Supplementary material for the paper : Discriminative Correlation Filter with Channel and Spatial Reliability DCF-CSR

This is the supplementary material for the paper ”Discriminative Correlation Filter with Channel and Spatial Reliability” submitted to the CVPR 2017. Due to spatial constraints, parts not crucial for understanding the DCF-CSR tracker formulation, but helpful for gaining insights, were moved here. 1. Derivation of the augmented Lagrangian minimizer This section provides the complete derivation of the closed-form solutions for the relations (9,10) in the submitted paper [3]. The augmented Lagrangian from Equation (5) in [3] is L(ĥc,h, l̂) = ‖ĥc diag(f̂)− ĝ‖ + λ 2 ‖hm‖ + (1) [̂l(ĥc − ĥm) + l̂(ĥc − ĥm)] + μ‖ĥc − ĥm‖, with hm = (m h). For the purposes of derivation we will rewrite (1) into a fully vectorized form L(ĥc,h, l̂) = ‖ĥc diag(f̂)− ĝ‖ + λ 2 ‖hm‖+ (2) [̂ l(ĥc − √ DFMh) + l̂(ĥc − √ DFMh) ] + μ‖ĥc − √ DFMh‖, where F denotes D × D orthonormal matrix of Fourier coefficients, such that the Fourier transform is defined as x̂ = F(x) = √ DFx and M = diag(m). For clearer representation we denote the four terms in the summation (2) as L(ĥc,h, l̂) = L1 + L2 + L3 + L4, (3) where L1 = ( ĥc diag(f̂)− ĝ )( ĥc diag(f̂)− ĝ )T , (4)