Numerical Analysis of Image Patterns
Alan Conrad Bovik, Nanda Gopal, T. Emmoth · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1989
We find similarities between spatial pattern analysis and other low-level cooperative visual processes. Numerical algorithms for computing intrinsic scene attributes, e.g. shape-from-X (shading, texture, etc.) and optical flow typically involve estimating generalized orientation components via iterative constraint propagation. Smoothing or regularizing terms imposed on the constraint equations often enhance the uniqueness / stability (well-posedness) of the solutions. The numerical approach to visual pattern analysis developed here proceeds analogously via estimation of emergent 2-D image frequencies. Unlike shape-from-X or optical flow paradigms, constraints are derived from the responses of multiple oriented spatial frequency channels rather than directly from the image irradiance measurements. By using channel filters that are sufficiently concentrated in both space and frequency, highly accurate spatial frequency estimates are computed on a local basis. Two methods are proposed. In the first, constrained estimates of the emergent image frequencies are obtained by resolving the responses of multiple channel filters in a process similar to photometric stereo. The second approach formulates the estimation of frequencies as an extremum problem regularized by a smoothing term. An iterative constraint propagation algorithm is developed analogous to those used in variational / relaxational approaches to shape-from-X (shading, texture) and optical flow. Examples illustrate each approach using synthetic and natural images.