648 research outputs found
Anisotropic Laplace-Beltrami Operators for Shape Analysis
International audienceThis paper introduces an anisotropic Laplace-Beltrami operator for shape analysis. While keeping useful properties of the standard Laplace-Beltrami operator, it introduces variability in the directions of principal curvature, giving rise to a more intuitive and semantically meaningful diffusion process. Although the benefits of anisotropic diffusion have already been noted in the area of mesh processing (e.g. surface regularization), focusing on the Laplacian itself, rather than on the diffusion process it induces, opens the possibility to effectively replace the omnipresent Laplace-Beltrami operator in many shape analysis methods. After providing a mathematical formulation and analysis of this new operator, we derive a practical implementation on discrete meshes. Further, we demonstrate the effectiveness of our new operator when employed in conjunction with different methods for shape segmentation and matching
Geometric and Photometric Data Fusion in Non-Rigid Shape Analysis
In this paper, we explore the use of the diffusion geometry framework for the fusion of geometric and photometric information in local and global shape descriptors. Our construction is based on the definition of a diffusion process on the shape manifold embedded into a high-dimensional space where the embedding coordinates represent the photometric information. Experimental results show that such data fusion is useful in coping with different challenges of shape analysis where pure geometric and pure photometric methods fai
On Nonrigid Shape Similarity and Correspondence
An important operation in geometry processing is finding the correspondences
between pairs of shapes. The Gromov-Hausdorff distance, a measure of
dissimilarity between metric spaces, has been found to be highly useful for
nonrigid shape comparison. Here, we explore the applicability of related shape
similarity measures to the problem of shape correspondence, adopting spectral
type distances. We propose to evaluate the spectral kernel distance, the
spectral embedding distance and the novel spectral quasi-conformal distance,
comparing the manifolds from different viewpoints. By matching the shapes in
the spectral domain, important attributes of surface structure are being
aligned. For the purpose of testing our ideas, we introduce a fully automatic
framework for finding intrinsic correspondence between two shapes. The proposed
method achieves state-of-the-art results on the Princeton isometric shape
matching protocol applied, as usual, to the TOSCA and SCAPE benchmarks
Registration of 3D Point Clouds and Meshes: A Survey From Rigid to Non-Rigid
Three-dimensional surface registration transforms multiple three-dimensional data sets into the same coordinate system so as to align overlapping components of these sets. Recent surveys have covered different aspects of either rigid or nonrigid registration, but seldom discuss them as a whole. Our study serves two purposes: 1) To give a comprehensive survey of both types of registration, focusing on three-dimensional point clouds and meshes and 2) to provide a better understanding of registration from the perspective of data fitting. Registration is closely related to data fitting in which it comprises three core interwoven components: model selection, correspondences and constraints, and optimization. Study of these components 1) provides a basis for comparison of the novelties of different techniques, 2) reveals the similarity of rigid and nonrigid registration in terms of problem representations, and 3) shows how overfitting arises in nonrigid registration and the reasons for increasing interest in intrinsic techniques. We further summarize some practical issues of registration which include initializations and evaluations, and discuss some of our own observations, insights and foreseeable research trends
Functional correspondence by matrix completion
In this paper, we consider the problem of finding dense intrinsic
correspondence between manifolds using the recently introduced functional
framework. We pose the functional correspondence problem as matrix completion
with manifold geometric structure and inducing functional localization with the
norm. We discuss efficient numerical procedures for the solution of our
problem. Our method compares favorably to the accuracy of state-of-the-art
correspondence algorithms on non-rigid shape matching benchmarks, and is
especially advantageous in settings when only scarce data is available
An interactive analysis of harmonic and diffusion equations on discrete 3D shapes
AbstractRecent results in geometry processing have shown that shape segmentation, comparison, and analysis can be successfully addressed through the spectral properties of the Laplace–Beltrami operator, which is involved in the harmonic equation, the Laplacian eigenproblem, the heat diffusion equation, and the definition of spectral distances, such as the bi-harmonic, commute time, and diffusion distances. In this paper, we study the discretization and the main properties of the solutions to these equations on 3D surfaces and their applications to shape analysis. Among the main factors that influence their computation, as well as the corresponding distances, we focus our attention on the choice of different Laplacian matrices, initial boundary conditions, and input shapes. These degrees of freedom motivate our choice to address this study through the executable paper, which allows the user to perform a large set of experiments and select his/her own parameters. Finally, we represent these distances in a unified way and provide a simple procedure to generate new distances on 3D shapes
WxBS: Wide Baseline Stereo Generalizations
We have presented a new problem -- the wide multiple baseline stereo (WxBS)
-- which considers matching of images that simultaneously differ in more than
one image acquisition factor such as viewpoint, illumination, sensor type or
where object appearance changes significantly, e.g. over time. A new dataset
with the ground truth for evaluation of matching algorithms has been introduced
and will be made public.
We have extensively tested a large set of popular and recent detectors and
descriptors and show than the combination of RootSIFT and HalfRootSIFT as
descriptors with MSER and Hessian-Affine detectors works best for many
different nuisance factors. We show that simple adaptive thresholding improves
Hessian-Affine, DoG, MSER (and possibly other) detectors and allows to use them
on infrared and low contrast images.
A novel matching algorithm for addressing the WxBS problem has been
introduced. We have shown experimentally that the WxBS-M matcher dominantes the
state-of-the-art methods both on both the new and existing datasets.Comment: Descriptor and detector evaluation expande
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