Efficient graph cut optimization for shape from focus

Abstract

Shape From Focus refers to the inverse problem of recovering the depth in every point of a scene from a set of differently focused 2D images. Recently, some authors stated it in the variational framework and solved it by minimizing a non-convex functional. However, the global optimality on the solution is not guaranteed and evaluations are often application-specific. To overcome these limits, we propose to globally and efficiently minimize a convex functional by decomposing it into a sequence of binary problems using graph cuts. To illustrate the genericity of such a decomposition-based approach, data-driven strategies are considered, allowing us to optimize (in terms of reconstruction error) the choice of the depth values for a given number of possible depths. We provide qualitative and quantitative evaluation on Middlebury datasets and we show that, according to classic statistics on error values, the proposed approach exhibits high performance and robustness against corrupted data. proaches (where X denotes the cue to infer the shape, e.g. stereo, motion, 5 shading, focus, defocus, etc) or a mixture of them. This topic gave rise to a huge amount of papers and still represents a great interest for researchers in the computer vision community. Indeed, it has numerous applications, especially in robotics, both for localization and environment analysis, in monitoring or video-surveillance either for security or for medical technical assistance, or in 10 microscopy and chemistry [1]. More specifically, let us remind that stereovision relies on the disparities between matched pixels of an image pair [2], shape-from-shading exploits the variations of brightness of a single image [3, 4] and shape-from-motion deduces depth from matched points of interest [5]. Shape-from-focus (SFF) [6] and 15shape-from-defocus (SFD) [7] represent alternatives approaches that share the idea of using the focus to estimate the 3D structure of a scene from differently focused images acquired by a monocular camera. Thus, an object appears focused only in a limited range (depth of field) and is progressively blurred as the camera moves away from this range. For both approaches, active and passive 20 sensors exist, depending on whether or not a structured light composed of patterns is projected onto the scene to alleviate ambiguities. In this paper, we will focus on the passive device. In addition to the depth map, both approaches generally also provide an estimation of the all-in-focus image of the scene, i.e. the image obtained by selecting for each pixel, the intensity at which it appears 25 the most focused, or sharp. Now, SFF and SFD differ on one main point. SFD estimates the depth by measuring the relative blurriness between a reference image and the remaining ones. The blurring process needs to be explicitly modeled, a very few images are usually required and the approach can be applied to dynamic scenes. Similarly, 30 [8,9] have chosen to solve the inverse problem by precisely modeling the defocusing process with the help of an all-...

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