Edge Image Description Using Angular Radial Partitioning A.Chalechale, A. Mertins and G. Naghdy IEE Proc.-Vis. Image Signal Processing, 2004 Slides by David Anthony Torres Computer Science and Engineering — University of California at San Diego Angular Radial Partitioning • Partition edge map into Image: I(ρ,θ) angular and radial bin. • Partition into M (cid:215)N bins ! M radial parts ! N angular parts • Index a bin by (k,i) ρ=kR/M, k =1..M θ=2πi/N, i =1..N Angular Radial Partitioning • Sector feature f(k,i) = # edge pixels in (k,i) • A feature f(k,i) is shifted when we rotate by τ= π = 2 l / N for l 0,1, 2,... Angular Radial Partitioning • Denote image rotation by I (ρ,θ) = I(ρ,θ-τ) τ • Feature rotates as well f (k,i) = f(k,i-l) τ Take 1-D Fourier Transform • • Take 1-D Fourier Transform Take 1-D Fourier Transform Take 1-D Fourier Transform Rotational Invariance Transforms contain rotational invariance • ower-spectra are the same • Because their p • Choose {||F(k,u)||} for k=0..M-1 and u=0..N-1 as image features.