Related papers: Connections Between Frames with Rational Eigenstep…

Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper we develop systematically these notions, including their mutual…

We consider the problem of matching a template to a noisy signal. Motivated by some recent proposals in the signal processing literature, we suggest a rank-based method and study its asymptotic properties using some well-established…

Estimating fundamental matrices is a classic problem in computer vision. Traditional methods rely heavily on the correctness of estimated key-point correspondences, which can be noisy and unreliable. As a result, it is difficult for these…

Vision-based Simultaneous Localization And Mapping (VSLAM) is a mature problem in Robotics. Most VSLAM systems are feature based methods, which are robust and present high accuracy, but yield sparse maps with limited application for further…

This paper proposes the geometric relationship of epipolar geometry and orientation- and scale-covariant, e.g., SIFT, features. We derive a new linear constraint relating the unknown elements of the fundamental matrix and the orientation…

Feature matching between image pairs is a fundamental problem in computer vision that drives many applications, such as SLAM. Recently, semi-dense matching approaches have achieved substantial performance enhancements and established a…

Frame theory is a powerful tool in the domain of signal processing and communication. Among its numerous configurations, the ones which have drawn much attention recently are Equiangular Tight Frame (ETF) and Grassmannian Frame. These…

Density Functional Theory (DFT) is one of the most used ab initio theoretical frameworks in materials science. It derives the ground state properties of a multi-atomic ensemble directly from the computation of its one-particle density \nr…

Image captioning can automatically generate captions for the given images, and the key challenge is to learn a mapping function from visual features to natural language features. Existing approaches are mostly supervised ones, i.e., each…

Supervised Fine-Tuning (SFT) is the standard paradigm for domain adaptation, yet it frequently incurs the cost of catastrophic forgetting. In sharp contrast, on-policy Reinforcement Learning (RL) effectively preserves general capabilities.…

In recent years, there have been an increasing number of applications of tensor completion based on the tensor train (TT) format because of its efficiency and effectiveness in dealing with higher-order tensor data. However, existing tensor…

We propose a novel algorithm for the joint refinement of structure and motion parameters from image data directly without relying on fixed and known correspondences. In contrast to traditional bundle adjustment (BA) where the optimal…

Novel contour descriptors, called eigencontours, based on low-rank approximation are proposed in this paper. First, we construct a contour matrix containing all object boundaries in a training set. Second, we decompose the contour matrix…

We provide a new method for constructing equiangular tight frames (ETFs). The construction is valid in both the real and complex settings, and shows that many of the few previously-known examples of ETFs are but the first representatives of…

We explore some connections between association schemes and the analyses of the semidefinite programming (SDP) based convex relaxations of combinatorial optimization problems in the Lov\'{a}sz--Schrijver lift-and-project hierarchy. Our…

Equiangular tight frames (ETFs) may be used to construct examples of feasible points for semidefinite programs arising in sum-of-squares (SOS) optimization. We show how generalizing the calculations in a recent work of the authors' that…

Establishing dense correspondences across semantically similar images remains a challenging task due to the significant intra-class variations and background clutters. Traditionally, a supervised learning was used for training the models,…

An equiangular tight frame (ETF) is a set of unit vectors whose coherence achieves the Welch bound, and so is as incoherent as possible. Though they arise in many applications, only a few methods for constructing them are known. Motivated…

Due to their importance in both data analysis and numerical algorithms, low rank approximations have recently been widely studied. They enable the handling of very large matrices. Tight error bounds for the computationally efficient…

We introduce MultiMatch, a novel semi-supervised learning (SSL) algorithm combining the paradigms of co-training and consistency regularization with pseudo-labeling. At its core, MultiMatch features a pseudo-label weighting module designed…