A fourier interpretation of the Frei-Chen edge masks

Abstract The orthogonal set of 3 × 3 Frei-Chen edge detection makes was proposed based on a vector space approach. The way the masks were chosen was not fully explained. We introduce an interpretation of the Frei-Chen masks in terms of eight-dimensional Fourier transform coefficient vectors. The linear transformation between the nine-dimensional Frei-Chen space and the eight-dimensional Fourier transform space is derived. We also propose a modified set of eight orthogonal masks based on the frequency space analysis.