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Optimal edge detector design I: parameter selection and noise effects.

W H Lunscher¹, M P Beddoes

¹Develcon Electronics Limited, Saskatoon, Canada.

IEEE Transactions on Pattern Analysis and Machine Intelligence

|August 27, 2011

Summary

This study optimizes the Laplacian of Gaussian (LoG) edge detection filter by developing a parameter selection method based on edge spacing and blur. This ensures optimal edge localization and filter performance, even with Gaussian noise.

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Area of Science:

Computer Vision
Image Processing
Signal Processing

Background:

The Laplacian of Gaussian (LoG) filter is optimal for edge detection via zero crossings.
Its main advantage is adjustable response via Gaussian standard deviation, but parameter selection is unclear.

Purpose of the Study:

To establish a clear method for selecting the LoG filter's Gaussian standard deviation parameter.
To optimize edge detection filter performance and address noise sensitivity.

Main Methods:

Reviewed arguments by Marr & Hildreth, and Dickey & Shanmugam on LoG filter optimality.
Applied the LoG filter to ideal periodic edge models blurred by Gaussian point-spread functions.
Developed a parameter design procedure based on observed responses to edge spacing and blur.

Main Results:

A procedure for selecting the LoG filter's Gaussian standard deviation parameter was derived.
The method links filter response to edge spacing and blur standard deviation.
Addressed optimal filter performance in the presence of additive Gaussian noise.

Conclusions:

The developed procedure provides a method for optimal LoG filter parameter selection.
This enhances edge detection accuracy and robustness.
Further work addresses coefficient word size in a companion paper.