Despite of having no explicit shape model, multi-atlas approaches to image segmentation have proved to be a top-performer for several diverse datasets and imaging modalities. In this paper, we show how one can directly incorporate shape regularization into the multi-atlas framework. Unlike traditional methods, our proposed approach does not rely on label fusion on the voxel level. Instead, each registered atlas is viewed as an estimate of the position of a shape model. We evaluate and compare our method on two public benchmarks: (i) the VISCERAL Grand Challenge on multi-organ segmentation of whole-body CT images and (ii) the Hammers brain atlas of MR images for segmenting the hippocampus and the amygdala. For this wide spectrum of both easy and hard segmentation tasks, our experimental quantitative results are on par or better than state-of-the-art. More importantly, we obtain qualitatively better segmentation boundaries, for instance, preserving fine structures.

This paper describes a new method of finding thin, elongated structures in images and volumes. We use shortest paths to minimize very general functionals of higher-order curve properties, such as curvature and torsion. Our method uses line graphs to find the optimal path on a given discretization, often in the order of seconds on a single computer. The curves are then refined using local optimization making it possible to recover very smooth curves. We are able to place constraints on our curves such as maximum integrated curvature, or a maximum curvature at any point of the curve. To our knowledge, we are the first to perform experiments in three dimensions with curvature and torsion regularization. The largest graphs we process have over a hundred billion arcs. Experiments on medical images and in multi-view reconstruction show the significance and practical usefulness of higher order regularization.

Stereo matching is an inherently difficult problem due to ambiguous and noisy texture. The non-convexity and non-differentiability makes local linear (or quadratic) approximations poor, thereby preventing the use of standard local descent methods. Therefore recent methods are predominantly based on discretization and/or random sampling of some class of approximating surfaces (e.g. planes). While these methods are very efficient in generating a rough surface estimate, via either fusion of proposals or label propagation, the end result is usually not as smooth as desired. In this paper we show that, if the objective function is decomposed correctly, local refinement of candidate solutions can be performed using an ADMM approach. This allows searching over more general function classes, thereby resulting in visually more appealing smooth surface estimations.

It is commonly believed that higher order smoothness should be modeled using higher order interactions. For example, 2nd order derivatives for deformable (active) contours are represented by triple cliques. Similarly, the 2nd order regularization methods in stereo predominantly use MRF models with scalar (1D) disparity labels and triple clique interactions. In this paper we advocate a largely overlooked alternative approach to stereo where 2nd order surface smoothness is represented by pairwise interactions with 3D-labels, e.g. tangent planes. This general paradigm has been criticized due to perceived computational complexity of optimization in higher-dimensional label space. Contrary to popular beliefs, we demonstrate that representing 2nd order surface smoothness with 3D labels leads to simpler optimization problems with (nearly) sub modular pairwise interactions. Our theoretical and experimental results demonstrate advantages over state-of-the-art methods for 2nd order smoothness stereo.

Energies with high-order non-sub modular 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 pair wise 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.

This paper describes a method of finding thin, elongated structures in images and volumes. We use shortest paths to minimize very general functionals of higher-order curve properties, such as curvature and torsion. Our globally optimal method uses line graphs and its runtime is polynomial in the size of the discretization, often in the order of seconds on a single computer. To our knowledge, we are the first to perform experiments in three dimensions with curvature and torsion regularization. The largest graphs we process have almost one hundred billion arcs. Experiments on medical images and in multi-view reconstruction show the significance and practical usefulness of regularization based on curvature while torsion is still only tractable for small-scale problems.

We introduce a multi-region model for simultaneous segmentation of medical images. In contrast to many other models, geometric constraints such as inclusion and exclusion between the regions are enforced, which makes it possible to correctly segment different regions even if the intensity distributions are identical. We efficiently optimize the model using a combination of graph cuts and Lagrangian duality which is faster and more memory efficient than current state of the art. As the method is based on global optimization techniques, the resulting segmentations are independent of initialization. We apply our framework to the segmentation of the left and right ventricles, myocardium and the left ventricular papillary muscles in magnetic resonance imaging and to lung segmentation in full-body X-ray computed tomography. We evaluate our approach on a publicly available benchmark with competitive results.