Related papers: Divergence-Free Shape Interpolation and Correspond…
Diffeomorphic deformable image registration is one of the crucial tasks in medical image analysis, which aims to find a unique transformation while preserving the topology and invertibility of the transformation. Deep convolutional neural…
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…
In this paper we consider the fundamental operations dilation and erosion of mathematical morphology. Many powerful image filtering operations are based on their combinations. We establish homomorphism between max-plus semi-ring of integers…
The paper aims at proposing an efficient and stable quasi-interpolation based method for numerically computing the Helmholtz-Hodge decomposition of a vector field. To this end, we first explicitly construct a matrix kernel in a general form…
Deep implicit functions (DIFs), as a kind of 3D shape representation, are becoming more and more popular in the 3D vision community due to their compactness and strong representation power. However, unlike polygon mesh-based templates, it…
Although it is important both in theory as well as in applications, a theory of Birkhoff interpolation with main emphasis on the shape of the set of nodes is still missing. Although we will consider various shapes (e.g. we find all the…
We present a deep learning framework for accurate visual correspondences and demonstrate its effectiveness for both geometric and semantic matching, spanning across rigid motions to intra-class shape or appearance variations. In contrast to…
Despite being vastly ignored in the literature, coping with topological noise is an issue of increasing importance, especially as a consequence of the increasing number and diversity of 3D polygonal models that are captured by devices of…
Volume conservation and shape preservation are two well-known issues related to the advection and remeshing in front tracking. To address these issues, this paper proposes a divergence-preserving velocity interpolation method and a…
We present the first utterly self-supervised network for dense correspondence mapping between non-isometric shapes. The task of alignment in non-Euclidean domains is one of the most fundamental and crucial problems in computer vision. As 3D…
Video frame interpolation task has recently become more and more prevalent in the computer vision field. At present, a number of researches based on deep learning have achieved great success. Most of them are either based on optical flow…
Deformable shape modeling approaches that describe objects in terms of their medial axis geometry (e.g., m-reps [Pizer et al., 2003]) yield rich geometrical features that can be useful for analyzing the shape of sheet-like biological…
Finding correspondences in wide baseline setups is a challenging problem. Existing approaches have focused largely on developing better feature descriptors for correspondence and on accurate recovery of epipolar line constraints. This paper…
We present a new approach to unsupervised shape correspondence learning between pairs of point clouds. We make the first attempt to adapt the classical locally linear embedding algorithm (LLE) -- originally designed for nonlinear…
We introduce Lipschitz continuous and $C^{1,1}$ geometric approximation and interpolation methods for sampled bounded uniformly continuous functions over compact sets and over complements of bounded open sets in $\mathbb{R}^n$ by using…
Decomposition of shapes into (approximate) convex parts is essential for applications such as part-based shape representation, shape matching, and collision detection. In this paper, we propose a novel convex decomposition using a…
Deep Implicit Functions (DIFs) have gained popularity in 3D computer vision due to their compactness and continuous representation capabilities. However, addressing dense correspondences and semantic relationships across DIF-encoded shapes…
We consider defining the embedding of a triangle mesh into $R^3$, up to translation, rotation, and scale, by its vector of dihedral angles. Theoretically, we show that locally, almost everywhere, the map from realizable vectors of dihedrals…
Many algorithms for the computation of correspondences between deformable shapes rely on some variant of nearest neighbor matching in a descriptor space. Such are, for example, various point-wise correspondence recovery algorithms used as a…
This paper is concerned with applications of the theory of approximation and interpolation based on compensated convex transforms developed in [K. Zhang, E. Crooks, A. Orlando, Compensated convexity methods for approximations and…