Feasibility of automated 3-dimensional magnetic resonance imaging pancreas segmentation.

PurposeWith the advent of MR guided radiotherapy, internal organ motion can be imaged simultaneously during treatment. In this study, we evaluate the feasibility of pancreas MRI segmentation using state-of-the-art segmentation methods.Methods and materialT2 weighted HASTE and T1 weighted VIBE images were acquired on 3 patients and 2 healthy volunteers for a total of 12 imaging volumes. A novel dictionary learning (DL) method was used to segment the pancreas and compared to t mean-shift merging (MSM), distance regularized level set (DRLS), graph cuts (GC) and the segmentation results were compared to manual contours using Dice's index (DI), Hausdorff distance and shift of the-center-of-the-organ (SHIFT).ResultsAll VIBE images were successfully segmented by at least one of the auto-segmentation method with DI >0.83 and SHIFT ≤2 mm using the best automated segmentation method. The automated segmentation error of HASTE images was significantly greater. DL is statistically superior to the other methods in Dice's overlapping index. For the Hausdorff distance and SHIFT measurement, DRLS and DL performed slightly superior to the GC method, and substantially superior to MSM. DL required least human supervision and was faster to compute.ConclusionOur study demonstrated potential feasibility of automated segmentation of the pancreas on MRI images with minimal human supervision at the beginning of imaging acquisition. The achieved accuracy is promising for organ localization

An Appearance-Based Framework for 3D Hand Shape Classification and Camera Viewpoint Estimation

An appearance-based framework for 3D hand shape classification and simultaneous camera viewpoint estimation is presented. Given an input image of a segmented hand, the most similar matches from a large database of synthetic hand images are retrieved. The ground truth labels of those matches, containing hand shape and camera viewpoint information, are returned by the system as estimates for the input image. Database retrieval is done hierarchically, by first quickly rejecting the vast majority of all database views, and then ranking the remaining candidates in order of similarity to the input. Four different similarity measures are employed, based on edge location, edge orientation, finger location and geometric moments.National Science Foundation (IIS-9912573, EIA-9809340

Searching edges in the overlap of two plane graphs

Consider a pair of plane straight-line graphs, whose edges are colored red and blue, respectively, and let n be the total complexity of both graphs. We present a O(n log n)-time O(n)-space technique to preprocess such pair of graphs, that enables efficient searches among the red-blue intersections along edges of one of the graphs. Our technique has a number of applications to geometric problems. This includes: (1) a solution to the batched red-blue search problem [Dehne et al. 2006] in O(n log n) queries to the oracle; (2) an algorithm to compute the maximum vertical distance between a pair of 3D polyhedral terrains one of which is convex in O(n log n) time, where n is the total complexity of both terrains; (3) an algorithm to construct the Hausdorff Voronoi diagram of a family of point clusters in the plane in O((n+m) log^3 n) time and O(n+m) space, where n is the total number of points in all clusters and m is the number of crossings between all clusters; (4) an algorithm to construct the farthest-color Voronoi diagram of the corners of n axis-aligned rectangles in O(n log^2 n) time; (5) an algorithm to solve the stabbing circle problem for n parallel line segments in the plane in optimal O(n log n) time. All these results are new or improve on the best known algorithms.Comment: 22 pages, 6 figure

Degenerations of ideal hyperbolic triangulations

Let M be a cusped 3-manifold, and let T be an ideal triangulation of M. The deformation variety D(T), a subset of which parameterises (incomplete) hyperbolic structures obtained on M using T, is defined and compactified by adding certain projective classes of transversely measured singular codimension-one foliations of M. This leads to a combinatorial and geometric variant of well-known constructions by Culler, Morgan and Shalen concerning the character variety of a 3-manifold.Comment: 31 pages, 11 figures; minor changes; to appear in Mathematische Zeitschrif

Approximating the Maximum Overlap of Polygons under Translation

Let $P$ and $Q$ be two simple polygons in the plane of total complexity $n$, each of which can be decomposed into at most $k$ convex parts. We present an $(1-\varepsilon)$-approximation algorithm, for finding the translation of $Q$, which maximizes its area of overlap with $P$. Our algorithm runs in $O(c n)$ time, where $c$ is a constant that depends only on $k$ and $\varepsilon$. This suggest that for polygons that are "close" to being convex, the problem can be solved (approximately), in near linear time

Optimal rates of convergence for persistence diagrams in Topological Data Analysis

Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in general metric spaces, with a statistical approach. We show that the use of persistent homology can be naturally considered in general statistical frameworks and persistence diagrams can be used as statistics with interesting convergence properties. Some numerical experiments are performed in various contexts to illustrate our results