Related papers: A Direct Prediction of the Shape Parameter -- a pu…
The search for the optimal shape parameter for Radial Basis Function (RBF) kernel approximation has been an outstanding research problem for decades. In this work, we establish a theoretical framework for this problem by leveraging a…
The task of establishing correspondences between two 3D shapes is a long-standing challenge in computer vision. While numerous studies address full-full and partial-full 3D shape matching, only a limited number of works have explored the…
We study a popular algorithm for fitting polynomial curves to scattered data based on the least squares with gradient weights. We show that sometimes this algorithm admits a substantial reduction of complexity, and, furthermore, find…
The finite Gamma mixture model is often used to describe randomness in income data, insurance data, and data from other applications. The popular likelihood approach, however, does not work for this model because the likelihood function is…
This work studies an inverse scattering problem when limited-aperture data are available that are from just one or a few incident fields. This inverse problem is highly ill-posed due to the limited receivers and a few incident fields…
Although 3D shape matching and interpolation are highly interrelated, they are often studied separately and applied sequentially to relate different 3D shapes, thus resulting in sub-optimal performance. In this work we present a unified…
We investigate the inverse scattering problem for tracking the location and orientation of a moving scatterer using a single incident field. We solve the problem by adopting the optimization approach with the objective function defined by…
In this paper a new distribution is proposed. This new model provides more flexibility to modeling data with upside-down bathtub hazard rate function. A significant account of mathematical properties of the new distribution is presented.…
This paper deals with projective shape analysis, which is a study of finite configurations of points modulo projective transformations. The topic has various applications in machine vision. We introduce a convenient projective shape space,…
Shape completion is the problem of completing partial input shapes such as partial scans. This problem finds important applications in computer vision and robotics due to issues such as occlusion or sparsity in real-world data. However,…
We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph…
We develop a statistical theory of waveform shaping of incident waves that aim to efficiently deliver energy at weakly lossy targets which are embedded inside chaotic enclosures. Our approach utilizes the universal features of chaotic…
We introduce an intrinsic estimator for the scalar curvature of a data set presented as a finite metric space. Our estimator depends only on the metric structure of the data and not on an embedding in $\mathbb{R}^n$. We show that the…
The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…
Scattering methods are widely used in many research areas to analyze and resolve material structures. Given the importance, a large number of full textbooks are devoted to this topic. However, technical details in experiments and…
Complex eigenfrequencies of the exterior of a scatterer are considered as signatures of the scatterer's shape. A parameter characterizing the ratio of the maximum transverse and longitudinal dimensions of a body is found.
We present a mathematical and algorithmic scheme for learning the principal geometric elements in an image or 3D object. We build on recent work that convexifies the basic problem of finding a combination of a small number shapes that…
A previous paper [J. Phys. B: At. Mol. Opt. Phys. 50, 215302 (2017)] showed that partial wave analysis becomes applicable to nonrelativistic Coulomb scattering if wavepackets are used. The scattering geometry considered was special: that of…
In this paper we describe a probabilistic method for estimating the position of an object along with its covariance matrix using neural networks. Our method is designed to be robust to outliers, have bounded gradients with respect to the…
Shape2SAS is a web application that allows researchers and students to build intuition and understanding of small-angle scattering. It is available at https://somo.chem.utk.edu/shape2sas. The user defines a model of arbitrary shape by…