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67
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 1422 (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.
Shape from Shading: A Survey
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1999
"... ... this paper, six wellknown SFS algorithms are implemented and compared. The performance of the algorithms was analyzed on synthetic images using mean and standard deviation of depth (Z) error, mean of surface gradient (p, q) error, and CPU timing. Each algorithm works well for certain images, ..."
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Cited by 306 (1 self)
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... this paper, six wellknown SFS algorithms are implemented and compared. The performance of the algorithms was analyzed on synthetic images using mean and standard deviation of depth (Z) error, mean of surface gradient (p, q) error, and CPU timing. Each algorithm works well for certain images, but performs poorly for others. In general, minimization approaches are more robust, while the other approaches are faster. The implementation of these algorithms in C and images used in this paper are available by anonymous ftp under the pub/tech_paper/survey directory at eustis.cs.ucf.edu (132.170.108.42). These are also part of the electronic version of paper.
A Simple Algorithm for Shape from Shading
, 1992
"... In this paper we describe a simple shape from shading algorithm which recovers depth from a brightness image, typically in fewer than ten iterations. This algorithm, which is a simplification of the algorithm of Oliensis and Dupuis, is based on a minimum downhill principle which guarantees continuou ..."
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Cited by 73 (3 self)
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In this paper we describe a simple shape from shading algorithm which recovers depth from a brightness image, typically in fewer than ten iterations. This algorithm, which is a simplification of the algorithm of Oliensis and Dupuis, is based on a minimum downhill principle which guarantees continuous surfaces and stable results. The algorithm is applicable to a broad variety of objects and reflectance maps. 1 Introduction Until the recent publications of Oliensis and Dupuis [[5],[6],[7]] most researchers in shape from shading were convinced that recovering depth from a brightness image necessarily required some regularization technique in order to guarantee a physically plausible surface [4]. It also seemed evident that only an iterative process with typically several thousand iterations would lead to a good approximation of the true surface. Linear methods [8] with an elegant solution in the Fourier domain form an exception to that rule, but they can only be applied to a limited numb...
On 3D Surface Reconstruction Using Shape from Shadows
, 1998
"... In this paper we discuss new results on the Shape From Darkness problem: using the motion of cast shadows to recover scene structure. Our approach is based on collecting a set of images from a fixed viewpoint as a known light source moves "across the sky". Previously published solutions to ..."
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Cited by 49 (0 self)
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In this paper we discuss new results on the Shape From Darkness problem: using the motion of cast shadows to recover scene structure. Our approach is based on collecting a set of images from a fixed viewpoint as a known light source moves "across the sky". Previously published solutions to this problem have performed the reconstruction only for cross sections of the scene. In this paper, we present a reconstruction algorithm and discuss the reconstruction of an entire 3D scene under various light source trajectories. We also consider the constraints on reconstruction. We conclude with experimental results that illustrate the convergence properties of the solution process and its robustness properties. I. Introduction In this paper, we consider surface reconstruction from shadow information. That is, to use the shape and geometric properties of observed shadows to infer the shape of the surfaces casting the shadows as well as those that the shadows are cast upon. This problem is somet...
Analysis of Shape from Shading Techniques
 PROC IEEE CVPR
, 1994
"... Since the first shapefromshading technique was developed by Horn in the early 1970s, different approaches have been continuously emerging in the past two decades. Some of them improve existing techniques, while others are completely new approaches. However, there is no literature on the comparison ..."
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Cited by 45 (0 self)
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Since the first shapefromshading technique was developed by Horn in the early 1970s, different approaches have been continuously emerging in the past two decades. Some of them improve existing techniques, while others are completely new approaches. However, there is no literature on the comparison and performance analysis of these techniques. This is exactly what is addressed in this paper.
Subpixel Distance Maps and Weighted Distance Transforms
 JOURNAL OF MATHEMATICAL IMAGING AND VISION
, 1994
"... A new framework for computing the Euclidean distance and weighted distance from the boundary of a given digitized shape is presented. The distance is calculated with subpixel accuracy. The algorithm is based on an equal distance contour evolution process. The moving contour is embedded as a level ..."
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Cited by 34 (8 self)
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A new framework for computing the Euclidean distance and weighted distance from the boundary of a given digitized shape is presented. The distance is calculated with subpixel accuracy. The algorithm is based on an equal distance contour evolution process. The moving contour is embedded as a level set in a time varying function of higher dimension. This representation of the evolving contour makes possible the use of an accurate and stable numerical scheme, due to Osher and Sethian [22]. The relation between the classical shape from shading problem and the weighted distance transform is presented, as well as an algorithm that calculates the geodesic distance transform on surfaces.
Symmetric ShapefromShading Using Selfratio Image
 INT’L J. COMPUTER VISION
, 2001
"... In this paper, we present a symmetric shapefromshading (SFS) approach to recover both shape and albedo for symmetric objects. Lambertian surfaces with unknown varying albedo and orthographic projections are assumed. In our formulation of symmetric SFS, wehave two image irradiance equations. One i ..."
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Cited by 32 (2 self)
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In this paper, we present a symmetric shapefromshading (SFS) approach to recover both shape and albedo for symmetric objects. Lambertian surfaces with unknown varying albedo and orthographic projections are assumed. In our formulation of symmetric SFS, wehave two image irradiance equations. One is the standard equation used in SFS, and the other is a selfratio image irradiance equation. This new image irradiance equation relates the selfratio image which is defined as the ratio of twohalves of the input image to light source and surface shape. The introduction of the selfratio image facilitates the direct use of symmetry cue. Based on the selfratio image, a new modelbased symmetric sourcefromshading algorithm is also presented. We then propose symmetric SFS algorithms to recover both shape and albedo from a single image and present experimental results. The new
Enforcing Integrability for Surface Reconstruction Algorithms Using Belief Propagation in Graphical Models
 In: Proc. Conf. Computer Vision and Pattern Recognition
, 2001
"... Accurate calculation of the three dimensional shape of an object is one of the classic research areas of computer vision. Many of the existing methods are based on surface normal estimation, and subsequent integration of surface gradients. In general, these methods do not produce valid surface due t ..."
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Cited by 31 (0 self)
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Accurate calculation of the three dimensional shape of an object is one of the classic research areas of computer vision. Many of the existing methods are based on surface normal estimation, and subsequent integration of surface gradients. In general, these methods do not produce valid surface due to violation of surface integrability. We introduce a new method for shape reconstruction by integration of valid surface gradient maps. The essence of the new approach is in the strict enforcement of the surface integrability via belief propagation across graphical model. The graphical model is selected in such a way to extract information from underlying, possibly noisy, surface gradient estimators, utilize the surface integrability constraint, and produce the maximum aposteriori estimate of a valid surface. We demonstrate the algorithm for two classic shape reconstruction techniques; shapefromshading and photometric stereo. On a set of real and synthetic examples the new approach is shown to be fast and accurate, in the sense that shape can be rendered even in the presence of high levels of noise and sharp occlusion boundaries. 1
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 28 (7 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.
A unifying and rigorous shape from shading method adapted to realistic data and applications
 In Journal of Mathematical Imaging and Vision
, 2006
"... Abstract. We propose a new method for the Lambertian Shape From Shading (SFS) problem based on the notion of CrandallLions viscosity solution. This method has the advantage of requiring the knowledge of the solution (the surface to be reconstructed) only on some part of the boundary and/or of the s ..."
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Cited by 24 (4 self)
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Abstract. We propose a new method for the Lambertian Shape From Shading (SFS) problem based on the notion of CrandallLions viscosity solution. This method has the advantage of requiring the knowledge of the solution (the surface to be reconstructed) only on some part of the boundary and/or of the singular set (the set of the points at maximal intensity). Moreover it unifies in an unique mathematical formulation the works of Rouy et al. [50, 34], Falcone et al. [21], Prados et al. [49, 46, 48], based on the notion of viscosity solutions and the work of Dupuis and Oliensis [17] dealing with classical solutions and value functions. Also, it allows to generalize their results to the “perspective SFS ” problem recently simultaneously introduced in [46, 55, 13]. While the theoretical part has been developed in [44], in this paper we give some stability results and we describe numerical schemes for the SFS based on this method. We construct provably convergent and robust algorithms. Finally, we apply our SFS method to real images and we suggest some reallife applications.