Determination of Stationary Points and Their Bindings in Dataset using RBF Methods

TL;DR

This paper introduces an RBF-based algorithm to identify stationary points and their relationships in sampled datasets without prior knowledge of the underlying function, applicable in fields like computer vision and physics.

Contribution

It presents a novel RBF interpolation method to find stationary points and their bindings directly from sampled data, without needing the sampling function.

Findings

Successfully identifies stationary points in sampled datasets.

Detects geometric bindings such as lines and circles among stationary points.

Applicable to various fields like computer vision and chemical physics.

Abstract

Stationary points of multivariable function which represents some surface have an important role in many application such as computer vision, chemical physics, etc. Nevertheless, the dataset describing the surface for which a sampling function is not known is often given. Therefore, it is necessary to propose an approach for finding the stationary points without knowledge of the sampling function. In this paper, an algorithm for determining a set of stationary points of given sampled surface and detecting the bindings between these stationary points (such as stationary points lie on line segment, circle, etc.) is presented. Our approach is based on the piecewise RBF interpolation of the given dataset.