Discontinuities of plane functions projected from a surface with methods for finding these

TL;DR

This paper presents a method to identify points of non-smoothness in plane functions derived from smooth surface mappings in three dimensions, with applications in numerical image processing techniques.

Contribution

It introduces a new approach to detect discontinuities in plane functions based on their surface origins, enhancing analysis in numerical and image processing tasks.

Findings

Method effectively locates discontinuities in projected plane functions.

Applicable to functions induced by smooth 3D surface mappings.

Potential improvements in numerical and image processing accuracy.

Abstract

A result is given to find points where a real valued function on the plane is not smooth. Provided this function is induced by a smooth mapping from three dimensions to the plane, from a function on surfaces in three dimensions. This has applications to numerical methods such as image processing.