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14
Capturing 3D stretchable surfaces from single images in closed form
 In CVPR
, 2009
"... We present a closedform solution to the problem of recovering the 3D shape of a nonrigid potentially stretchable surface from 3Dto2D correspondences. In other words, we can reconstruct a surface from a single image without a priori knowledge of its deformations in that image. Stateoftheart so ..."
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Cited by 8 (4 self)
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We present a closedform solution to the problem of recovering the 3D shape of a nonrigid potentially stretchable surface from 3Dto2D correspondences. In other words, we can reconstruct a surface from a single image without a priori knowledge of its deformations in that image. Stateoftheart solutions to nonrigid 3D shape recovery rely on the fact that distances between neighboring surface points must be preserved and are therefore limited to inelastic surfaces. Here, we show that replacing the inextensibility constraints by shading ones removes this limitation while still allowing 3D reconstruction in closedform. We demonstrate our method and compare it to an earlier one using both synthetic and real data. 1.
P.: Reconstructing sharply folding surfaces: A convex formulation
, 2009
"... In recent years, 3D deformable surface reconstruction from single images has attracted renewed interest. It has been shown that preventing the surface from either shrinking or stretching is an effective way to resolve the ambiguities inherent to this problem. However, while the geodesic distances on ..."
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Cited by 8 (0 self)
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In recent years, 3D deformable surface reconstruction from single images has attracted renewed interest. It has been shown that preventing the surface from either shrinking or stretching is an effective way to resolve the ambiguities inherent to this problem. However, while the geodesic distances on the surface may not change, the Euclidean ones decrease when folds appear. Therefore, when applied to discrete surface representations, such constantdistance constraints are only effective for smoothly deforming surfaces, and become inaccurate for more flexible ones that can exhibit sharp folds. In such cases, surface points must be allowed to come closer to each other. In this paper, we show that replacing the equality constraints of earlier approaches by inequality constraints that let the mesh representation of the surface shrink but not expand yields not only a more faithful representation, but also a convex formulation of the reconstruction problem. As a result, we can accurately reconstruct surfaces undergoing complex deformations that include sharp folds from individual images. 1.
Exploring Ambiguities for Monocular NonRigid Shape Estimation
"... Recovering the 3D shape of deformable surfaces from single images is difficult because many different shapes have very similar projections. This is commonly addressed by restricting the set of possible shapes to linear combinations of deformation modes and by imposing additional geometric constraint ..."
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Cited by 5 (4 self)
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Recovering the 3D shape of deformable surfaces from single images is difficult because many different shapes have very similar projections. This is commonly addressed by restricting the set of possible shapes to linear combinations of deformation modes and by imposing additional geometric constraints. Unfortunately, because image measurements are noisy, such constraints do not always guarantee that the correct shape will be recovered. To overcome this limitation, we introduce an efficient approach to exploring the set of solutions of an objective function based on pointcorrespondences and to proposing a small set of candidate 3D shapes. This allows the use of additional image information to choose the best one. As a proof of concept, we use either motion or shading cues to this end and show that we can handle a complex objective function without having to solve a difficult nonlinear minimization problem. Key words: 3D shape recovery, deformation model, nonrigid surfaces. 1
Simultaneous Correspondence and NonRigid3D Reconstructionofthe Coronary TreefromSingle XrayImages
"... We present a novel approach to simultaneously reconstruct the 3D structure of a nonrigid coronary tree and estimate point correspondences between an input Xray image and a reference 3D shape. At the core of our approach liesanoptimizationschemethatiterativelyfitsagenerative 3Dmodelofincreasingcomp ..."
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Cited by 2 (2 self)
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We present a novel approach to simultaneously reconstruct the 3D structure of a nonrigid coronary tree and estimate point correspondences between an input Xray image and a reference 3D shape. At the core of our approach liesanoptimizationschemethatiterativelyfitsagenerative 3Dmodelofincreasingcomplexityandguidesthematching process. As a result, and in contrast to existing approaches that assume rigidity or quasirigidity of the structure, our method is able to retrieve large nonlinear deformations even when the input data is corrupted by the presence of noise and partial occlusions. We extensively evaluate our approach under synthetic and real data and demonstrate a remarkable improvement compared tostateoftheart.
Laplacian Meshes for Monocular 3D Shape Recovery
"... Abstract. We show that by extending the Laplacian formalism, which was first introduced in the Graphics community to regularize 3D meshes, we can turn the monocular 3D shape reconstruction of a deformable surface given correspondences with a reference image into a wellposed problem. Furthermore, th ..."
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Abstract. We show that by extending the Laplacian formalism, which was first introduced in the Graphics community to regularize 3D meshes, we can turn the monocular 3D shape reconstruction of a deformable surface given correspondences with a reference image into a wellposed problem. Furthermore, this does not require any training data and eliminates the need to prealign the reference shape with the one to be reconstructed, as was done in earlier methods. 1
1 Monocular 3D Reconstruction of Locally Textured Surfaces
"... Abstract—Most recent approaches to monocular nonrigid 3D shape recovery rely on exploiting point correspondences and work best when the whole surface is welltextured. The alternative is to rely either on contours or shading information, which has only been demonstrated in very restrictive settings ..."
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Abstract—Most recent approaches to monocular nonrigid 3D shape recovery rely on exploiting point correspondences and work best when the whole surface is welltextured. The alternative is to rely either on contours or shading information, which has only been demonstrated in very restrictive settings. Here, we propose a novel approach to monocular deformable shape recovery that can operate under complex lighting and handle partially textured surfaces. At the heart of our algorithm are a learned mapping from intensity patterns to the shape of local surface patches and a principled approach to piecing together the resulting local shape estimates. We validate our approach quantitatively and qualitatively using both synthetic and real data.
SUBMITTED TO IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 1 Stochastic Exploration of Ambiguities for NonRigid Shape Recovery
"... Abstract—Recovering the 3D shape of deformable surfaces from single images is known to be a highly ambiguous problem because many different shapes may have very similar projections. This is commonly addressed by restricting the set of possible shapes to linear combinations of deformation modes and b ..."
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Abstract—Recovering the 3D shape of deformable surfaces from single images is known to be a highly ambiguous problem because many different shapes may have very similar projections. This is commonly addressed by restricting the set of possible shapes to linear combinations of deformation modes and by imposing additional geometric constraints. Unfortunately, because image measurements are noisy, such constraints do not always guarantee that the correct shape will be recovered. To overcome this limitation, we introduce a stochastic sampling approach to efficiently explore the set of solutions of an objective function based on point correspondences. This allows to propose a small set of ambiguous candidate 3D shapes and then use additional image information to choose the best one. As a proof of concept, we use either motion or shading cues to this end and show that we can handle a complex objective function without having to solve a difficult nonlinear minimization problem. The advantages of our method are demonstrated on a variety of problems including both real and synthetic data. Index Terms—Deformable surfaces, Monocular shape estimation. 1
Singleview Perspective ShapefromTexture with Focal Length Estimation: A Piecewise Affine Approach
"... We present a new formulation to the well known problem of shapefromtexture from a single image by casting the task as a multiplane based camera pose estimation problem. Our first contribution is methodological: we show that by using a piecewise affine model, instead of a perspective one, we can a ..."
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We present a new formulation to the well known problem of shapefromtexture from a single image by casting the task as a multiplane based camera pose estimation problem. Our first contribution is methodological: we show that by using a piecewise affine model, instead of a perspective one, we can avoid the numerical instabilities in the estimation of the surface pose compared with the fullperspective model, yet retaining high accuracy. Our second contribution is to show that the information provided by a smooth textured surface makes it possible to perform shapefromtexture and camera focal length calibration jointly. This advances stateoftheart where a calibrated camera is nearly always assumed in order to compute 3D shape from a single image. We validate both these contributions on simulated and real image data. 1.
Informàtica Industrial (CSICUPC)
"... Recent works have shown that 3D shape of nonrigid surfaces can be accurately retrieved from a single image given a set of 3Dto2D correspondences between that image and another one for which the shape is known. However, existing approaches assume that such correspondences can be readily establishe ..."
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Recent works have shown that 3D shape of nonrigid surfaces can be accurately retrieved from a single image given a set of 3Dto2D correspondences between that image and another one for which the shape is known. However, existing approaches assume that such correspondences can be readily established, which is not necessarily true when large deformations produce significant appearance changes between the input and the reference images. Furthermore, it is either assumed that the pose of the camera isknown, or the estimatedsolution isposeambiguous. Inthispaperwerelaxalltheseassumptionsand,givena setof3Dand2Dunmatchedpoints,wepresentanapproach tosimultaneouslysolvetheircorrespondences,computethe camera pose and retrieve the shape of the surface in the
Mathieu Salzmann
"... We present a closedform solution to the problem of recovering the 3D shape of a nonrigid potentially stretchable surface from 3Dto2D correspondences. In other words, we can reconstruct a surface from a single image without a priori knowledge of its deformations in that image. Stateoftheart so ..."
Abstract
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We present a closedform solution to the problem of recovering the 3D shape of a nonrigid potentially stretchable surface from 3Dto2D correspondences. In other words, we can reconstruct a surface from a single image without a priori knowledge of its deformations in that image. Stateoftheart solutions to nonrigid 3D shape recovery rely on the fact that distances between neighboring surface points must be preserved and are therefore limited to inelastic surfaces. Here, we show that replacing the inextensibility constraints by shading ones removes this limitation while still allowing 3D reconstruction in closedform. We demonstrate our method and compare it to an earlier one using both synthetic and real data. 1.