Image focus volume regularization for shape from focus through 3D weighted least squares

Abstract In shape from focus (SFF) methods, the accuracy of the depth map highly depends on the quality of image focus volume. Generally, a linear filtering or averaging using a 2D mask is applied on each slice of the focus volume to filter out the noisy focus measures. This approach may not provide optimal results due to the inherent problems associated with linear filtering. In this paper, the image focus volume is regularized by applying 3D weighted least squares (3D-WLS) approach that enhances the volume to better reconstruct the 3D shape. The weights for the regularization have been computed from the image sequence, and here image sequence acts like a structural prior and guidance volume. Such kind of guided filtering of focus volume has not been carried out earlier. 3D-WLS optimization problem has been solved in an efficient separable manner, such that the solution has been approximated by solving a sequence of 1D linear sub-problems. Sequentially for each dimension, a tridiagonal matrix is used to solve the three-point inhomogeneous Laplacian matrix. Experiments conducted on real and synthetic image sequences demonstrate the effectiveness of the proposed method.