Digital step edges from zero crossing of second directional derivatives

Area of Science:

• Computer Vision
• Image Processing
• Computational Mathematics

Background:

• Edge detection is crucial for image analysis.
• Existing methods like Prewitt and Marr-Hildreth have limitations.
• The facet model offers a novel approach to surface estimation for edge detection.

Purpose of the Study:

• To introduce and evaluate a novel step edge detection method using the facet model.
• To compare the performance of the facet model operator against established edge detection techniques.
• To define a precise criterion for identifying step edges based on directional derivatives.

Main Methods:

• Utilizing the facet model for estimating the underlying gray tone intensity surface from noisy pixel data.
• Defining step edges based on the zero crossing of the second directional derivative in the gradient direction.
• Employing a functional form based on tensor products of discrete orthogonal polynomials up to degree three for surface estimation.

Main Results:

• The facet model-based zero crossing of the second directional derivative operator demonstrated superior performance in step edge detection.
• The Prewitt gradient operator showed moderate performance, ranking second.
• The Marr-Hildreth zero crossing of the Laplacian operator performed the worst among the tested methods.

Conclusions:

• The facet model provides a robust and accurate method for step edge detection.
• The proposed operator surpasses traditional methods in identifying step edges.
• Accurate estimation of the underlying intensity surface is key to effective edge detection.