Statistical design of ternary phase-only filters for distortion invariance

<title>Distortion invariant binary and ternary phase-only filter for distortion invariance using factor analysis</title>

“…We have previously discussed the filter development, [2] so we only briefly review the discussion here. To construct the statistical filters, we considered a signal space where each spatial frequency of an image was represented as an axis.…”

“…Because the BPOF coefficients had the same magnitude, we simply summed the coefficients on a pixel-by-pixel basis across the training set and used this quantity as a measure of invariance for a particular spatial frequency. This quantity was represented by the function J [n,m] as N J[n,m] = H[n,m], (2) where :i [n,m] indicated that more consistent values were indicated by larger absolute values.…”

“…[2] Statistical approaches to distortion4nvariant filter design have been previously used. For exampie, Kumar et al modeled image differences of a training set as a stochastic process to design an optimal filter.…”