| Abstract: |
| Active contour models represent well-known computer vision techniques for image segmentation. They are divided into parametric and geodesic active contours (GAC). In this work we introduce a novel PDE-based segmentation approach inspired by the GAC models and level-set method.
The proposed segmentation scheme evolves level-set based active contours toward the boundaries of some certain objects in the analyzed image. A second-order nonlinear anisotropic diffusion model is introduced here for this task. Its curve evolution equation is based on a level-set function u, representing the evolving function, and image function v. It uses a properly chosen stopping function whose arguments are based on v, and a positive monotonically decreasing diffusivity conductance function receiving combinations of gradients and Laplacians of u as arguments.
A rigorous mathematical treatment is performed on this nonlinear parabolic PDE model, its validity being investigated. We demonstrate that it admits a unique weak solution under some certain assumptions. Then it is solved numerically applying a finite difference-based approximation algorithm developed by us. That algorithm provides successful results when applied to image objects. The discrete u is initialized as a square contour covering almost the entire image and evolves to objects` edges in few iterations (less than 100).
The proposed active contour-based segmentation solution can be applied successfully to important computer vision tasks, like object detection and tracking. |
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