Figure 1:

Illustration of Filter-Rectify Filter (FRF) model of second-order texture processing applied to compound density-defined and feature-defined boundaries. The original image (leftmost image) is first analyzed by Gabor filters defined at the spatial scale of the micro-patterns. The output of these first-stage filters is then half-wave rectified (here by the relu() function) to yield two images which represent the locations of each kind of micro-pattern (center-left images). These images are then analyzed on a global scale by a set of second-stage filters which look for differences in the density of each kind of micro-pattern on opposite sides of the boundary (center-right images). The full-wave rectified (here by the abs() function) outputs of these second-stage filters are then added to attain an output image (rightmost image).

(a) FRF model applied to a compound density boundary comprised of two density boundaries (vertical and horizontal Gabors) super-imposed with the same phase of density modulation (0-degree phase shift). Note that there are peaks in the second-stage filter responses at the edges (where the image transitions from zero to non-zero contrast) as well as at the boundary (where the texture density changes).

(b) FRF model applied to a compound feature boundary comprised of two density boundaries (vertical and horizontal Gabors) super-imposed with opposite phases of density modulation (180-degree phase shift). As in (a) there are peaks in the second-stage filter responses at the edges, as well as at the boundary where the texture pattern changes (feature boundary).