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Topological equivalence between a 3D object and the reconstruction of its digital image
 IEEE Trans. Pattern Anal. Mach. Intell
, 2007
"... Digitization is not as easy as it looks. If one digitizes a 3D object even with a dense sampling grid, the reconstructed digital object may have topological distortions and, in general, there exists no upper bound for the Hausdorff distance. This explains why so far no algorithm has been known whic ..."
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Digitization is not as easy as it looks. If one digitizes a 3D object even with a dense sampling grid, the reconstructed digital object may have topological distortions and, in general, there exists no upper bound for the Hausdorff distance. This explains why so far no algorithm has been known which guarantees topology preservation. However, as we will show, it is possible to repair the obtained digital image in a locally bounded way so that it is homeomorphic and close to the 3D object. The resulting digital object is always wellcomposed, which has nice implications for a lot of image analysis problems. Moreover, we will show that the surface of the original object is homeomorphic to the result of the marching cubes algorithm. This is really surprising since it means that the wellknown topological problems of the marching cubes reconstruction simply do not occur for digital images of rregular objects. Based on the trilinear interpolation, we also construct a smooth isosurface from the digital image that has the same topology as the original surface. Finally, we give a surprisingly simple topology preserving reconstruction method by using overlapping balls instead of cubical voxels. This is the first approach of digitizing 3D objects which guarantees topology preservation and gives an upper bound for the geometric distortion. Since the output can be chosen as a pure voxel presentation, a union of balls, a reconstruction by trilinear interpolation, a smooth isosurface, or the piecewise linear marching cubes surface, the results are directly applicable to a huge class of image analysis algorithms. Moreover, we show how one can efficiently estimate the volume and the surface area of 3D objects by looking at their digitizations. Measuring volume and surface area of digital objects are important problems in 3D image analysis. Good estimators should be multigrid convergent, i.e., the error goes to zero with increasing sampling density. We will show that every presented reconstruction method can be used for
COMPUTER VISION ON MULTICORE PROCESSORS: ARTICULATED BODY TRACKING
"... The recent emergence of multicore processors enables a new trend in the usage of computers. Computer vision applications, which require heavy computation and lots of bandwidth, usually cannot run in realtime. Recent multicore processors can potentially serve the needs of such workloads. In additio ..."
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The recent emergence of multicore processors enables a new trend in the usage of computers. Computer vision applications, which require heavy computation and lots of bandwidth, usually cannot run in realtime. Recent multicore processors can potentially serve the needs of such workloads. In addition, more advanced algorithms can be developed utilizing the new computation paradigm. In this paper, we study the performance of an articulated body tracker on multicore processors. The articulated body tracking workload encapsulates most of the important aspects of a computer vision workload. It takes multiple camera inputs of a scene with a single human object, extracts useful features, and performs statistical inference to find the body pose. We show the importance of properly parallelizing the workload in order to achieve great performance: speedups of 26 on 32 cores. We conclude that: (1) datadomain parallelization is better than functiondomain parallelization for computer vision applications; (2) datadomain parallelism by image regions and particles is very effective; (3) reducing serial code in edge detection brings significant performance improvements; (4) domain knowledge about low/mid/high level of vision computation is helpful in parallelizing the workload. 1.
Gool. Monocular tracking with a mixture of viewdependent learned models
 In IV Conference on Articulated Motion and Deformable Objects, AMDO
, 2006
"... Abstract. This paper considers the problem of monocular human body tracking using learned models. We propose to learn the joint probability distribution of appearance and body pose using a mixture of viewdependent models. In such a way the multimodal and nonlinear relationships can be captured reli ..."
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Abstract. This paper considers the problem of monocular human body tracking using learned models. We propose to learn the joint probability distribution of appearance and body pose using a mixture of viewdependent models. In such a way the multimodal and nonlinear relationships can be captured reliably. We formulate inference algorithms that are based on generative models while exploiting the advantages of a learned model when compared to the traditionally used geometric body models. Given static images or sequences, body poses and bounding box locations are inferred using silhouette based image descriptors. Prior information about likely body poses and a motion model are taken into account. We consider analytical computations and MonteCarlo techniques, as well as a combination of both. In a RaoBlackwellised particle filter, the tracking problem is partitioned into a part that is solved analytically, and a part that is solved with particle filtering. Tracking results are reported for human locomotion. 1
Multiactivity tracking in LLE body pose space
 In Proc. of IEEE ICCV 2nd Workshop on Human Motion
, 2007
"... Abstract. We present a method to simultaneously estimate 3d body pose and action categories from monocular video sequences. Our approach learns a lowdimensional embedding of the pose manifolds using Locally Linear Embedding (LLE), as well as the statistical relationship between body poses and their ..."
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Abstract. We present a method to simultaneously estimate 3d body pose and action categories from monocular video sequences. Our approach learns a lowdimensional embedding of the pose manifolds using Locally Linear Embedding (LLE), as well as the statistical relationship between body poses and their image appearance. In addition, the dynamics in these pose manifolds are modelled. Sparse kernel regressors capture the nonlinearities of these mappings efficiently. Body poses are inferred by a recursive Bayesian sampling algorithm with an activityswitching mechanism based on learned transfer functions. Using a rough foreground segmentation, we compare Binary PCA and distance transforms to encode the appearance. As a postprocessing step, the globally optimal trajectory through the entire sequence is estimated, yielding a single pose estimate per frame that is consistent throughout the sequence. We evaluate the algorithm on challenging sequences with subjects that are alternating between running and walking movements. Our experiments show how the dynamical model helps to track through poorly segmented lowresolution image sequences where tracking otherwise fails, while at the same time reliably classifying the activity type. 1
Discernibility Concept in Classification Problems
"... The main idea behind this project is that the pattern classification process can be enhanced by taking into account the geometry of class structure in datasets of interest. In contrast to previous work in the literature, this research not only develops a measure of discernibility of individual patte ..."
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The main idea behind this project is that the pattern classification process can be enhanced by taking into account the geometry of class structure in datasets of interest. In contrast to previous work in the literature, this research not only develops a measure of discernibility of individual patterns but also consistently applies it to various stages of the classification process. The applications of the discernibility concept cover a wide range of issues from preprocessing to the actual classification and beyond that. Specifically, we apply it for: (a) finding feature subsets of similar classification quality (applicable in diverse ensembles), (b) feature selection, (c) data reduction, (d) reject option, and (e) enhancing the kNN classifier. Also, a number of auxiliary algorithms and measures are developed to facilitate the proposed methodology. Experiments have been carried out using datasets of the University of California at Irvine (UCI) repository. The experiments provide numerical evidence that the proposed approach does improve the performance of various classifiers. This, together with its simplicity renders it a novel,
Parametric computation of the Legendre–Fenchel conjugate
 J. Convex Anal
"... Abstract. A new algorithm, named the Parametric Legendre Transform (PLT) algorithm, to compute the LegendreFenchel conjugate of a convex function of one variable is presented. It returns a parameterization of the graph of the conjugate except for some affine parts corresponding to nondifferentiable ..."
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Abstract. A new algorithm, named the Parametric Legendre Transform (PLT) algorithm, to compute the LegendreFenchel conjugate of a convex function of one variable is presented. It returns a parameterization of the graph of the conjugate except for some affine parts corresponding to nondifferentiable points of the function. The approach is extended to the computation of the Moreau envelope, resulting in a simple yet efficient algorithm. Theoretical results, the description (and extension) of the algorithm, its approximation error and the convergence, as well as the comparison with known algorithms are included. 1.
Approximation of Euclidean distances by chamfer distances
"... Chamfer distances play an important role in the theory of distance transforms. Though the determination of the exact Euclidean distance transform is also a well investigated area, the classical chamfering method based upon ”small ” neighborhoods still outperforms it e.g. in terms of computation time ..."
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Chamfer distances play an important role in the theory of distance transforms. Though the determination of the exact Euclidean distance transform is also a well investigated area, the classical chamfering method based upon ”small ” neighborhoods still outperforms it e.g. in terms of computation time. In this paper we determine the best possible maximum relative error of chamfer distances under various boundary conditions. In each case some best approximating sequences are explicitly given. Further, because of possible practical interest, we give all best approximating sequences in case of small (i.e. 5×5 and 7×7) neighborhoods.
Ray tracing implicit surfaces on the GPU
"... In this paper we examine the methods of rendering implicit surfaces with a perpixel approach. Ray tracing the implicit model directly has several benefits as opposed to processing tessellated meshes, but also invokes new kinds of problems. The main challenge is efficiently finding the first raysur ..."
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In this paper we examine the methods of rendering implicit surfaces with a perpixel approach. Ray tracing the implicit model directly has several benefits as opposed to processing tessellated meshes, but also invokes new kinds of problems. The main challenge is efficiently finding the first raysurface intersection point where the surface is not given in an explicit form. Our implementation uses the sphere tracing algorithm to attack this problem and runs on the GPU to achieve high frame rates. We also discuss secondary issues like shading and texturing implicit models.
3D Object Digitization: Volume and Surface Area Estimation
 Proc. IEEE Int’l Conf. Image Analysis
, 2006
"... 2 Preliminaries Measuring volume and surface area of objects given its digitizations are important problems in 3D image analysis. Good estimators should be multigrid convergent, i.e. the error goes to zero with increasing sampling density. We will give such estimators both for volume and for surface ..."
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2 Preliminaries Measuring volume and surface area of objects given its digitizations are important problems in 3D image analysis. Good estimators should be multigrid convergent, i.e. the error goes to zero with increasing sampling density. We will give such estimators both for volume and for surface area estimation based on simple counting of voxels. 1
Research Article Adding Image Constraints to Inverse Kinematics for Human Motion Capture
, 2009
"... Copyright © 2010 Antoni JaumeiCapó et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In order to study human motion in biomech ..."
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Copyright © 2010 Antoni JaumeiCapó et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In order to study human motion in biomechanical applications, a critical component is to accurately obtain the 3D joint positions of the user’s body. Computer vision and inverse kinematics are used to achieve this objective without markers or special devices attached to the body. The problem of these systems is that the inverse kinematics is “blinded ” with respect to the projection of body segments into the images used by the computer vision algorithms. In this paper, we present how to add image constraints to inverse kinematics in order to estimate human motion. Specifically, we explain how to define a criterion to use images in order to guide the posture reconstruction of the articulated chain. Tests with synthetic images show how the scheme performs well in an ideal situation. In order to test its potential in real situations, more experiments with task specific image sequences are also presented. By means of a quantitative study of different sequences, the results obtained show how this approach improves the performance of inverse kinematics in this application. 1.