相关论文: Frames, Graphs and Erasures
Document image dewarping remains a challenging task in the deep learning era. While existing methods have improved by leveraging text line awareness, they typically focus only on a single horizontal dimension. In this paper, we propose a…
Estimating high-dimensional precision matrices is a fundamental problem in modern statistics, with the graphical lasso and its $\ell_1$-penalty being a standard approach for recovering sparsity patterns. However, many statistical models,…
Several coded exposure techniques have been proposed for acquiring high frame rate videos at low bandwidth. Most recently, a Coded-2-Bucket camera has been proposed that can acquire two compressed measurements in a single exposure, unlike…
Representation learning on graphs has been gaining attention due to its wide applicability in predicting missing links, and classifying and recommending nodes. Most embedding methods aim to preserve certain properties of the original graph…
An important yet challenging problem in understanding indoor scene is recovering indoor frame structure from a monocular image. It is more difficult when occlusions and illumination vary, and object boundaries are weak. To overcome these…
Matrix congruence can be used to mimic linear maps between homogeneous quadratic polynomials in $n$ variables. We introduce a generalization, called standard-form congruence, which mimics affine maps between non-homogeneous quadratic…
The graph matching optimization problem is an essential component for many tasks in computer vision, such as bringing two deformable objects in correspondence. Naturally, a wide range of applicable algorithms have been proposed in the last…
In this paper we demonstrate that there are distinct differences between real and complex equiangular tight frames (ETFs) with regards to erasures. For example, we prove that there exist arbitrarily large non-trivial complex equiangular…
One may associate several frames to a given polytope, such as its collection of vertices, edges, or facet normal vectors. In this note, we use these frames to generate geometric inequalities for the simplex in $\mathbb{R}^d$ and polytopes…
A good classification method should yield more accurate results than simple heuristics. But there are classification problems, especially high-dimensional ones like the ones based on image/video data, for which simple heuristics can work…
Computing the excess as a method of measuring the redundancy of frames was recently introduced to address certain issues in frame theory. In this paper, the concept of excess for fusion frames is studied. Then, several explicit methods are…
Large electron microscopy image datasets for connectomics are typically composed of thousands to millions of partially overlapping two-dimensional images (tiles), which must be registered into a coherent volume prior to further analysis. A…
Many robotics and mapping systems contain multiple sensors to perceive the environment. Extrinsic parameter calibration, the identification of the position and rotation transform between the frames of the different sensors, is critical to…
Bi-linear feature learning models, like the gated autoencoder, were proposed as a way to model relationships between frames in a video. By minimizing reconstruction error of one frame, given the previous frame, these models learn "mapping…
It is well known that the spectrum and the Smith normal form of a matrix can be computed in polynomial time. Thus, it is interesting to explore how good are these parameters for distinguishing graphs. This is relevant since it is related to…
In the study of computer codes, filling space as uniformly as possible is important to describe the complexity of the investigated phenomenon. However, this property is not conserved by reducing the dimension. Some numeric experiment…
The problem of 2-coloring uniform hypergraphs has been extensively studied over the last few decades. An n-uniform hypergraph is not 2-colorable if its vertices can't be colored with two colors, Red and Blue, such that every hyperedge…
In modern communication systems such as the Internet, random losses of information can be mitigated by oversampling the source. This is equivalent to expanding the source using overcomplete systems of vectors (frames), as opposed to the…
The task of approximating points with circular arcs is performed in many applications, such as polyline compression, noise filtering, and feature recognition. However, the development of algorithms that perform a significant amount of…
MDS array codes are widely used in storage systems to protect data against erasures. We address the \emph{rebuilding ratio} problem, namely, in the case of erasures, what is the the fraction of the remaining information that needs to be…