Abstract
In this paper, nonlinear image operators for extracting functional feature of spatial grayness variation are proposed. First, we show that a degree of degeneration of an extended gradient covariance matrix between grayness f and its gradient fx, fy indicates a degree of fit of the variations to an exponential functional shape. Then, in order to express the degeneration independently on contrast and resolution, we derive several dimensionless and normalized equations from inequalities between second and third order eigenvalue polynomials of the matrix. After adding noise suppressing capability to the equation, we obtain four types of feature operator triplets Ri, Pi, Qi (i=1, 2, 3, 4) which discriminate 1) significant variations, 2) exponential variations, and 3) anti-exponential variations of varying degrees. By analysing maximal conditions of Qi under which grayness loses completely the above defined exponentiality, we show Qi functions as image structure finders which respond in selective but scale/orientation insensitive manners to homogeneous and inhomogeneous peaks/dips/saddles, and flat and inclined ridges/valleys. Those functions of the proposed operators are confirmed with several computer simulations under ideal and noisy conditions.
