Algorithm for computing the Fourier descriptors of a binary outline

The Fourier descriptors {A_n, α_n}₁ ^∞ are proper for the analysis and synthesis of closed plane curves. Using tactile matrix sensors for the exploration of the 2D-shapes, binary imprints are often generated. An algorithm for computing the Fourier descriptors of the polygonal curve γ (Freeman outline) obtained by processing a binary imprint is proposed. First the coordinates of the curve starting point as well as the parameters δ₀, a*_p, Δl_p, Δφ_p are determined; then L and the Fourier descriptors are computed. The most important properties of {A_n, α_n}₁^∞ are presented and verified using the program that implements this algorithm. Knowing the Fourier descriptors of the shape binary outlines, much useful information for the description and tactile recognition of the shape have been obtained