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47
Variational shape and reflectance estimation under changing light and viewpoints
 IN PROCEEDINGS OF THE 9TH EUROPEAN CONFERENCE ON COMPUTER VISION
, 2006
"... Fitting parameterized 3D shape and general reflectance models to 2D image data is challenging due to the high dimensionality of the problem. The proposed method combines the capabilities of classical and photometric stereo, allowing for accurate reconstruction of both textured and nontextured sur ..."
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Cited by 24 (9 self)
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Fitting parameterized 3D shape and general reflectance models to 2D image data is challenging due to the high dimensionality of the problem. The proposed method combines the capabilities of classical and photometric stereo, allowing for accurate reconstruction of both textured and nontextured surfaces. In particular, we present a variational method implemented as a PDEdriven surface evolution interleaved with reflectance estimation. The surface is represented on an adaptive mesh allowing topological change. To provide the input data, we have designed a capture setup that simultaneously acquires both viewpoint and light variation while minimizing selfshadowing. Our capture method is feasible for realworld application as it requires a moderate amount of input data and processing time. In experiments, models of people and everyday objects were captured from a few dozen images taken with a consumer digital camera. The capture process recovers a photoconsistent model of spatially varying Lambertian and specular reflectance and a highly accurate geometry.
Convergence analysis of a discretization scheme for Gaussian curvature over triangular surfaces. Computer Aided Geometric Design
"... In this paper, we study the convergent property of a well known discretized scheme of Gaussian curvature, derived from GaussBonnet theorem, over triangulated surface. Suppose the triangulation is obtained from a sampling of a smooth parametric surface, we show theoretically that the discretized app ..."
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Cited by 16 (5 self)
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In this paper, we study the convergent property of a well known discretized scheme of Gaussian curvature, derived from GaussBonnet theorem, over triangulated surface. Suppose the triangulation is obtained from a sampling of a smooth parametric surface, we show theoretically that the discretized approximation has quadratic convergence rate for a special triangulation scenario of the surface. Numerical results which justify the theoretical analysis are also presented. Key words: Gaussian Curvature; Surface triangulation; Convergence. 1
Robust Voronoibased Curvature and Feature Estimation
 SIAM/ACM JOINT CONFERENCE ON GEOMETRIC AND PHYSICAL MODELING
, 2009
"... Many algorithms for shape analysis and shape processing rely on accurate estimates of di erential information such as normals and curvature. In most settings, however, care must be taken around nonsmooth areas of the shape where these quantities are not easily de ned. This problem is particularly pr ..."
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Cited by 16 (3 self)
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Many algorithms for shape analysis and shape processing rely on accurate estimates of di erential information such as normals and curvature. In most settings, however, care must be taken around nonsmooth areas of the shape where these quantities are not easily de ned. This problem is particularly prominent with pointcloud data, which are discontinuous everywhere. In this paper we present an e cient and robust method for extracting principal curvatures, sharp features and normal directions of a piecewise smooth surface from its point cloud sampling, with theoretical guarantees. Our method is integral in nature and uses convolved covariance matrices of Voronoi cells of the point cloud which makes it provably robust in the presence of noise. We show analytically that our method recovers correct principal curvatures and principal curvature directions in smooth parts of the shape, and correct feature directions and feature angles at the sharp edges of a piecewise smooth surface, with the error bounded by the Hausdor distance between the point cloud and the underlying surface. Using the same analysis we provide theoretical guarantees for a modi cation of a previously proposed normal estimation technique. We illustrate the correctness of both principal curvature information and feature extraction in the presence of varying levels of noise and sampling density on a variety of models.
Environmental Influence on the Evolution of Morphological Complexity in Machines
, 2013
"... Whether, when, how, and why increased complexity evolves in biological populations is a longstanding open question. In this work we combine a recently developed method for evolving virtual organisms with an informationtheoretic metric of morphological complexity in order to investigate how the comp ..."
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Cited by 7 (1 self)
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Whether, when, how, and why increased complexity evolves in biological populations is a longstanding open question. In this work we combine a recently developed method for evolving virtual organisms with an informationtheoretic metric of morphological complexity in order to investigate how the complexity of morphologies, which are evolved for locomotion, varies across different environments. We first demonstrate that selection for locomotion results in the evolution of organisms with morphologies that increase in complexity over evolutionary time beyond what would be expected due to random chance. This provides evidence that the increase in complexity observed is a result of a driven rather than a passive trend. In subsequent experiments we demonstrate that morphologies having greater complexity evolve in complex environments, when compared to a simple environment when a cost of complexity is imposed. This suggests that in some niches, evolution may act to complexify the body plans of organisms while in other niches selection favors simpler body plans.
Discrete distortion for 3D data analysis
 Visualization in Medicine and Life Sciences (VMLS), Mathematics and Visualization
, 2011
"... Summary. We investigate a morphological approach to the analysis and understanding of threedimensional scalar fields, and we consider applications to 3D medical and molecular images as examples. We consider a discrete model of the scalar field obtained by discretizing its 3D domain into a tetrahedr ..."
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Cited by 4 (4 self)
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Summary. We investigate a morphological approach to the analysis and understanding of threedimensional scalar fields, and we consider applications to 3D medical and molecular images as examples. We consider a discrete model of the scalar field obtained by discretizing its 3D domain into a tetrahedral mesh. In particular, our meshes correspond to approximations at uniform or variable resolution extracted from a multiresolution model of the 3D scalar field, that we call a hierarchy of diamonds. We analyze the images based on the concept of discrete distortion, that we have introduced in [26], and on segmentations based on Morse theory. Discrete distortion is defined by considering the graph of the discrete 3D field, which is a tetrahedral hypersurface in R 4, and measuring the distortion of the transformation which maps the tetrahedral mesh discretizing the scalar field domain into the mesh representing its graph in R 4. We describe a segmentation algorithm to produce Morse decompositions of a 3D scalar field which uses a watershed approach and we apply it to 3D images by using as scalar field both intensity and discrete distortion. We present experimental results by considering the influence of resolution on distortion computation. In particular, we show that the salient features of the distortion field appear prominently in lower resolution approximations to the dataset. 1
Differential tangential expansion as a mechanism for cortical gyrification
 Cerebral Cortex
, 2013
"... Gyrification, the developmental buckling of the cortex, is not a random process—the forces that mediate expansion do so in such a way as to generate consistent patterns of folds across individuals and even species. Although the origin of these forces is unknown, some theories have suggested that the ..."
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Cited by 4 (0 self)
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Gyrification, the developmental buckling of the cortex, is not a random process—the forces that mediate expansion do so in such a way as to generate consistent patterns of folds across individuals and even species. Although the origin of these forces is unknown, some theories have suggested that they may be related to external cortical factors such as axonal tension. Here, we investigate an alternative hypothesis, namely, whether the differential tangential expansion of the cortex alone can account for the degree and patternspecificity of gyrification. Using intrinsic curvature as a measure of differential expansion, we initially explored whether this parameter and the local gyrification index (used to quantify the degree of gyrification) varied in a regionalspecific pattern across the cortical surface in a manner that was replicable across independent datasets of neurotypicals. Having confirmed this consistency, we further demonstrated that within each dataset, the degree of intrinsic curvature of the cortex was predictive of the degree of cortical folding at a global and regional level. We conclude that differential expansion is a plausible primary mechanism for gyrification, and propose that this perspective offers a compelling mechanistic account of the colocalization of cytoarchitecture and cortical folds.
Voronoibased curvature and feature estimation from point clouds, Visualization and Computer Graphics
 IEEE Transactions on
, 2011
"... Abstract—We present an efficient and robust method for extracting curvature information, sharp features and normal directions of a piecewise smooth surface from its point cloud sampling in a unified framework. Our method is integral in nature and uses convolved covariance matrices of Voronoi cells o ..."
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Cited by 3 (0 self)
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Abstract—We present an efficient and robust method for extracting curvature information, sharp features and normal directions of a piecewise smooth surface from its point cloud sampling in a unified framework. Our method is integral in nature and uses convolved covariance matrices of Voronoi cells of the point cloud which makes it provably robust in the presence of noise. We show that these matrices contain information related to curvature in the smooth parts of the surface, and information about the directions and angles of sharp edges around the features of a piecewisesmooth surface. Our method is applicable in both two and three dimensions, and can be easily parallelized, making it possible to process arbitrarily large point clouds, which was a challenge for Voronoibased methods. In addition, we describe a MonteCarlo version of our method, which is applicable in any dimension. We illustrate the correctness of both principal curvature information and feature extraction in the presence of varying levels of noise and sampling density on a variety of models. As a sample application, we use our feature detection method to segment point cloud samplings of piecewisesmooth surfaces.
Brain image analysis using spherical splines
 In Proceedings of the Fifth International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition, Lecture Note in Computer Science (LNCS) 3757
, 2005
"... Abstract. We propose a novel technique based on spherical splines for brain surface representation and analysis. This research is strongly inspired by the fact that, for brain surfaces, it is both necessary and natural to employ spheres as their natural domains. We develop an automatic and efficient ..."
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Cited by 2 (1 self)
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Abstract. We propose a novel technique based on spherical splines for brain surface representation and analysis. This research is strongly inspired by the fact that, for brain surfaces, it is both necessary and natural to employ spheres as their natural domains. We develop an automatic and efficient algorithm, which transforms a brain surface to a single spherical spline whose maximal error deviation from the original data is less than the userspecified tolerance. Compared to the discrete meshbased representation, our spherical spline offers a concise (low storage requirement) digital form with high continuity (C n−1 continuity for a degree n spherical spline). Furthermore, this representation enables the accurate evaluation of differential properties, such as curvature, principal direction, and geodesic, without the need for any numerical approximations. Thus, certain shape analysis procedures, such as segmentation, gyri and sulci tracing, and 3D shape matching, can be carried out both robustly and accurately. We conduct several experiments in order to demonstrate the efficacy of our approach for the quantitative measurement and analysis of brain surfaces. 1
Local versus global in quasiconformal mapping for medical imaging
, 2007
"... A method and algorithm of flattening of folded surfaces for twodimensional representation and analysis of medical images are presented. The method is based on extension of classical results of Gehring and Väisälä regarding the existence of quasiconformal and quasiisometric mappings. The proposed ..."
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Cited by 2 (2 self)
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A method and algorithm of flattening of folded surfaces for twodimensional representation and analysis of medical images are presented. The method is based on extension of classical results of Gehring and Väisälä regarding the existence of quasiconformal and quasiisometric mappings. The proposed algorithm is basically local and, therefore, suitable for extensively folded surfaces encountered in medical imaging. The theory and algorithm guarantee minimal distance, angle and area distortion. Yet, it is relatively simple, robust and computationally efficient, since it does not require computational derivatives. Both random starting point and curvaturebased versions of the algorithm are presented. We demonstrate the algorithm using medical data obtained from real CT images of the colon and MRI scan of the human cortex. Further applications of the algorithm, for image processing in general are also considered. Moreover, the globality of this algorithm is also studied, via extreme length methods for which we develop a technique for computing straightest geodesics on polyhedral surfaces.