Equivariant localization and completion in cyclic homology and derived loop spaces

We prove an equivariant localization theorem over an algebraically closed field of characteristic zero for smooth quotient stacks by reductive groups $X/G$ in the setting of derived loop spaces as well as Hochschild homology and its cyclic variants. We show that the derived loop spaces of the stack $X/G$ and its classical $z$-fixed point stack $\pi_0(X^z)/G^z$ become equivalent after completion along a semisimple parameter $[z] \in G//G$, implying the analogous statement for Hochschild and cyclic homology of the dg category of perfect complexes $\text{Perf}(X/G)$. We then prove an analogue of the Atiyah-Segal completion theorem in the setting of periodic cyclic homology, where the completion of the periodic cyclic homology of $\text{Perf}(X/G)$ at the identity $[e] \in G//G$ is identified with a 2-periodic version of the derived de Rham cohomology of $X/G$. Together, these results identify the completed periodic cyclic homology of a stack $X/G$ over a parameter $[z] \in G//G$ with the 2-periodic derived de Rham cohomology of its $z$-fixed points.Comment: Pre-publication version. 42 pages. Comments welcom

Deep learning for cardiac image segmentation: A review

Deep learning has become the most widely used approach for cardiac image segmentation in recent years. In this paper, we provide a review of over 100 cardiac image segmentation papers using deep learning, which covers common imaging modalities including magnetic resonance imaging (MRI), computed tomography (CT), and ultrasound (US) and major anatomical structures of interest (ventricles, atria and vessels). In addition, a summary of publicly available cardiac image datasets and code repositories are included to provide a base for encouraging reproducible research. Finally, we discuss the challenges and limitations with current deep learning-based approaches (scarcity of labels, model generalizability across different domains, interpretability) and suggest potential directions for future research

Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age

Simultaneous Localization and Mapping (SLAM)consists in the concurrent construction of a model of the environment (the map), and the estimation of the state of the robot moving within it. The SLAM community has made astonishing progress over the last 30 years, enabling large-scale real-world applications, and witnessing a steady transition of this technology to industry. We survey the current state of SLAM. We start by presenting what is now the de-facto standard formulation for SLAM. We then review related work, covering a broad set of topics including robustness and scalability in long-term mapping, metric and semantic representations for mapping, theoretical performance guarantees, active SLAM and exploration, and other new frontiers. This paper simultaneously serves as a position paper and tutorial to those who are users of SLAM. By looking at the published research with a critical eye, we delineate open challenges and new research issues, that still deserve careful scientific investigation. The paper also contains the authors' take on two questions that often animate discussions during robotics conferences: Do robots need SLAM? and Is SLAM solved

Semantic Localization and Mapping in Robot Vision

Integration of human semantics plays an increasing role in robotics tasks such as mapping, localization and detection. Increased use of semantics serves multiple purposes, including giving computers the ability to process and present data containing human meaningful concepts, allowing computers to employ human reasoning to accomplish tasks. This dissertation presents three solutions which incorporate semantics onto visual data in order to address these problems. First, on the problem of constructing topological maps from sequence of images. The proposed solution includes a novel image similarity score which uses dynamic programming to match images using both appearance and relative positions of local features simultaneously. An MRF is constructed to model the probability of loop-closures and a locally optimal labeling is found using Loopy-BP. The recovered loop closures are then used to generate a topological map. Results are presented on four urban sequences and one indoor sequence. The second system uses video and annotated maps to solve localization. Data association is achieved through detection of object classes, annotated in prior maps, rather than through detection of visual features. To avoid the caveats of object recognition, a new representation of query images is introduced consisting of a vector of detection scores for each object class. Using soft object detections, hypotheses about pose are refined through particle filtering. Experiments include both small office spaces, and a large open urban rail station with semantically ambiguous places. This approach showcases a representation that is both robust and can exploit the plethora of existing prior maps for GPS-denied environments while avoiding the data association problems encountered when matching point clouds or visual features. Finally, a purely vision-based approach for constructing semantic maps given camera pose and simple object exemplar images. Object response heatmaps are combined with known pose to back-project detection information onto the world. These update the world model, integrating information over time as the camera moves. The approach avoids making hard decisions on object recognition, and aggregates evidence about objects in the world coordinate system. These solutions simultaneously showcase the contribution of semantics in robotics and provide state of the art solutions to these fundamental problems

Modélisation statistique des structures anatomiques de la rétine à partir d'images de fond d'oeil

L’examen non-invasif du fond d’oeil permet d’identifier sur la rétine les signes de nombreuses pathologies oculaires qui développent de graves symptômes pour le patient pouvant entraîner la cécité. Le réseau vasculaire rétinien peut de surcroît présenter des signes précurseurs de pathologies cardiovasculaires et cérébro-vasculaires. La rétine, où apparaissent ces pathologies, est constituée de plusieurs structures anatomiques dont la variabilité est importante au sein d’une population saine. Pour autant, les évaluations cliniques actuelles ne prennent pas en compte cette variabilité ce qui ne permet pas de détecter précocement ces pathologies. Ces évaluations se basent sur un ensemble restreint de mesures prélevées à partir de structures dont la segmentation manuelle est réalisable par les experts. De plus, elles sont basées sur un seuillage empirique déterminé par les cliniciens et appliqué sur chacune des mesures afin d’établir un diagnostic. Ainsi, les évaluations cliniques actuelles sont affectées par la grande variabilité des structures anatomiques de la rétine au sein de la population et elles n’évaluent pas les anomalies trop difficiles à mesurer manuellement. Dans ce contexte, il convient de proposer de nouvelles mesures cliniques qui tiennent compte de la variabilité normale à l’aide d’une modélisation statistique des structures anatomiques de la rétine. Cette modélisation statistique permet de mieux comprendre et identifier ce qui est normal et comment l’anatomie et ses attributs varient au sein d’une population saine. Cela permet ainsi d’identifier la présence de pathologies à l’aide de nouvelles mesures cliniques construites en tenant compte de la variabilité des attributs de l’anatomie. La modélisation statistique des structures anatomiques de la rétine est cependant difficile étant donné les variations morphologiques et topologiques de ces structures. Les changements morphologiques et topologiques du réseau vasculaire rétinien compliquent son analyse statistique ainsi que les outils de recalage, de segmentation et de représentation sémantique s’y appliquant. Les questions de recherches adressées dans cette thèse sont la production d’outils capables d’analyser la variabilité des structures anatomiques de la rétine et l’élaboration de nouvelles mesures cliniques tenant compte de la variabilité normale de ces structures. Pour répondre à ces questions de recherche, trois objectifs de recherche sont formulés. ----------ABSTRACT: Non-invasive retinal fundus examination allows clinicians to identify signs of many ocular conditions that develop critical symptoms affecting the patient and even leading to blindness. In addition, the retinal vascular network may present early signs of cardiovascular and cerebrovascular diseases. The retina, where these pathologies appear, is composed of several anatomical structures whose variability is considerable within a healthy population. Yet, current clinical evaluations do not take into account this variability, and this does not allow early detection of these pathologies. These evaluations are based on a limited set of measurements taken from structures whose manual segmentation is achievable by the experts. In addition, they are based on empirical thresholding determined by the clinicians and applied to each of the measurements to establish a diagnosis. Thus, current clinical assessments are affected by the large variability of anatomical structures of the retina within a healthy population and do not evaluate abnormalities that are too difficult to measure manually. In this context, it is advisable to propose new clinical measurements that take into account the normal variability using statistical modeling of the anatomical structures of the retina. Such a statistical modeling approach helps us to better understand and identify what is normal and how the anatomy and its attributes vary across a healthy population. This makes it possible to identify the presence of pathologies using new clinical measurements constructed by taking into account the variability of the anatomy’s attributes. Statistical modeling of the anatomical structures of the retina is difficult, however, given the morphological and topological variations of these structures. Morphological and topological changes in the retinal vascular network complicate its statistical analysis as well as the registration methods, segmentation and semantic representation applied to it. The research questions proposed in this thesis pertain to creating tools capable of analyzing the variability of the anatomical structures of the retina and proposing new clinical measures that take into account the normal variability of those structures. To answer these research questions, three research objectives are formulated