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Auxiliary variables and twostep iterative algorithms in computer vision problems
 J. Math. Imag. Vision
, 1995
"... Abstract. We present a new mathematical formulation of some curve and surface reconstmctien algorithms by the introduction of auxiliary variables. For deformable models and templates, the extraction of a shape is obtained through the minimization of an energy composed of an internal regularization t ..."
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Cited by 39 (10 self)
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Abstract. We present a new mathematical formulation of some curve and surface reconstmctien algorithms by the introduction of auxiliary variables. For deformable models and templates, the extraction of a shape is obtained through the minimization of an energy composed of an internal regularization term (not necessary in the case of parametric models) and an external attraction potential. Twostep iterative algorithms have been often used where, at each iteration, the model is first locally deformed according to the potential data attraction and then globally smoothed (or fitted in the parametric case). We show how these approaches can be interpreted as the introduction of auxiliary variables and the minimization of a twovariables energy. The first variable corresponds to the original model we are looking for, while the second variable represents an auxiliary shape close to the first one. This permits to transform an implicit data constraint defined by a non convex potential into an explicit convex reconstruction problem. This approach is much simpler since each iteration is composed of two simple to solve steps. Our formulation permits a more precise setting of parameters in the iterative scheme to ensure convergence to a minimum. We show some mathematical properties and results on this new auxiliary problem, in particular when the potential is a function of the distance to the closest feature point. We then illustrate our approach for some deformable models and templates.
Superquadrics and freeform deformations : a global model to fit and track 3D medical data
, 1995
"... Recovery of 3D data with simple parametric models has been the subject of many studies over the last ten years. Many have used the notion of superquadrics, introduced for graphics in [4]. It appears, however, that although superquadrics can describe a wide variety of forms, they are too simple to r ..."
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Cited by 19 (9 self)
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Recovery of 3D data with simple parametric models has been the subject of many studies over the last ten years. Many have used the notion of superquadrics, introduced for graphics in [4]. It appears, however, that although superquadrics can describe a wide variety of forms, they are too simple to recover and describe complex shapes. This paper describes a method to øt to 3D points and then track a parametric deformable surface. We suppose that a 3D image has been segmented to get a set of 3D points. A ørst estimate consists of our version of a superquadric fit with global tapering. We then apply the technique of freeform deformations, as introduced by [9] in computer graphics to refine the estimate. We present experimental results with real 3D medical images, where the original points are laid on an isosurface. This is also applied to give efficient tracking of the deformation of the myocardium
Parameterization of Closed Surfaces for Parametric Surface Description
, 2000
"... A procedure for the parameterization of surface meshes of objects with spherical topology is presented. The generation of such a parameterization has been formulated and solved as a large constrained optimization problem by Brechbühler, but the convergence of this algorithm becomes unstable for obje ..."
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Cited by 16 (0 self)
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A procedure for the parameterization of surface meshes of objects with spherical topology is presented. The generation of such a parameterization has been formulated and solved as a large constrained optimization problem by Brechbühler, but the convergence of this algorithm becomes unstable for object meshes consisting of several thousand vertices. We propose a new more stable algorithm to overcome this problem using multiresolution meshes.
Polygonal and Polyhedral Contour Reconstruction in Computed Tomography
, 2004
"... This paper is about threedimensional (3D) reconstruction of a binary image from its Xray tomographic data. We study the special case of a compact uniform polyhedron totally included in a uniform background and directly perform the polyhedral surface estimation. We formulate this problem as a nonl ..."
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Cited by 13 (3 self)
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This paper is about threedimensional (3D) reconstruction of a binary image from its Xray tomographic data. We study the special case of a compact uniform polyhedron totally included in a uniform background and directly perform the polyhedral surface estimation. We formulate this problem as a nonlinear inverse problem using the Bayesian framework. Vertice estimation is done without using a voxel approximation of the 3D image. It is based on the construction and optimization of a regularized criterion that accounts for surface smoothness. We investigate original deterministic local algorithms, based on the exact computation of the line projections, their update, and their derivatives with respect to the vertice coordinates. Results are first derived in the twodimensional (2D) case, which consists of reconstructing a 2D object of deformable polygonal contour from its tomographic data. Then, we investigate the 3D extension that requires technical adaptations. Simulation results illustrate the performance of polygonal and polyhedral reconstruction algorithms in terms of quality and computation time.
Shape Recovery from Medical Image Data using Extended Superquadrics
 ASME 2005 Design Engineering Technical Conferences and Computers and Information in Engineering Conference
"... Without whom, I am nothing Reverse engineering of accurate 3D models and 2D contours of real objects from surface measurements is recognized as an important research goal in various application domains. These domains have ranged widely from, industrial product design to computer generated imagery fo ..."
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Cited by 4 (1 self)
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Without whom, I am nothing Reverse engineering of accurate 3D models and 2D contours of real objects from surface measurements is recognized as an important research goal in various application domains. These domains have ranged widely from, industrial product design to computer generated imagery for film and multimedia, and in more recent years extending to the life sciences realm. Despite the large body of work on 3D modeling, most models of shape lack the descriptive power to bridge the gap between reconstruction, recognition, and analysis due, mostly, to conflicting requirements. To obtain meaningful information from noisy sensor data reconstruction models, researchers have traditionally required the use of large numbers of shape parameters to adequately capture the salient features. In contrast, search and recognition techniques have fostered the use of shape parameterizations and abstractions, which drastically reduce information. The extension of such shape models to encompass various analysis modalities (in the form of FEA, kinematics and dynamics)
Auxiliary Variables for Deformable Models
 In International Conference on Computer Vision
, 1995
"... We present a new mathematical formulation for curve and surface reconstruction algorithms by introduction of auxiliary variables. For deformable models and templates, twostep iterative algorithms have been often used where, at each iteration, the model is first locally deformed according to the pot ..."
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Cited by 2 (1 self)
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We present a new mathematical formulation for curve and surface reconstruction algorithms by introduction of auxiliary variables. For deformable models and templates, twostep iterative algorithms have been often used where, at each iteration, the model is first locally deformed according to the potential data attraction and then globally smoothed. We show how these approaches can be interpreted as the introduction of auxiliary variables and the minimization of a twovariables energy. This permits to transform an implicit data constraint defined by a non convex potential into an explicit convex reconstruction problem. We show some mathematical properties and results on this new auxiliary problem, in particular when the potential is a function of the distance to the closest feature point. We then illustrate our approach for some deformable models and templates and image restoration.
GENETIC ALGORITHMS FOR 3D RECONSTRUCTION WITH SUPERSHAPES
"... Supershape model is a recent primitive that represents numerous 3D shapes with several symmetry axes. The main interest of this model is its capability to reconstruct more complex shape than superquadric model with only one implicit equation. In this paper we propose a genetic algorithms to reconstr ..."
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Supershape model is a recent primitive that represents numerous 3D shapes with several symmetry axes. The main interest of this model is its capability to reconstruct more complex shape than superquadric model with only one implicit equation. In this paper we propose a genetic algorithms to reconstruct a point cloud using those primitives. We used the pseudoEuclidean distance to introduce a threshold to handle real data imperfection and speed up the process. Simulations using our proposed fitness functions and a fitness function based on insideoutside function show that our fitness function based on the pseudoEuclidean distance performs better. Index Terms — 3D Reconstruction, genetic algorithms, supershapes, pseudoEuclidean distance
Deformable Models with Locally Adaptive Resolution using Riemannian Metrics defined from Image Structure Tensor
"... Deformable models are extensively used in the context of image segmentation. To improve both their convergence and their robustness many methods have been developed. However they generally result in a tradeoff between the number of the shape parameters, and the genericity of the deformable model. O ..."
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Deformable models are extensively used in the context of image segmentation. To improve both their convergence and their robustness many methods have been developed. However they generally result in a tradeoff between the number of the shape parameters, and the genericity of the deformable model. Our goal is to build a deformable model that can handle arbitrary complex shapes while keeping a complexity as independent as possible from the size of input data. On this purpose, we propose a deformable model that locally adapts its resolution to the geometry of the objects in the images. The main idea is to change the Euclidean metric with a deformed Riemannian metric that geometrically expands the space in the interesting areas of the image.
Journal of Electronic Imaging 13(3), 411–417 (July 2004).
"... Superquadric representation of automotive parts applying part decomposition Abstract. Superquadrics are able to represent a large variety of objects with only a few parameters and a single equation. We present a superquadric representation strategy for automotive parts composed of 3D triangle meshe ..."
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Superquadric representation of automotive parts applying part decomposition Abstract. Superquadrics are able to represent a large variety of objects with only a few parameters and a single equation. We present a superquadric representation strategy for automotive parts composed of 3D triangle meshes. Our strategy consists of two major steps of part decomposition and superquadric fitting. The originalities of this approach include the following two features. First, our approach can represent multipart objects with superquadrics successfully by applying part decomposition. Second, superquadrics recovered from our approach have the highest confidence and accuracy due to the 3D watertight surfaces utilized. A novel, generic 3D part decomposition algorithm based on curvature analysis is also proposed. Experimental results demonstrate that the proposed part decomposition algorithm is able to segment multipart objects into meaningful single parts efficiently. The proposed superquadric representation strategy can then represent each individual part of the original objects with a superquadric model successfully. © 2004 SPIE and IS&T. [DOI: 10.1117/1.1762516] 1
Rigid, Affine and Locally Affine Registration of FreeForm Surfaces
 IJCV
, 1994
"... : In this paper, we propose a new framework to perform nonrigid surface registration. It is based on various extensions of an iterative algorithm recently presented by several researchers ([BM92], [Zha93], [CM92], [ML92], [CLSB92]) to rigidly register surfaces represented by a set of 3D points, whe ..."
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: In this paper, we propose a new framework to perform nonrigid surface registration. It is based on various extensions of an iterative algorithm recently presented by several researchers ([BM92], [Zha93], [CM92], [ML92], [CLSB92]) to rigidly register surfaces represented by a set of 3D points, when a prior estimate of the displacement is available. Our framework consists of three stages: ffl First, we search for the best rigid displacement to superpose the two surfaces. We show how to efficiently use curvatures to superpose principal frames at possible corresponding points in order to find a prior rough estimate of the displacement and initialize the iterative algorithm. ffl Second, we search for the best affine transformation. We introduce differential information in points coordinates: this allows us to match locally similar points. Then, we show how principal frames and curvatures are transformed by an affine transformation. Finally, we introduce this differential information in...