Related papers: Variational Shape Approximation of Point Set Surfa…

For many applications, we need to use techniques to represent convex shapes and objects. In this work, we use level set method to represent shapes and find a necessary and sufficient condition on the level set function to guarantee the…

This work extends our previous study from S. Shrestha et al. (2024) by introducing a new abstract framework for Variational Multiscale (VMS) methods at the discrete level. We introduce the concept of what we define as the optimal projector…

We discuss adaptive mesh point selection for the solution of scalar IVPs. We consider a method that is optimal in the sense of the speed of convergence, and aim at minimizing the local errors. Although the speed of convergence cannot be…

Existing 3D surface representation approaches are unable to accurately classify pixels and their orientation lying on the boundary of an object. Thus resulting in coarse representations which usually require post-processing steps to extract…

The automation of user interface development has the potential to accelerate software delivery by mitigating intensive manual implementation. Despite the advancements in Large Multimodal Models for design-to-code translation, existing…

Amodal segmentation aims to recover complete object shapes, including occluded regions with no visual appearance, whereas conventional segmentation focuses solely on visible areas. Existing methods typically rely on strong prompts, such as…

Although Vision Transformers (ViTs) have recently advanced computer vision tasks significantly, an important real-world problem was overlooked: adapting to variable input resolutions. Typically, images are resized to a fixed resolution,…

Position representation is crucial for building position-aware representations in Transformers. Existing position representations suffer from a lack of generalization to test data with unseen lengths or high computational cost. We…

Vessels are complex structures in the body that have been studied extensively in multiple representations. While voxelization is the most common of them, meshes and parametric models are critical in various applications due to their…

This paper deals with a modified iterative projection method for approximating a solution of the hierarchical fixed point problem for a sequene of nearly nonexpansive mappings with respect to a nonexpansive mapping. It is shown that under…

Let $P$ be a polygonal curve in $\mathbb{R}^D$ of length $n$, and $S$ be a point set of size $k$. The Curve/Point Set Matching problem consists of finding a polygonal curve $Q$ on $S$ such that its Fr\'echet distance from $P$ is less than a…

We consider the method of alternating projections for finding a point in the intersection of two closed sets, possibly nonconvex. Assuming only the standard transversality condition (or a weaker version thereof), we prove local linear…

We show that the theory of varifolds can be suitably enriched to open the way to applications in the field of discrete and computational geometry. Using appropriate regularizations of the mass and of the first variation of a varifold we…

We consider the variational inequality problem over the intersection of fixed point sets of firmly nonexpansive operators. In order to solve the problem, we present an algorithm and subsequently show the strong convergence of the generated…

Since their introduction in the shape analysis community, functional maps have met with considerable success due to their ability to compactly represent dense correspondences between deformable shapes, with applications ranging from shape…

Attention within windows has been widely explored in vision transformers to balance the performance, computation complexity, and memory footprint. However, current models adopt a hand-crafted fixed-size window design, which restricts their…

We present a new method for performing Boolean operations on volumes represented as triangle meshes. In contrast to existing methods which treat meshes as 3D polyhedra and try to partition the faces at their exact intersection curves, we…

There has recently been great interest in neural rendering methods. Some approaches use 3D geometry reconstructed with Multi-View Stereo (MVS) but cannot recover from the errors of this process, while others directly learn a volumetric…

We propose a novel approach for probabilistic generative modeling of 3D shapes. Unlike most existing models that learn to deterministically translate a latent vector to a shape, our model, Point-Voxel Diffusion (PVD), is a unified,…

We present a robust method to find region-level correspondences between shapes, which are invariant to changes in geometry and applicable across multiple shape representations. We generate simplified shape graphs by jointly decomposing the…