Generalized sequential tree-reweighted message passing

This paper addresses the problem of approximate MAP-MRF inference in general graphical models. Following [36], we consider a family of linear programming relaxations of the problem where each relaxation is specified by a set of nested pairs of factors for which the marginalization constraint needs to be enforced. We develop a generalization of the TRW-S algorithm [9] for this problem, where we use a decomposition into junction chains, monotonic w.r.t. some ordering on the nodes. This generalizes the monotonic chains in [9] in a natural way. We also show how to deal with nested factors in an efficient way. Experiments show an improvement over min-sum diffusion, MPLP and subgradient ascent algorithms on a number of computer vision and natural language processing problems

Combinatorial Solutions for Shape Optimization in Computer Vision

This thesis aims at solving so-called shape optimization problems, i.e. problems where the shape of some real-world entity is sought, by applying combinatorial algorithms. I present several advances in this field, all of them based on energy minimization. The addressed problems will become more intricate in the course of the thesis, starting from problems that are solved globally, then turning to problems where so far no global solutions are known. The first two chapters treat segmentation problems where the considered grouping criterion is directly derived from the image data. That is, the respective data terms do not involve any parameters to estimate. These problems will be solved globally. The first of these chapters treats the problem of unsupervised image segmentation where apart from the image there is no other user input. Here I will focus on a contour-based method and show how to integrate curvature regularity into a ratio-based optimization framework. The arising optimization problem is reduced to optimizing over the cycles in a product graph. This problem can be solved globally in polynomial, effectively linear time. As a consequence, the method does not depend on initialization and translational invariance is achieved. This is joint work with Daniel Cremers and Simon Masnou. I will then proceed to the integration of shape knowledge into the framework, while keeping translational invariance. This problem is again reduced to cycle-finding in a product graph. Being based on the alignment of shape points, the method actually uses a more sophisticated shape measure than most local approaches and still provides global optima. It readily extends to tracking problems and allows to solve some of them in real-time. I will present an extension to highly deformable shape models which can be included in the global optimization framework. This method simultaneously allows to decompose a shape into a set of deformable parts, based only on the input images. This is joint work with Daniel Cremers. In the second part segmentation is combined with so-called correspondence problems, i.e. the underlying grouping criterion is now based on correspondences that have to be inferred simultaneously. That is, in addition to inferring the shapes of objects, one now also tries to put into correspondence the points in several images. The arising problems become more intricate and are no longer optimized globally. This part is divided into two chapters. The first chapter treats the topic of real-time motion segmentation where objects are identified based on the observations that the respective points in the video will move coherently. Rather than pre-estimating motion, a single energy functional is minimized via alternating optimization. The main novelty lies in the real-time capability, which is achieved by exploiting a fast combinatorial segmentation algorithm. The results are furthermore improved by employing a probabilistic data term. This is joint work with Daniel Cremers. The final chapter presents a method for high resolution motion layer decomposition and was developed in combination with Daniel Cremers and Thomas Pock. Layer decomposition methods support the notion of a scene model, which allows to model occlusion and enforce temporal consistency. The contributions are twofold: from a practical point of view the proposed method allows to recover fine-detailed layer images by minimizing a single energy. This is achieved by integrating a super-resolution method into the layer decomposition framework. From a theoretical viewpoint the proposed method introduces layer-based regularity terms as well as a graph cut-based scheme to solve for the layer domains. The latter is combined with powerful continuous convex optimization techniques into an alternating minimization scheme. Lastly I want to mention that a significant part of this thesis is devoted to the recent trend of exploiting parallel architectures, in particular graphics cards: many combinatorial algorithms are easily parallelized. In Chapter 3 we will see a case where the standard algorithm is hard to parallelize, but easy for the respective problem instances

A linear framework for region-based image segmentation and inpainting involving curvature penalization

We present the first method to handle curvature regularity in region-based image segmentation and inpainting that is independent of initialization. To this end we start from a new formulation of length-based optimization schemes, based on surface continuation constraints, and discuss the connections to existing schemes. The formulation is based on a \emph{cell complex} and considers basic regions and boundary elements. The corresponding optimization problem is cast as an integer linear program. We then show how the method can be extended to include curvature regularity, again cast as an integer linear program. Here, we are considering pairs of boundary elements to reflect curvature. Moreover, a constraint set is derived to ensure that the boundary variables indeed reflect the boundary of the regions described by the region variables. We show that by solving the linear programming relaxation one gets quite close to the global optimum, and that curvature regularity is indeed much better suited in the presence of long and thin objects compared to standard length regularity

The coevolution of play and the cortico-cerebellar system in primates.

Primates are some of the most playful animals in the natural world, yet the reason for this remains unclear. One hypothesis posits that primates are so playful because playful activity functions to help develop the sophisticated cognitive and behavioural abilities that they are also renowned for. If this hypothesis were true, then play might be expected to have coevolved with the neural substrates underlying these abilities in primates. Here, we tested this prediction by conducting phylogenetic comparative analyses to determine whether play has coevolved with the cortico-cerebellar system, a neural system known to be involved in complex cognition and the production of complex behaviour. We used phylogenetic generalised least squares analyses to compare the relative volume of the largest constituent parts of the primate cortico-cerebellar system (prefrontal cortex, non-prefrontal heteromodal cortical association areas, and posterior cerebellar hemispheres) to the mean percentage of time budget spent in play by a sample of primate species. Using a second categorical data set on play, we also used phylogenetic analysis of covariance to test for significant differences in the volume of the components of the cortico-cerebellar system among primate species exhibiting one of three different levels of adult-adult social play. Our results suggest that, in general, a positive association exists between the amount of play exhibited and the relative size of the main components of the cortico-cerebellar system in our sample of primate species. Although the explanatory power of this study is limited by the correlational nature of its analyses and by the quantity and quality of the data currently available, this finding nevertheless lends support to the hypothesis that play functions to aid the development of cognitive and behavioural abilities in primates

Validation of plaster endocast morphology through 3D CT image analysis

A crucial component of research on brain evolution has been the comparison of fossil endocranial surfaces with modern human and primate endocrania. The latter have generally been obtained by creating endocasts out of rubber latex shells filled with plaster. The extent to which the method of production introduces errors in endocast replicas is unknown. We demonstrate a powerful method of comparing complex shapes in 3-dimensions (3D) that is broadly applicable to a wide range of paleoanthropological questions. Pairs of virtual endocasts (VEs) created from high-resolution CT scans of corresponding latex/plaster endocasts and their associated crania were rigidly registered (aligned) in 3D space for two Homo sapiens and two Pan troglodytes specimens. Distances between each cranial VE and its corresponding latex/plaster VE were then mapped on a voxel-by-voxel basis. The results show that between 79.7% and 91.0% of the voxels in the four latex/plaster VEs are within 2 mm of their corresponding cranial VEs surfaces. The average error is relatively small, and variation in the pattern of error across the surfaces appears to be generally random overall. However, inferior areas around the cranial base and the temporal poles were somewhat overestimated in both human and chimpanzee specimens, and the area overlaying Broca's area in humans was somewhat underestimated. This study gives an idea of the size of possible error inherent in latex/plaster endocasts, indicating the level of confidence we can have with studies relying on comparisons between them and, e.g., hominid fossil endocasts. Am J Phys Anthropol, 2007. © 2006 Wiley-Liss, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/55857/1/20499_ftp.pd

Endocast morphology of Homo naledi from the Dinaledi Chamber, South Africa

Hominin cranial remains from the Dinaledi Chamber, South Africa, represent multiple individuals of the species Homo naledi. This species exhibits a small endocranial volume comparable to Australopithecus, combined with several aspects of external cranial anatomy similar to larger-brained species of Homo such as Homo habilis and Homo erectus. Here, we describe the endocast anatomy of this recently discovered species. Despite the small size of the H. naledi endocasts, they share several aspects of structure in common with other species of Homo, not found in other hominins or great apes, notably in the organization of the inferior frontal and lateral orbital gyri. The presence of such structural innovations in a small-brained hominin may have relevance to behavioral evolution within the genus Homo

An introduction to continuous optimization for imaging

International audienceA large number of imaging problems reduce to the optimization of a cost function , with typical structural properties. The aim of this paper is to describe the state of the art in continuous optimization methods for such problems, and present the most successful approaches and their interconnections. We place particular emphasis on optimal first-order schemes that can deal with typical non-smooth and large-scale objective functions used in imaging problems. We illustrate and compare the different algorithms using classical non-smooth problems in imaging, such as denoising and deblurring. Moreover, we present applications of the algorithms to more advanced problems, such as magnetic resonance imaging, multilabel image segmentation, optical flow estimation, stereo matching, and classification

Topography of the Chimpanzee Corpus Callosum

The corpus callosum (CC) is the largest commissural white matter tract in mammalian brains, connecting homotopic and heterotopic regions of the cerebral cortex. Knowledge of the distribution of callosal fibers projecting into specific cortical regions has important implications for understanding the evolution of lateralized structures and functions of the cerebral cortex. No comparisons of CC topography in humans and great apes have yet been conducted. We investigated the topography of the CC in 21 chimpanzees using high-resolution magnetic resonance imaging (MRI) and diffusion tensor imaging (DTI). Tractography was conducted based on fiber assignment by continuous tracking (FACT) algorithm. We expected chimpanzees to display topographical organization similar to humans, especially concerning projections into the frontal cortical regions. Similar to recent studies in humans, tractography identified five clusters of CC fibers projecting into defined cortical regions: prefrontal; premotor and supplementary motor; motor; sensory; parietal, temporal and occipital. Significant differences in fractional anisotropy (FA) were found in callosal regions, with highest FA values in regions projecting to higher-association areas of posterior cortical (including parietal, temporal and occipital cortices) and prefrontal cortical regions (p<0.001). The lowest FA values were seen in regions projecting into motor and sensory cortical areas. Our results indicate chimpanzees display similar topography of the CC as humans, in terms of distribution of callosal projections and microstructure of fibers as determined by anisotropy measures