Partial Functional Correspondence
TLDR
In this paper, a method for computing partial functional correspondence between non-rigid shapes is proposed, which uses perturbation analysis to show how removal of shape parts changes the Laplace-Beltrami eigenfunctions, and exploit it as a prior on the spectral representation of the correspondence.Abstract:
In this paper, we propose a method for computing partial functional correspondence between non-rigid shapes. We use perturbation analysis to show how removal of shape parts changes the Laplace-Beltrami eigenfunctions, and exploit it as a prior on the spectral representation of the correspondence. Corresponding parts are optimization variables in our problem and are used to weight the functional correspondence; we are looking for the largest and most regular in the Mumford-Shah sense parts that minimize correspondence distortion. We show that our approach can cope with very challenging correspondence settings.read more
Citations
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Journal ArticleDOI
Image Matching from Handcrafted to Deep Features: A Survey
TL;DR: This survey introduces feature detection, description, and matching techniques from handcrafted methods to trainable ones and provides an analysis of the development of these methods in theory and practice, and briefly introduces several typical image matching-based applications.
Proceedings ArticleDOI
Deformable Shape Completion with Graph Convolutional Autoencoders
TL;DR: In this article, a variational autoencoder with graph convolutional operations is used to learn a latent space for complete realistic shapes, which is then optimized to find the representation in this latent space that best fits the generated shape to the known partial input.
Proceedings ArticleDOI
Deep Functional Maps: Structured Prediction for Dense Shape Correspondence
TL;DR: In this paper, a deep residual network is proposed to learn dense correspondence between deformable 3D shapes by taking dense descriptor fields defined on two shapes as input, and outputs a soft map between the two given objects.
Proceedings ArticleDOI
Unsupervised Learning of Dense Shape Correspondence
TL;DR: This work introduces the first completely unsupervised correspondence learning approach for deformable 3D shapes, understanding that natural deformations approximately preserve the metric structure of the surface, yielding a natural criterion to drive the learning process toward distortion-minimizing predictions.
Journal ArticleDOI
Recent Trends, Applications, and Perspectives in 3D Shape Similarity Assessment
TL;DR: 3D shape analysis frameworks able to quantify the deformation of a shape into another in terms of the variation of real functions yields a new interpretation of the 3D shape similarity assessment, and the most promising directions for future research developments are discussed.
References
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Optimal approximations by piecewise smooth functions and associated variational problems
David Mumford,Jayant Shah +1 more
TL;DR: In this article, the authors introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision, and study their application in computer vision.
Proceedings ArticleDOI
Surface simplification using quadric error metrics
Michael Garland,Paul S. Heckbert +1 more
TL;DR: This work has developed a surface simplification algorithm which can rapidly produce high quality approximations of polygonal models, and which also supports non-manifold surface models.
Journal ArticleDOI
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
Luminita A. Vese,Tony F. Chan +1 more
TL;DR: A new multiphase level set framework for image segmentation using the Mumford and Shah model, for piecewise constant and piecewise smooth optimal approximations, and validated by numerical results for signal and image denoising and segmentation.
Book ChapterDOI
Discrete Differential-Geometry Operators for Triangulated 2-Manifolds
TL;DR: A unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures on arbitrary triangle meshes, using averaging Voronoi cells and the mixed Finite-Element/Finite-Volume method is proposed.
Book ChapterDOI
Unique signatures of histograms for local surface description
TL;DR: A novel comprehensive proposal for surface representation is formulated, which encompasses a new unique and repeatable local reference frame as well as a new 3D descriptor.