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75
Geodesic Active Contours
, 1997
"... A novel scheme for the detection of object boundaries is presented. The technique is based on active contours evolving in time according to intrinsic geometric measures of the image. The evolving contours naturally split and merge, allowing the simultaneous detection of several objects and both in ..."
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Cited by 1367 (47 self)
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A novel scheme for the detection of object boundaries is presented. The technique is based on active contours evolving in time according to intrinsic geometric measures of the image. The evolving contours naturally split and merge, allowing the simultaneous detection of several objects and both interior and exterior boundaries. The proposed approach is based on the relation between active contours and the computation of geodesics or minimal distance curves. The minimal distance curve lays in a Riemannian space whose metric is defined by the image content. This geodesic approach for object segmentation allows to connect classical "snakes" based on energy minimization and geometric active contours based on the theory of curve evolution. Previous models of geometric active contours are improved, allowing stable boundary detection when their gradients suffer from large variations, including gaps. Formal results concerning existence, uniqueness, stability, and correctness of the evolution are presented as well. The scheme was implemented using an efficient algorithm for curve evolution. Experimental results of applying the scheme to real images including objects with holes and medical data imagery demonstrate its power. The results may be extended to 3D object segmentation as well.
Geodesic Active Regions and Level Set Methods for Supervised Texture Segmentation
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2002
"... This paper presents a novel variational framework to deal with frame partition problems in Computer Vision. This framework exploits boundary and regionbased segmentation modules under a curvebased optimization objective function. The task of supervised texture segmentation is considered to demonst ..."
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Cited by 300 (9 self)
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This paper presents a novel variational framework to deal with frame partition problems in Computer Vision. This framework exploits boundary and regionbased segmentation modules under a curvebased optimization objective function. The task of supervised texture segmentation is considered to demonstrate the potentials of the proposed framework. The textured feature space is generated by filtering the given textured images using isotropic and anisotropic filters, and analyzing their responses as multicomponent conditional probability density functions. The texture segmentation is obtained by unifying region and boundarybased information as an improved Geodesic Active Contour Model. The defined objective function is minimized using a gradientdescent method where a level set approach is used to implement the obtained PDE. According to this PDE, the curve propagation towards the final solution is guided by boundary and regionbased segmentation forces, and is constrained by a regularity force. The level set implementation is performed using a fast front propagation algorithm where topological changes are naturally handled. The performance of our method is demonstrated on a variety of synthetic and real textured frames.
Deformotion  Deforming Motion, Shape Average and the Joint Registration and Segmentation of Images
 International Journal of Computer Vision
, 2002
"... What does it mean for a deforming object to be "moving" (see Fig. 1)? How can we separate the overall motion (a finitedimensional group action) from the more general deformation (a di#eomorphism)? In this paper we propose a definition of motion for a deforming object and introduce a notio ..."
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Cited by 121 (16 self)
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What does it mean for a deforming object to be "moving" (see Fig. 1)? How can we separate the overall motion (a finitedimensional group action) from the more general deformation (a di#eomorphism)? In this paper we propose a definition of motion for a deforming object and introduce a notion of "shape average" as the entity that separates the motion from the deformation. Our definition allows us to derive novel and e#cient algorithms to register nonequivalent shapes using regionbased methods, and to simultaneously approximate and register structures in greyscale images. We also extend the notion of shape average to that of a "moving average" in order to track moving and deforming objects through time.
Optimal Algorithm for Shape from Shading and Path Planning
, 2001
"... An optimal algorithm for the reconstruction of a surface from its shading image is presented. The algorithm solves the 3D reconstruction from a single shading image problem. The shading image is treated as a penalty function and the height of the reconstructed surface is a weighted distance. A cons ..."
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Cited by 75 (2 self)
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An optimal algorithm for the reconstruction of a surface from its shading image is presented. The algorithm solves the 3D reconstruction from a single shading image problem. The shading image is treated as a penalty function and the height of the reconstructed surface is a weighted distance. A consistent numerical scheme based on Sethian’s fast marching method is used to compute the reconstructed surface. The surface is a viscosity solution of an Eikonal equation for the vertical light source case. For the oblique light source case, the reconstructed surface is the viscosity solution to a different partial differential equation. A modification of the fast marching method yields a numerically consistent, computationally optimal, and practically fast algorithm for the classical shape from shading problem. Next, the fast marching method coupled with a back tracking via gradient descent along the reconstructed surface is shown to solve the path planning problem in robot navigation.
New constraints on datacloseness and needle map consistency for shapefromshading
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1999
"... AbstractÐThis paper makes two contributions to the problem of needlemap recovery using shapefromshading. First, we provide a geometric update procedure which allows the image irradiance equation to be satisfied as a hard constraint. This not only improves the data closeness of the recovered needl ..."
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Cited by 62 (25 self)
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AbstractÐThis paper makes two contributions to the problem of needlemap recovery using shapefromshading. First, we provide a geometric update procedure which allows the image irradiance equation to be satisfied as a hard constraint. This not only improves the data closeness of the recovered needlemap, but also removes the necessity for extensive parameter tuning. Second, we exploit the improved ease of control of the new shapefromshading process to investigate various types of needlemap consistency constraint. The first set of constraints are based on needlemap smoothness. The second avenue of investigation is to use curvature information to impose topographic constraints. Third, we explore ways in which the needlemap is recovered so as to be consistent with the image gradient field. In each case we explore a variety of robust error measures and consistency weighting schemes that can be used to impose the desired constraints on the recovered needlemap. We provide an experimental assessment of the new shapefromshading framework on both real world images and synthetic images with known ground truth surface normals. The main conclusion drawn from our analysis is that the datacloseness constraint improves the efficiency of shapefromshading and that both the topographic and gradient consistency constraints improve the fidelity of the recovered needlemap. Index Terms±Shapefromshading, hard constraints, curvature consistency, gradient consistency, robust statistics. 1
Shape from shading: a wellposed problem
, 2004
"... Shape From Shading is known to be an illposed problem. We show in this paper that if we model the problem in a different way than it is usually done, more precisely by taking into account the 1/r2 attenuation term of the illumination, Shape From Shading becomes completely wellposed. Thus the shadin ..."
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Cited by 47 (4 self)
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Shape From Shading is known to be an illposed problem. We show in this paper that if we model the problem in a different way than it is usually done, more precisely by taking into account the 1/r2 attenuation term of the illumination, Shape From Shading becomes completely wellposed. Thus the shading allows to recover (almost) any surface from only one image (of this surface) without any additional data (in particular, without the knowledge of the heights of the solution at the local intensity “minima”, contrary to [6, 23, 8, 25, 12]) and without regularity assumptions (contrary to [17, 10], for example). More precisely, we formulate the problem as that of solving a new Partial Differential Equation (PDE), we develop a complete mathematical study of this equation and we design a new provably convergent numerical method. Finally, we present results of our new Shape From Shading method on various synthetic and real images. 1. Introduction and
Numerical Methods for Shapefromshading: A New Survey with Benchmarks
, 2007
"... Many algorithms have been suggested for the shapefromshading problem, and some years have passed since the publication of the survey paper by Zhang et al. [1]. In this new survey paper, we try to update their presentation including some recent methods which seem to be particularly representative o ..."
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Cited by 44 (4 self)
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Many algorithms have been suggested for the shapefromshading problem, and some years have passed since the publication of the survey paper by Zhang et al. [1]. In this new survey paper, we try to update their presentation including some recent methods which seem to be particularly representative of three classes of methods: methods based on partial differential equations, methods using optimization, and methods approximating the image irradiance equation. One of the goals of this paper is to set the comparison of these methods on a firm basis. To this end, we provide a brief description of each method, highlighting its basic assumptions and mathematical properties. Moreover, we propose some numerical benchmarks in order to compare the methods in terms of their efficiency and accuracy in the reconstruction of surfaces corresponding to synthetic, as well as to real images.
Prior knowledge, level set representations & visual grouping
 Int. J. Comput. Vision
, 2008
"... In this paper, we propose a level set method for shapedriven object extraction. We introduce a voxelwise probabilistic level set formulation to account for prior knowledge. To this end, objects are represented in an implicit form. Constraints on the segmentation process are imposed by seeking a pr ..."
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Cited by 39 (9 self)
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In this paper, we propose a level set method for shapedriven object extraction. We introduce a voxelwise probabilistic level set formulation to account for prior knowledge. To this end, objects are represented in an implicit form. Constraints on the segmentation process are imposed by seeking a projection to the image plane of the prior model modulo a similarity transformation. The optimization of a statistical metric between the evolving contour and the model leads to motion equations that evolve the contour toward the desired image properties while recovering the pose of the object in the new image. Upon convergence, a solution that is similarity invariant with respect to the model and the corresponding transformation are recovered. Promising experimental results demonstrate the potential of such an approach.
Minimal surfaces: a geometric three dimensional segmentation approach
, 1997
"... A novel geometric approach for three dimensional object segmentation is presented. The scheme is based on geometric deformable surfaces moving towards the objects to be detected. We show that this model is related to the computation of surfaces of minimal area (local minimal surfaces). The space w ..."
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Cited by 27 (6 self)
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A novel geometric approach for three dimensional object segmentation is presented. The scheme is based on geometric deformable surfaces moving towards the objects to be detected. We show that this model is related to the computation of surfaces of minimal area (local minimal surfaces). The space where these surfaces are computed is induced from the three dimensional image in which the objects are to be detected. The general approach also shows the relation between classical deformable surfaces obtained via energy minimization and geometric ones derived from curvature flows in the surface evolution framework. The scheme is stable, robust, and automatically handles changes in the surface topology during the deformation. Results related to existence, uniqueness, stability, and correctness of the solution to this geometric deformable model are presented as well. Based on an efficient numerical algorithm for surface evolution, we present a number of examples of object detection in real and synthetic images.
Terrain Analysis Using Radar ShapefromShading
 IEEE TRANS. ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2003
"... This paper develops a maximum a posteriori (MAP) probability estimation framework for shapefromshading (SFS) from synthetic aperture radar (SAR) images. The aim is to use this method to reconstruct surface topography from a single radar image of relatively complex terrain. Our MAP framework make ..."
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Cited by 24 (14 self)
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This paper develops a maximum a posteriori (MAP) probability estimation framework for shapefromshading (SFS) from synthetic aperture radar (SAR) images. The aim is to use this method to reconstruct surface topography from a single radar image of relatively complex terrain. Our MAP framework makes explicit how the recovery of local surface orientation depends on the whereabouts of terrain edge features and the available radar reflectance information. To apply the resulting process to real world radar data, we require probabilistic models for the appearance of terrain features and the relationship between the orientation of surface normals and the radar reflectance. We show that the SAR data can be modeled using a RayleighBessel distribution and use this distribution to develop a maximum likelihood algorithm for detecting and labeling terrain edge features. Moreover, we show how robust statistics can be used to estimate the characteristic parameters of this distribution. We also develop an empirical model for the SAR reflectance function. Using the reflectance model, we perform Lambertian correction so that a conventional SFS algorithm can be applied to the radar data. The initial surface normal direction is constrained to point in the direction of the nearest ridge or ravine feature. Each surface normal must fall within a conical envelope whose axis is in the direction of the radar illuminant. The extent of the envelope depends on the corrected radar reflectance and the variance of the radar signal statistics. We explore various ways of smoothing the field of surface normals using robust statistics. Finally, we show how to reconstruct the terrain surface from the smoothed field of surface normal vectors. The proposed algorithm is applied to various SAR da...