Numerical Optimization Of Kernel Based Image Derivatives

Abstract

This short-paper gives results obtained with existing deriva- tive kernels such as the Sobel-operator and Scharr kernel, and introduces orientation optimized kernels. The optimized kernels are found using an minimizer on the absolute angular errors of an image containing circular patterns with varying spatial frequencies. Results show that a 3 3 truncated area sampled Gaussian is as rotation invariant as any other kernel, it is only a matter of choosing the right sigma. When using 5 5 sized derivative kernels, the Gaussian derivatives are outperformed in angle accuracy by angle error optimized kernels.