Energies with high-order non-submodular interactions have been shown to be very useful in vision due to their high modeling power. Optimization of such energies, however, is generally NP-hard. A naive approach that works for small problem instances is exhaustive search, that is, enumeration of all possible labelings of the underlying graph. We propose a general minimization approach for large graphs based on enumeration of labelings of certain small patches. This partial enumeration technique reduces complex high-order energy formulations to pairwise Constraint Satisfaction Problems with unary costs (uCSP), which can be efficiently solved using standard methods like TRW-S. Our approach outperforms a number of existing state-of-the-art algorithms on well known difficult problems (e.g. curvature regularization, stereo, deconvolution); it gives near global minimum and better speed. Our main application of interest is curvature regularization. In the context of segmentation, our partial enumeration technique allows to evaluate curvature directly on small patches using a novel integral geometry approach.
Our patch-based curvature models could be seen as extensions of functional lifting @cite_1 or label elevation @cite_37 . Analogously to the line processes in @cite_28 , these second-order regularization methods use variables describing both location and orientation of the boundary. Thus, their curvature is the first-order (pair-wise) energy. Our patch variables include enough information about the local boundary to reduce the curvature to unary terms.
@cite_28 @cite_37 @cite_1
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We present a method for fast, approximate registration of whole-slide images (WSIs) of histopathology serial sections. Popular histopathology slide registration methods in the existing literature tend towards intensity-based approaches. 1, 2 Further input, in the form of an approximate initial transformation to be applied to one of the two WSIs, is then usually required, and this transformation needs to be optimised. Such a transformation is not readily available in this context and thus there is a need for fast approximation of these parameters. Fast registration is achieved by comparison of the external boundaries of adjacent tissue sections, using local curvature on multiple scales to assess similarity. Our representation of curvature is a modified version of the Curvature Scale Space (CSS) 3 image. We substitute zero crossings with signed local absolute maxima of curvature to improve the registration's robustness to the subtle morphological differences of adjacent sections. A pairwise matching is made between curvature maxima at scales increasing exponentially, the matching minimizes the distance between maxima pairs at each scale. The boundary points corresponding to the matched maxima pairs are used to estimate the desired transformation. Our method is highly robust to translation, rotation, and linear scaling, and shows good performance in cases of moderate non-linear scaling. On our set of test images the algorithm shows improved reliability and processing speed in comparison to existing CSS based registration methods. This paper addresses the problem of exactly inferring the maximum a posteriori solutions of discrete multi-label MRFs or CRFs with higher order cliques. We present a framework to transform special classes of multi-label higher order functions to submodular second order Boolean functions (referred to as Fs 2), which can be minimized exactly using graph cuts and we characterize those classes. The basic idea is to use two or more Boolean variables to encode the states of a single multi-label variable. There are many ways in which this can be done and much interesting research lies in finding ways which are optimal or minimal in some sense. We study the space of possible encodings and find the ones that can transform the most general class of functions to Fs 2. Our main contributions are two-fold. First, we extend the subclass of submodular energy functions that can be minimized exactly using graph cuts. Second, we show how higher order potentials can be used to improve single view 3D reconstruction results. We believe that our work on exact minimization of higher order energy functions will lead to similar improvements in solutions of other labelling problems. In this paper, we introduce a feature-preserving denoising algorithm. It is built on the premise that the underlying surface of a noisy mesh is piecewise smooth, and a sharp feature lies on the intersection of multiple smooth surface regions. A vertex close to a sharp feature is likely to have a neighborhood that includes distinct smooth segments. By defining the consistent subneighborhood as the segment whose geometry and normal orientation most consistent with those of the vertex, we can completely remove the influence from neighbors lying on other segments during denoising. Our method identifies piecewise smooth subneighborhoods using a robust density-based clustering algorithm based on shared nearest neighbors. In our method, we obtain an initial estimate of vertex normals and curvature tensors by robustly fitting a local quadric model. An anisotropic filter based on optimal estimation theory is further applied to smooth the normal field and the curvature tensor field. This is followed by second-order bilateral filtering, which better preserves curvature details and alleviates volume shrinkage during denoising. The support of these filters is defined by the consistent subneighborhood of a vertex. We have applied this algorithm to both generic and CAD models, and sharp features, such as edges and corners, are very well preserved. We present a new shape-from-distortion framework for recovering specular (reflective refractive) surfaces. While most existing approaches rely on accurate correspondences between 2D pixels and 3D points, we focus on analyzing the curved images of 3D lines which we call curved line images or CLIs. Our approach models CLIs of local reflections or refractions using the recently proposed general linear cameras (GLCs). We first characterize all possible CLIs in a GLC. We show that a 3D line will appear as a conic in any GLC. For a fixed GLC, the conic type is invariant to the position and orientation of the line and is determined by the GLC parameters. Furthermore, CLIs under single reflection refraction can only be lines or hyperbolas. Based on our new theory, we develop efficient algorithms to use multiple CLIs to recover the GLC camera parameters. We then apply the curvature-GLC theory to derive the Gaussian and mean curvatures from the GLC intrinsics. This leads to a complete distortion-based reconstruction framework. Unlike conventional correspondence-based approaches that are sensitive to image distortions, our approach benefits from the CLI distortions. Finally, we demonstrate applying our framework for recovering curvature fields on both synthetic and real specular surfaces.