Active Contour Directed by the Poisson Gradient Vector Field and Edge Tracking

This paper develops a new active contour (AC) model capable of multiple complex objects segmentation in the presence of heavy noise. The model segments images in the framework of two types of partial differential equations (PDEs): the Euler–Lagrange and Poisson PDEs. The former is used to build an evolution algorithm, while the Poisson solution gradient vector field (PGVF) directs the evolution toward the boundaries of all image objects. The AC halts on boundaries and PGVF separatrices, splits on the latter, and leaves at least one segment (called label) on every boundary. Each label tracks its boundary until the corresponding object is enveloped. The advantages of the new method are validated on a number of skin lesions, road, and aircraft images of varying sizes and in the presence of Gaussian noise. The obtained results are compared against results by contemporary and established active contours and neural networks.