Related papers: Compression for Smooth Shape Analysis
The discrete Laplace operator is ubiquitous in spectral shape analysis, since its eigenfunctions are provably optimal in representing smooth functions defined on the surface of the shape. Indeed, subspaces defined by its eigenfunctions have…
Current point cloud processing algorithms do not have the capability to automatically extract semantic information from the observed scenes, except in very specialized cases. Furthermore, existing mesh analysis paradigms cannot be directly…
The present paper suggests a new approach for geometric representation of 3D spatial models and provides a new compression algorithm for 3D meshes, which is based on mathematical theory of convex geometry. In our approach we represent a 3D…
We propose a method to simultaneously compute scalar basis functions with an associated functional map for a given pair of triangle meshes. Unlike previous techniques that put emphasis on smoothness with respect to the Laplace--Beltrami…
Surface parameterizations and registrations are important in computer graphics and imaging, where 1-1 correspondences between meshes are computed. In practice, surface maps are usually represented and stored as 3D coordinates each vertex is…
Implicit neural representations (INRs) have been successfully used to compress a variety of 3D surface representations such as Signed Distance Functions (SDFs), voxel grids, and also other forms of structured data such as images, videos,…
Many computational algorithms applied to geometry operate on discrete representations of shape. It is sometimes necessary to first simplify, or coarsen, representations found in modern datasets for practicable or expedited processing. The…
One challenge that remains open in 3D deep learning is how to efficiently represent 3D data to feed deep networks. Recent works have relied on volumetric or point cloud representations, but such approaches suffer from a number of issues…
This paper presents a new progressive compression method for triangular meshes. This method, in fact, is based on a schema of irregular multi-resolution analysis and is centered on the optimization of the rate-distortion trade-off. The…
Some forms of novel visual media enable the viewer to explore a 3D scene from arbitrary viewpoints, by interpolating between a discrete set of original views. Compared to 2D imagery, these types of applications require much larger amounts…
The eigenfunctions of the Laplace Beltrami operator (Manifold Harmonics) define a function basis that can be used in spectral analysis on manifolds. In [21] the authors recast the problem as an orthogonality constrained optimization problem…
Meshes are commonly used as 3D maps since they encode the topology of the scene while being lightweight. Unfortunately, 3D meshes are mathematically difficult to handle directly because of their combinatorial and discrete nature. Therefore,…
In the industrial practice, additive manufacturing processes are often followed by post-processing operations such as subtractive machining, milling, etc. to achieve the desired surface quality and dimensional accuracy. Hence, a given part…
We propose a novel 3D shape correspondence method based on the iterative alignment of so-called smooth shells. Smooth shells define a series of coarse-to-fine shape approximations designed to work well with multiscale algorithms. The main…
Implicit Neural Representations (INRs) have been demonstrated to achieve state-of-the-art compression of a broad range of modalities such as images, videos, 3D surfaces, and audio. Most studies have focused on building neural counterparts…
Dynamic MRI may capture temporal anatomical changes in soft tissue organs with high contrast but the obtained sequences usually suffer from limited volume coverage which makes the high resolution reconstruction of organ shape trajectories a…
Surfaces are typically represented as meshes, which can be extracted from volumetric fields via meshing or optimized directly as surface parameterizations. Volumetric representations occupy 3D space and have a large effective receptive…
Efficient transmission of 3D point cloud data is critical for advanced perception in centralized and decentralized multi-agent robotic systems, especially nowadays with the growing reliance on edge and cloud-based processing. However, the…
Surface reconstruction with preservation of geometric features is a challenging computer vision task. Despite significant progress in implicit shape reconstruction, state-of-the-art mesh extraction methods often produce aliased,…
Particle-based shape modeling (PSM) is a popular approach to automatically quantify shape variability in populations of anatomies. The PSM family of methods employs optimization to automatically populate a dense set of corresponding…