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39
Avoiding Local Minima for Deformable Curves in Image Analysis
 in Curves and Surfaces with Applications in CAGD
, 1997
"... We present an overview of part of our work over the past few years on snakes, balloons, and deformable models, with applications to image analysis. The main drawbacks of the active contour model being its initialization and minimization, we present three approaches that help to avoid being trapped i ..."
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Cited by 18 (12 self)
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We present an overview of part of our work over the past few years on snakes, balloons, and deformable models, with applications to image analysis. The main drawbacks of the active contour model being its initialization and minimization, we present three approaches that help to avoid being trapped in a local minimum of the energy. We introduced the balloon model to extract a contour being less demanding on the initial curve. In a more recent approach, based on minimal paths and geodesics, we find the global minimum of the energy between two points. A third approach is defined by a hybrid regionbased energy taking into account homogeneity of the region inside the contour.
Regularization of Orthonormal Vector Sets using Coupled PDE's
 PROCEEDINGS 1ST IEEE WORKSHOP ON VARIATIONAL AND LEVEL SET METHODS IN COMPUTER VISION
, 2001
"... We address the problem of restoring, while preserving possible discontinuities, fields of noisy orthonormal vector sets, taking the orthonormal constraints explicitly into account. We develop a variational solution for the general case where each image feature may correspond to multiple nD orthogon ..."
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Cited by 18 (6 self)
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We address the problem of restoring, while preserving possible discontinuities, fields of noisy orthonormal vector sets, taking the orthonormal constraints explicitly into account. We develop a variational solution for the general case where each image feature may correspond to multiple nD orthogonal vectors of unit norms. We first formulate the problem in a new variational framework, where discontinuities and orthonormal constraints are preserved by means of constrained minimization and functions regularization, leading to a set of coupled anisotropic diffusion PDE's. A geometric interpretation of the resulting equations, coming from the field of solid mechanics, is proposed for the 3D case. Two interesting restrictions of our framework are also tackled : the regularization of 3D rotation matrices and the Direction diffusion (the parallel with previous works is made). Finally, we present a number of denoising results and applications.
ParameterFree Elastic Deformation Approach for 2D and 3D Registration Using Prescribed Displacements
, 1999
"... A parameterfree approach for nonrigid image registration based on elasticity theory is presented. In contrast to traditional physicallybased numerical registration methods, no forces have to be computed from image data to drive the elastic deformation. Instead, displacements obtained with the ..."
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Cited by 12 (2 self)
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A parameterfree approach for nonrigid image registration based on elasticity theory is presented. In contrast to traditional physicallybased numerical registration methods, no forces have to be computed from image data to drive the elastic deformation. Instead, displacements obtained with the help of mapping boundary structures in the source and target image are incorporated as hard constraints into elastic image deformation. As a consequence, our approach does not contain any parameters of the deformation model such as elastic constants. The approach guarantees the exact correspondence of boundary structures in the images assuming that correct input data are available. The implemented incremental method allows to cope with large deformations. The theoretical background, the finite element discretization of the elastic model, and experimental results for 2D and 3D synthetic as well as real medical images are presented.
Adaptive Rest condition potentials: first and second order edgepreserving regularization
 COMPUTER VISION AND IMAGE UNDERSTANDING
, 2002
"... A new regularization formulation for inverse problems in computer vision and image processing is introduced, which allows one to reconstruct second order piecewise smooth images, that is, images consisting of an assembly of regions with almost constant value, almost constant slope or almost constant ..."
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Cited by 11 (4 self)
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A new regularization formulation for inverse problems in computer vision and image processing is introduced, which allows one to reconstruct second order piecewise smooth images, that is, images consisting of an assembly of regions with almost constant value, almost constant slope or almost constant curvature. This formulation is based on the idea of using potential functions that correspond to springs or thin plates with an adaptive rest condition. Efficient algorithms for computing the solution, and examples illustrating the performance of this scheme, compared with other known regularization schemes are presented as well.
Analyzing the Deformation of the Left Ventricle of the Heart with a Parametric Deformable Model
, 1996
"... We present a new approach to analyze the deformation of the left ventricle of the heart, based on a parametric model that gives a compact representation of a set of points in a 3D image. We present four different approaches to tracking surfaces in a sequence of 3D cardiac images. Following tracking, ..."
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Cited by 10 (2 self)
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We present a new approach to analyze the deformation of the left ventricle of the heart, based on a parametric model that gives a compact representation of a set of points in a 3D image. We present four different approaches to tracking surfaces in a sequence of 3D cardiac images. Following tracking, we then infer quantitative parameters which are useful for the physician, suchas the variation of volume and wall thickness during a cardiac cycle, the ejection fraction or the twist component in the deformation of the ventricle. We explicit the computation of these parameters using our model. Experimental results are shown in time sequences of two kinds of medical images, Nuclear Medicine and XRay Computed Tomography (CT).
Regularization in Image NonRigid Registration: I. Tradeoff between Smoothness and Intensity Similarity
, 2001
"... In this report, we first propose a new classification of nonrigid registration algorithms into three main categories: in one hand, the geometric algorithms, and in the other hand, intensity based methods that we split here into standard intensitybased (SIB) and pairandsmooth (P&S) algorithms ..."
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Cited by 8 (4 self)
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In this report, we first propose a new classification of nonrigid registration algorithms into three main categories: in one hand, the geometric algorithms, and in the other hand, intensity based methods that we split here into standard intensitybased (SIB) and pairandsmooth (P&S) algorithms. We then focus on the subset of SIB and P&S...
TwoStep ParameterFree Elastic Image Registration with Prescribed Point Displacements
 In Proc. 9th Int. Conf. on Image Analysis and Processing (ICIAP '97
, 1997
"... A twostep parameterfree approach for nonrigid medical image registration is presented. Displacements of boundary structures are computed in the first step and then incorporated as hard constraints for elastic image deformation in the second step. In comparison to traditional nonparametric method ..."
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Cited by 8 (6 self)
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A twostep parameterfree approach for nonrigid medical image registration is presented. Displacements of boundary structures are computed in the first step and then incorporated as hard constraints for elastic image deformation in the second step. In comparison to traditional nonparametric methods, no driving forces have to be computed from image data. The approach guarantees the exact correspondence of certain structures in the images and does not depend on parameters of the deformation model such as elastic constants. Numerical examples with synthetic and real images are presented. 1 Introduction Numerous applications in modern medical imaging deal with nonrigid image registration. Examples are imageatlas as well as multimodality image registration in neurosurgery. There, a threedimensional image (deformable template) has to be completely transformed onto another one (study). One group of methods dealing with nonrigid image registration is the socalled nonparametric metho...
A Robust and Convergent Iterative Approach for Determining the Dominant Plane From Two Views Without Correspondence and Calibration
, 1997
"... A robust, iterative approach is introduced for finding the dominant plane in a scene using binocular vision. Neither camera calibration nor stereo correspondence is required. Recently Cohen formalized a framework guaranteeing (local) convergence of iterative twostep methods. In this paper, the fram ..."
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Cited by 7 (1 self)
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A robust, iterative approach is introduced for finding the dominant plane in a scene using binocular vision. Neither camera calibration nor stereo correspondence is required. Recently Cohen formalized a framework guaranteeing (local) convergence of iterative twostep methods. In this paper, the framework is adopted, with a global step using tentative matches to estimate the planar projectivity, and a local step attempting to solve the stereo correspondence. A detected point in the first image is matched to an auxiliary point in the second image, on the line joining the transformed first image point, and its closest detected second image point. Convergence is assured, while achieving robustness to both mismatching and noncoplanar points. 1. Introduction Since active robots change their visual attention by altering the camera parameters, they continuously require a recalibration. Therefore active robots cannot reconstruct any metric information about its surroundings, but it is still p...
Diffusion PDE's on Vectorvalued Images: Local Approach and Geometric Viewpoint
 IEEE Signal Processing Magazine
, 2002
"... We study multivalued diffusion PDE's (Partial Differential Equations) and their application to color image processing. The analysis of classic scalar diffusion PDE's leads to a new multivalued regularization equation which is coherent with a local vector image geometry. Then, we are intere ..."
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Cited by 6 (3 self)
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We study multivalued diffusion PDE's (Partial Differential Equations) and their application to color image processing. The analysis of classic scalar diffusion PDE's leads to a new multivalued regularization equation which is coherent with a local vector image geometry. Then, we are interested in constrained regularization problems, where vector norm constraints have to be considered. A general extension for unit vector regularization is then proposed. Finally, experimental results of color image restoration are presented.
Regularization Tools And Models For Image And Signal Reconstruction
, 1999
"... The present paper proposes a synthetic overview of regularization techniques for the reconstruction of piecewise regular signals and images. The stress is put on Tikhonov penalized approach and on subsequent nonquadratic and halfquadratic generalizations. On one hand, a link is made between the det ..."
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Cited by 6 (0 self)
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The present paper proposes a synthetic overview of regularization techniques for the reconstruction of piecewise regular signals and images. The stress is put on Tikhonov penalized approach and on subsequent nonquadratic and halfquadratic generalizations. On one hand, a link is made between the detectionestimation formulation and the nonconvex penalization approach. On the other hand, it is highlighted that convex penalizing functions provide a good edgepreserving compromise between quadratic regularization and the numerically burdensome detectionestimation approach.