Approximation of images by basis functions for multiple region segmentation with level sets

Active contours and level sets provide a solid formal framework for image segmentation. The problem, stated as the minimization of a functional containing terms of conformity to data and regularization, is solved by curve evolution implemented via level set partial differential equations (PDE). The purpose of this study is to investigate approximation by basis functions as a model for image representation in segmentation by level set PDE. This model is mathematically yielding, affords more generality than current piecewise constant and Gaussian models, and can be just as efficient as the most general piecewise smooth model. We state the problem using this model to measure conformity of segmentation to data. The resulting functional is minimized via level set evolution PDE. Experimental results are shown to demonstrate the formulation.