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77
ShapeGoogle: geometric words and expressions for invariant shape retrieval
, 2010
"... The computer vision and pattern recognition communities have recently witnessed a surge of feature-based methods in object recognition and image retrieval applications. These methods allow representing images as collections of “visual words ” and treat them using text search approaches following the ..."
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Cited by 85 (13 self)
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The computer vision and pattern recognition communities have recently witnessed a surge of feature-based methods in object recognition and image retrieval applications. These methods allow representing images as collections of “visual words ” and treat them using text search approaches following the “bag of features ” paradigm. In this paper, we explore analogous approaches in the 3D world applied to the problem of non-rigid shape retrieval in large databases. Using multiscale diffusion heat kernels as “geometric words”, we construct compact and informative shape descriptors by means of the “bag of features ” approach. We also show that considering pairs of “geometric words ” (“geometric expressions”) allows creating spatially-sensitive bags of features with better discriminativity. Finally, adopting metric learning approaches, we show that shapes can be efficiently represented as binary codes. Our approach achieves state-of-the-art results on the SHREC 2010 large-scale shape retrieval benchmark.
Scale-invariant heat kernel signatures for non-rigid shape recognition
- In Proc. CVPR
, 2010
"... One of the biggest challenges in non-rigid shape retrieval and comparison is the design of a shape descriptor that would maintain invariance under a wide class of transformations the shape can undergo. Recently, heat kernel signature was introduced as an intrinsic local shape descriptor based on dif ..."
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Cited by 78 (18 self)
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One of the biggest challenges in non-rigid shape retrieval and comparison is the design of a shape descriptor that would maintain invariance under a wide class of transformations the shape can undergo. Recently, heat kernel signature was introduced as an intrinsic local shape descriptor based on diffusion scale-space analysis. In this paper, we develop a scale-invariant version of the heat kernel descriptor. Our construction is based on a logarithmically sampled scale-space in which shape scaling corresponds, up to a multiplicative constant, to a translation. This translation is undone using the magnitude of the Fourier transform. The proposed scale-invariant local descriptors can be used in the bag-of-features framework for shape retrieval in the presence of transformations such as isometric deformations, missing data, topological noise, and global and local scaling. We get significant performance improvement over state-of-the-art algorithms on recently established non-rigid shape retrieval benchmarks. 1.
Shape Google: a computer vision approach to invariant shape retrieval
- Proc. NORDIA
, 2009
"... Feature-based methods have recently gained popularity in computer vision and pattern recognition communities, in applications such as object recognition and image retrieval. In this paper, we explore analogous approaches in the 3D world applied to the problem of non-rigid shape search and retrieval ..."
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Cited by 58 (22 self)
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Feature-based methods have recently gained popularity in computer vision and pattern recognition communities, in applications such as object recognition and image retrieval. In this paper, we explore analogous approaches in the 3D world applied to the problem of non-rigid shape search and retrieval in large databases. 1.
The Wave Kernel Signature: A Quantum Mechanical Approach to Shape Analyis
, 2011
"... We introduce the Wave Kernel Signature (WKS) ..."
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Full and Partial Symmetries of Non-Rigid Shapes
- INTERNATIONAL JOURNAL OF COMPUTER VISION
"... Symmetry and self-similarity is the cornerstone of Nature, exhibiting itself through the shapes of natural creations and ubiquitous laws of physics. Since many natural objects are symmetric, the absence of symmetry can often be an indication of some anomaly or abnormal behavior. Therefore, detection ..."
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Cited by 42 (11 self)
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Symmetry and self-similarity is the cornerstone of Nature, exhibiting itself through the shapes of natural creations and ubiquitous laws of physics. Since many natural objects are symmetric, the absence of symmetry can often be an indication of some anomaly or abnormal behavior. Therefore, detection of asymmetries is important in numerous practical applications, including crystallography, medical imaging, and face recognition, to mention a few. Conversely, the assumption of underlying shape symmetry can facilitate solutions to many problems in shape reconstruction and analysis. Traditionally, symmetries are described as extrinsic geometric properties of the shape. While being adequate for rigid shapes, such a description is inappropriate for non-rigid ones: extrinsic symmetry can be broken as a result of shape deformations, while its intrinsic symmetry is preserved. In this paper, we present a generalization of symmetries for non-rigid shapes and a numerical framework for their analysis, addressing the problems of full and partial exact and approximate symmetry detection and classification.
Spectral Gromov-Wasserstein Distances for Shape Matching
"... We introduce a spectral notion of distance between shapes and study its theoretical properties. We show that our distance satisfies the properties of a metric on the class of isometric shapes, which means, in particular, that two shapes are at 0 distance if and only if they are isometric. Our constr ..."
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Cited by 27 (1 self)
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We introduce a spectral notion of distance between shapes and study its theoretical properties. We show that our distance satisfies the properties of a metric on the class of isometric shapes, which means, in particular, that two shapes are at 0 distance if and only if they are isometric. Our construction is similar to the recently proposed Gromov-Wasserstein distance, but rather than viewing shapes merely as metric spaces, we define our distance via the comparison of heat kernels. This allows us to relate our distance to previously proposed spectral invariants used for shape comparison, such as the spectrum of the Laplace-Beltrami operator. In addition, the heat kernel provides a natural notion of scale, which is useful for multi-scale shape comparison. We also prove a hierarchy of lower bounds for our distance, which provide increasing discriminative power at the cost of increase in computational complexity. 1.
Discrete minimum distortion correspondence problems for non-rigid shape matching
- Proc. Scale Space and Variational Methods
, 2011
"... Abstract. Similarity and correspondence are two fundamental archetype problems in shape analysis, encountered in numerous application in com-puter vision and pattern recognition. Many methods for shape similar-ity and correspondence boil down to the minimum-distortion correspon-dence problem, in whi ..."
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Cited by 20 (7 self)
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Abstract. Similarity and correspondence are two fundamental archetype problems in shape analysis, encountered in numerous application in com-puter vision and pattern recognition. Many methods for shape similar-ity and correspondence boil down to the minimum-distortion correspon-dence problem, in which two shapes are endowed with certain structure, and one attempts to find the matching with smallest structure distortion between them. Defining structures invariant to some class of shape trans-formations results in an invariant minimum-distortion correspondence or similarity. In this paper, we model shapes using local and global struc-tures, formulate the invariant correspondence problem as binary graph labeling, and show how different choice of structure results in invariance under various classes of deformations. 1
Shape Matching Based on Diffusion Embedding and on Mutual Isometric Consistency
"... We address the problem of matching two 3D shapes by representing them using the eigenvalues and eigenvectors of the discrete diffusion operator. This provides a representation framework useful for both scale-space shape descriptors and shape comparisons. We formally introduce a canonical diffusion e ..."
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Cited by 17 (3 self)
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We address the problem of matching two 3D shapes by representing them using the eigenvalues and eigenvectors of the discrete diffusion operator. This provides a representation framework useful for both scale-space shape descriptors and shape comparisons. We formally introduce a canonical diffusion embedding based on the combinatorial Laplacian; we reveal some interesting properties and we propose a unit hypersphere normalization of this embedding. We also propose a practical algorithm that seeks the largest set of mutually consistent point-to-point matches between two shapes based on isometric consistency between the two embeddings. We illustrate our method with several examples of matching shapes at various scales. 1.
Sparse modeling of intrinsic correspondences
- Computer Graphics Forum
"... We present a novel sparse modeling approach to non-rigid shape match-ing using only the ability to detect repeatable regions. As the input to our algorithm, we are given only two sets of regions in two shapes; no descriptors are provided so the correspondence between the regions is not know, nor we ..."
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Cited by 13 (1 self)
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We present a novel sparse modeling approach to non-rigid shape match-ing using only the ability to detect repeatable regions. As the input to our algorithm, we are given only two sets of regions in two shapes; no descriptors are provided so the correspondence between the regions is not know, nor we know how many regions correspond in the two shapes. We show that even with such scarce information, it is possible to estab-lish very accurate correspondence between the shapes by using methods from the field of sparse modeling, being this, the first non-trivial use of sparse models in shape correspondence. We formulate the problem of per-muted sparse coding, in which we solve simultaneously for an unknown permutation ordering the regions on two shapes and for an unknown cor-respondence in functional representation. We also propose a robust vari-ant capable of handling incomplete matches. Numerically, the problem is solved efficiently by alternating the solution of a linear assignment and a sparse coding problem. The proposed methods are evaluated qualitatively and quantitatively on standard benchmarks containing both synthetic and scanned objects. 1
Coupled quasi-harmonic bases
- In ACM SIGGRAPH
, 2004
"... The use of Laplacian eigenbases has been shown to be fruitful in many computer graphics applications. Today, state-of-the-art approaches to shape analysis, synthesis, and correspondence rely on these natural harmonic bases that allow using classical tools from harmonic analysis on manifolds. However ..."
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Cited by 13 (5 self)
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The use of Laplacian eigenbases has been shown to be fruitful in many computer graphics applications. Today, state-of-the-art approaches to shape analysis, synthesis, and correspondence rely on these natural harmonic bases that allow using classical tools from harmonic analysis on manifolds. However, many applications involving multiple shapes are obstacled by the fact that Laplacian eigenbases computed independently on different shapes are often incompatible with each other. In this paper, we propose the construction of common approximate eigenbases for multiple shapes using approximate joint diagonalization algorithms. We illustrate the benefits of the proposed approach on tasks from shape editing, pose transfer, correspondence, and similarity. 1
