Reinforcement of Linear Structure using Parametrized Relaxation Labeling

An approach for reinforcing underlying linear structure while suppressing unwanted noise, useful for analysis of medical images, has been presented. The method utilizes principles previously presented with regard to relaxation labeling processes, but differ in that the label set is now considered to be continuous and the distribution of label preference values for each object (pixel) parametrized by a single vector. Due to this parametrization, the total number of computations per pixel in the new method is now dependent only on the number of neighbors used in the computation, and not on the number of labels as well, as in previous methods. Thus, for a general reinforcement problem with m labels and n neighbors being considered for each pixel, the time complexity per object (pixel) per iteration goes as O (nm2) for the prototypical algorithm (e.g. (Zucker, et. al., 1977)) and is reduced by the approach presented here to O (n). The method uses a new approach for deciding local neighborhood influence and making a decision between reinforced linear structure with some magnitude and orientation and a no-structure condition based on the nonlinear (sigmoidal) thresholding of a linear vector sum. It should be noted that there is a similarity between this sigmoidal thresholding function and similar functions used in artificial neural networks (Hopfield, 1984). Ongoing work is being performed to further investigate such overlap. Also, it is planned to extend the approach in several ways. These include the ability to reinforce co-circularity, as well as to reinforce underlying planar structure by updating surface normals in true three-dimensional diagnostic imagery.