RESUMEN

A new method for nonrigid registration of multimodal images is presented. Due to the large interdependence of segmentation and registration, the approach is based on simultaneous segmentation and edge alignment. The two processes are directly coupled and thus benefit from using complementary information of the entire underlying data set. The approach is formulated as a bivariate, variational, free discontinuity problem in the Mumford–Shah framework. A geometric variable describing the contour set and a functional variable which represents the underlying deformation are simultaneously identified. The contour set is represented by a level-set function. We derive a regularized gradient flow and describe an efficient numerical implementation using finite element discretization and multigrid techniques. Finally, we illustrate the method in several applications, such as multimodal intrapatient registration and reconstruction by registration to a reference object.

RESUMEN

Human vision works equally well in a large dynamic range of light intensities, from only a few photons to typical midday sunlight. Contributing to such remarkable flexibility is a famous law in perceptual (both visual and aural) psychology and psychophysics known as Weber's Law. The current paper develops a new segmentation model based on the integration of Weber's Law and the celebrated Mumford-Shah segmentation model (Comm. Pure Appl. Math., vol. 42, pp. 577-685, 1989). Explained in detail are issues concerning why the classical Mumford-Shah model lacks light adaptivity, and why its "weberized" version can more faithfully reflect human vision's superior segmentation capability in a variety of illuminance conditions from dawn to dusk. It is also argued that the popular Gaussian noise model is physically inappropriate for the weberization procedure. As a result, the intrinsic thermal noise of photon ensembles is introduced based on Bose and Einstein's distributions in quantum statistics, which turns out to be compatible with weberization both analytically and computationally. The current paper focuses on both the theory and computation of the weberized Mumford-Shah model with Bose-Einstein noise. In particular, Ambrosio-Tortorelli's Γ-convergence approximation theory is adapted (Boll. Un. Mat. Ital. B, vol. 6, pp. 105-123, 1992), and stable numerical algorithms are developed for the associated pair of nonlinear Euler-Lagrange PDEs.