Matting and Depth Recovery of Thin Structures using a Focal Stack

Abstract

Thin structures such as fence, grass and vessels are common in photography and scientific imaging. They exhibit complex 3D structures with sharp depth variations/discontinuities and mutual occlusions. In this paper, we develop a method to estimate the occlusion matte and depths of thin structures from a focal image stack, which is obtained either by varying the focus/aperture of the lens or computed from a one-shot light field image. We propose an image formation model that explicitly describes the spatially varying optical blur and mutual occlusions for structures located at different depths. Based on the model, we derive an efficient MCMC inference algorithm that enables direct and analytical computations of the iterative update for the model/images without re-rendering images in the sampling process. Then, the depths of the thin structures are recovered using gradient descent with the differential terms computed using the image formation model. We apply the proposed method to scenes at both macro and micro scales. For macro-scale, we evaluate our method on scenes with complex 3D thin structures such as tree branches and grass. For micro-scale, we apply our method to in-vivo microscopic images of micro-vessels with diameters less than 50 μm. To our knowledge, the proposed method is the first approach to reconstruct the 3D structures of micro-vessels from non-invasive in-vivo image measurements.