A heuristic approach for finding best focused shape

The most popular shape from focus (SFF) methods in the literature are based on the concept of focused image surface (FIS)-the surface formed by the best focus points. According to paraxial-geometric optics, there is one-to-one correspondence between the shape of an object and the shape of its FIS. Therefore, the problem of three-dimensional (3-D) shape recovery from image focus can be described as the problem of determining the shape of the FIS. The conventional SFF method is inaccurate because of piecewise constant approximation of the FIS. The SFF method based on the FIS has shown better results by exhaustive search of the FIS shape using planar surface approximation at the cost of considerably higher computations. In this paper, search of the FIS shape is presented as an optimization problem, i.e., maximization of the focus measure in the 3-D image volume. The proposed method searches the optimal focus measure in the whole image volume, instead of the small volume as adopted in previous methods. The dynamic programming, instead of the approximation techniques, is used to search the optimal FIS shape. A direct application of dynamic programming on a 3-D data is impractical, because of higher computational complexity. Therefore a fast heuristic model based on dynamic programming is proposed for the search of FIS shape. The shape recovery results of the new method are better than previous methods. The proposed algorithm is significantly faster than the FIS algorithm, but a little slower than the conventional algorithm.