Despite significant progress achieved in the last decade to convert passive capsule endoscopes to actively controllable robots, robotic capsule endoscopy still has some challenges. In particular, a fully dense three-dimensional (3D) map reconstruction of the explored organ remains an unsolved problem. Such a dense map would help doctors detect the locations and sizes of the diseased areas more reliably, resulting in more accurate diagnoses. In this study, we propose a comprehensive medical 3D reconstruction method for endoscopic capsule robots, which is built in a modular fashion including preprocessing, keyframe selection, sparse-then-dense alignment-based pose estimation, bundle fusion, and shading-based 3D reconstruction. A detailed quantitative analysis is performed using a non-rigid esophagus gastroduodenoscopy simulator, four different endoscopic cameras, a magnetically activated soft capsule robot, a sub-millimeter precise optical motion tracker, and a fine-scale 3D optical scanner, whereas qualitative ex-vivo experiments are performed on a porcine pig stomach. To the best of our knowledge, this study is the first complete endoscopic 3D map reconstruction approach containing all of the necessary functionalities for a therapeutically relevant 3D map reconstruction.
Graph Signal Processing has become a very useful framework for signal operations and representations defined on irregular domains. Exploiting transformations that are defined on graph models can be highly beneficial when the graph encodes relationships between signals. In this work, we present the benefits of using Spectral Graph Wavelet Transform (SGWT) as a feature extractor for machine learning on brain graphs. First, we consider a synthetic regression problem in which the smooth graph signals are generated as input with additive noise, and the target is derived from the input without noise. This enables us to optimize the spectrum coverage using different wavelet shapes. Finally, we present the benefits obtained by SGWT on a functional Magnetic Resonance Imaging (fMRI) open dataset on human subjects, with several graphs and wavelet shapes, by demonstrating significant performance improvements compared to the state of the art.
Another facet of the elegant link between random processes on graphs and Laplacian-based numerical linear algebra is uncovered: based on random spanning forests, novel Monte-Carlo estimators for graph signal smoothing are proposed. These random forests are sampled efficiently via a variant of Wilson's algorithm -in time linear in the number of edges. The theoretical variance of the proposed estimators are analyzed, and their application to several problems are considered, such as Tikhonov denoising of graph signals or semisupervised learning for node classification on graphs.
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