Geometric Shape Features Extraction Using a Steady State Partial Differential Equation System

TL;DR

This paper introduces a unified PDE-based approach for extracting geometric features like thickness, orientation, and skeleton from binary images, avoiding derivatives and topological constraints, validated through analytical and numerical examples.

Contribution

The paper presents a novel PDE system that simultaneously extracts multiple shape features without derivatives or topological restrictions.

Findings

Successfully extracts shape features from binary images.

Validates method with analytical and numerical examples.

Demonstrates advantages over traditional methods.

Abstract

A unified method for extracting geometric shape features from binary image data using a steady state partial differential equation (PDE) system as a boundary value problem is presented in this paper. The PDE and functions are formulated to extract the thickness, orientation, and skeleton simultaneously. The main advantages of the proposed method is that the orientation is defined without derivatives and thickness computation is not imposed a topological constraint on the target shape. A one-dimensional analytical solution is provided to validate the proposed method. In addition, two-dimensional numerical examples are presented to confirm the usefulness of the proposed method.