04, 2003, ...
Note: OCR errors may be found in this Reference List extracted from the full text article. ACM ha... more Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references. ... {Baraff01} Baraff, David, "Physical based modeling: Rigid body simulation," SIGGRAPH ...
Proceedings of 13th International Conference on Pattern Recognition, 1996
Viewing images as distributions of light quanta enables an information theoretic study of image s... more Viewing images as distributions of light quanta enables an information theoretic study of image structures on dif- ferent scales. This article combines Shannon's entropy and Witkin and Koenderink's Scale-Space to establish a precise connection between the Heat Equation and the Thermody- namic Entropy in Scale-Space. Experimentally the entropy function is used to study global textures. A recent paper in by
This paper addresses the problem of mixing spectral bands and space in a smooth, linear, and casu... more This paper addresses the problem of mixing spectral bands and space in a smooth, linear, and casual manner. Such properties are of fundamental importance for many basic multi-spectral-image processing algorithms that probe inter-spectral structure. The example of color images is used in a simple spectral perspective. An example is given comparing the deep structure of the color and the gray gradient magnitude.
Elcvia Electronic Letters on Computer Vision and Image Analysis, 2007
Differential equations is an essential tool for describing the nature of the physical universe an... more Differential equations is an essential tool for describing the nature of the physical universe and naturally also an essential part of models for computer graphics and vision. Some examples are: light rays, which follow the shortest path, and are conveniently described using the ...
OpenTissue is a multidisciplinary, open source programming toolkit for physics-based simulation, ... more OpenTissue is a multidisciplinary, open source programming toolkit for physics-based simulation, collision detection, scientific visualization, and medical imaging. The toolkit was initiated in 2001, is driven by academia, and is used by several universities. It implements several cutting edge simulators using cutting edge programming techniques. OpenTissue is available under Windows and Linux, and it implements almost all algorithms presented in the accompanying book, Erleben et al. Physics-Based Animation, Charles River Media, 2005. This presentation will give an overview of OpenTissue: what it can do, how it is done, and where the toolkit is going
The estimation of the covariance matrix is an initial step in many multivariate statistical metho... more The estimation of the covariance matrix is an initial step in many multivariate statistical methods such as principal components analysis and factor analysis, but in many practical applications the dimensionality of the sample space is large compared to the number of samples, and the usual maximum likelihood estimate is poor. Typically, improvements are obtained by modelling or regularization. From a practical point of view, these methods are often computationally heavy and rely on approximations. As a fast substitute, we propose an easily calculable maximum a posteriori (MAP) estimator based on a new class of prior distributions generalizing the inverse Wishart prior, discuss its properties, and demonstrate the estimator on simulated and real data.
Kerawit Somchaipeng(1,2), Jon Sporring(2), Sven Kreiborg(1), and Peter Johansen(2) ... (1)3D-Lab,... more Kerawit Somchaipeng(1,2), Jon Sporring(2), Sven Kreiborg(1), and Peter Johansen(2) ... (1)3D-Lab, School of Dentistry, Dept. of Pediatric Dentistry, University of Copenhagen,Nørre Alle 20, DK-2200, Copenhagen N, Denmark ... (2)Dept. of Computer Science, University ...
Automatic segmentation is performed using watersheds of the gradient magnitude and compression te... more Automatic segmentation is performed using watersheds of the gradient magnitude and compression techniques. Linear Scale-Space is used to discover the neighbourhood structure and catchment basins are locally merged with Minimum Description Length. The algorithm can form a basis for a large range of automatic segmentation algorithms based on watersheds, scale-spaces, and compression.
Communications in Computer and Information Science, 2007
Density estimation employed in multi-pass global illumination algorithms give cause to a trade-of... more Density estimation employed in multi-pass global illumination algorithms give cause to a trade-off problem between bias and noise. The problem is seen most evident as blurring of strong illumination features. In particular this blurring erodes fine structures and sharp lines prominent in caustics. To address this problem we introduce a novel photon mapping algorithm based on nonlinear anisotropic diffusion. Our algorithm adapts according to the structure of the photon map such that smoothing occurs along edges and structures and not across. In this way we preserve the important illumination features, while eliminating noise. We call our method diffusion based photon mapping.
We consider ray bundles emanating from a source such as a camera or light source. We derive the f... more We consider ray bundles emanating from a source such as a camera or light source. We derive the full spatial and temporal structure to first order of the intersection of ray bundles with scene geometry, where scene geometry given as any implicit function. Further, we present the full details of 2 often used geometrical representations. The first order structure may be used as the linear approximation of the change of photons as the camera, objects, and light source change as function of space and time. Our work generalises previous work on ray differentials and photon differentials .
In this paper, we propose a multi-scale, multi-kernel shape, compactly supported kernel bundle fr... more In this paper, we propose a multi-scale, multi-kernel shape, compactly supported kernel bundle framework for stationary velocity field-based image registration (Wendland kernel bundle stationary velocity field, wKB-SVF). We exploit the possibility of directly choosing kernels to construct a reproducing kernel Hilbert space (RKHS) instead of imposing it from a differential operator. The proposed framework allows us to minimize computational cost without sacrificing the theoretical foundations of SVF-based diffeomorphic registration. In order to recover deformations occurring at different scales, we use compactly supported Wendland kernels at multiple scales and orders to parameterize the velocity fields, and the framework allows simultaneous optimization over all scales. The performance of wKB-SVF is extensively compared to the 14 non-rigid registration algorithms presented in a recent comparison paper. On both MGH10 and CUMC12 datasets, the accuracy of wKB-SVF is improved when compared to other registration algorithms. In a disease-specific application for intra-subject registration, atrophy scores estimated using the proposed registration scheme separates the diagnostic groups of Alzheimer's and normal controls better than the state-of-the-art segmentation technique. Experimental results show that wKB-SVF is a robust, flexible registration framework that allows theoretically well-founded and computationally efficient multi-scale representation of deformations and is equally well-suited for both inter- and intra-subject image registration.
A scale space approach is taken for building Bounding Volume Hierarchies (BVHs) for collision det... more A scale space approach is taken for building Bounding Volume Hierarchies (BVHs) for collision detection. A spherical bounding volume is generated at each node of the BVH using estimates of the mass distribution. Traditional top-down methods approximates the surface of an object in a coarse to fine manner, by recursively increasing resolution by some factor, e.g. 2. The method presented in this article analyzes the mass distribution of a solid object using a well founded scale-space based on the Diffusion Equation: the Gaussian Scale-Space. In the Gaussian scale-space, the deep structure of extremal mass points is naturally binary, and the linking process is therefore simple. The main contribution of this article is a novel approach for constructing BVHs using Multi-Scale Singularity Trees (MSSTs) for collision detection. The BVH-building algorithm extends the field with a new method based on volumetric shape rather than statistics of the surface geometry or geometrical constructs such as medial surfaces.
Bogusław Cyganek, Combined detector of locally-oriented structures and corners in images based on... more Bogusław Cyganek, Combined detector of locally-oriented structures and corners in images based on a scale-space tensor representation of local neighborhoods of pixels, Proceedings of the 2003 international conference on Computational science: PartII, June 02-04, 2003, ...
Note: OCR errors may be found in this Reference List extracted from the full text article. ACM ha... more Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references. ... {Baraff01} Baraff, David, "Physical based modeling: Rigid body simulation," SIGGRAPH ...
Proceedings of 13th International Conference on Pattern Recognition, 1996
Viewing images as distributions of light quanta enables an information theoretic study of image s... more Viewing images as distributions of light quanta enables an information theoretic study of image structures on dif- ferent scales. This article combines Shannon's entropy and Witkin and Koenderink's Scale-Space to establish a precise connection between the Heat Equation and the Thermody- namic Entropy in Scale-Space. Experimentally the entropy function is used to study global textures. A recent paper in by
This paper addresses the problem of mixing spectral bands and space in a smooth, linear, and casu... more This paper addresses the problem of mixing spectral bands and space in a smooth, linear, and casual manner. Such properties are of fundamental importance for many basic multi-spectral-image processing algorithms that probe inter-spectral structure. The example of color images is used in a simple spectral perspective. An example is given comparing the deep structure of the color and the gray gradient magnitude.
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Papers by Jon Sporring