157 research outputs found

    Learning the dynamics and time-recursive boundary detection of deformable objects

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    We propose a principled framework for recursively segmenting deformable objects across a sequence of frames. We demonstrate the usefulness of this method on left ventricular segmentation across a cardiac cycle. The approach involves a technique for learning the system dynamics together with methods of particle-based smoothing as well as non-parametric belief propagation on a loopy graphical model capturing the temporal periodicity of the heart. The dynamic system state is a low-dimensional representation of the boundary, and the boundary estimation involves incorporating curve evolution into recursive state estimation. By formulating the problem as one of state estimation, the segmentation at each particular time is based not only on the data observed at that instant, but also on predictions based on past and future boundary estimates. Although the paper focuses on left ventricle segmentation, the method generalizes to temporally segmenting any deformable object

    3D shape matching and registration : a probabilistic perspective

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    Dense correspondence is a key area in computer vision and medical image analysis. It has applications in registration and shape analysis. In this thesis, we develop a technique to recover dense correspondences between the surfaces of neuroanatomical objects over heterogeneous populations of individuals. We recover dense correspondences based on 3D shape matching. In this thesis, the 3D shape matching problem is formulated under the framework of Markov Random Fields (MRFs). We represent the surfaces of neuroanatomical objects as genus zero voxel-based meshes. The surface meshes are projected into a Markov random field space. The projection carries both geometric and topological information in terms of Gaussian curvature and mesh neighbourhood from the original space to the random field space. Gaussian curvature is projected to the nodes of the MRF, and the mesh neighbourhood structure is projected to the edges. 3D shape matching between two surface meshes is then performed by solving an energy function minimisation problem formulated with MRFs. The outcome of the 3D shape matching is dense point-to-point correspondences. However, the minimisation of the energy function is NP hard. In this thesis, we use belief propagation to perform the probabilistic inference for 3D shape matching. A sparse update loopy belief propagation algorithm adapted to the 3D shape matching is proposed to obtain an approximate global solution for the 3D shape matching problem. The sparse update loopy belief propagation algorithm demonstrates significant efficiency gain compared to standard belief propagation. The computational complexity and convergence property analysis for the sparse update loopy belief propagation algorithm are also conducted in the thesis. We also investigate randomised algorithms to minimise the energy function. In order to enhance the shape matching rate and increase the inlier support set, we propose a novel clamping technique. The clamping technique is realized by combining the loopy belief propagation message updating rule with the feedback from 3D rigid body registration. By using this clamping technique, the correct shape matching rate is increased significantly. Finally, we investigate 3D shape registration techniques based on the 3D shape matching result. Based on the point-to-point dense correspondences obtained from the 3D shape matching, a three-point based transformation estimation technique is combined with the RANdom SAmple Consensus (RANSAC) algorithm to obtain the inlier support set. The global registration approach is purely dependent on point-wise correspondences between two meshed surfaces. It has the advantage that the need for orientation initialisation is eliminated and that all shapes of spherical topology. The comparison of our MRF based 3D registration approach with a state-of-the-art registration algorithm, the first order ellipsoid template, is conducted in the experiments. These show dense correspondence for pairs of hippocampi from two different data sets, each of around 20 60+ year old healthy individuals

    Object Detection at the Optimal Scale with Hidden State Shape Models

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    Hidden State Shape Models (HSSMs) [2], a variant of Hidden Markov Models (HMMs) [9], were proposed to detect shape classes of variable structure in cluttered images. In this paper, we formulate a probabilistic framework for HSSMs which provides two major improvements in comparison to the previous method [2]. First, while the method in [2] required the scale of the object to be passed as an input, the method proposed here estimates the scale of the object automatically. This is achieved by introducing a new term for the observation probability that is based on a object-clutter feature model. Second, a segmental HMM [6, 8] is applied to model the "duration probability" of each HMM state, which is learned from the shape statistics in a training set and helps obtain meaningful registration results. Using a segmental HMM provides a principled way to model dependencies between the scales of different parts of the object. In object localization experiments on a dataset of real hand images, the proposed method significantly outperforms the method of [2], reducing the incorrect localization rate from 40% to 15%. The improvement in accuracy becomes more significant if we consider that the method proposed here is scale-independent, whereas the method of [2] takes as input the scale of the object we want to localize

    Learning the dynamics of deformable objects and recursive boundary estimation using curve evolution techniques

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    Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 161-176).The primary objective of this thesis is to develop robust algorithms for the incorporation of statistical information in the problem of estimating object boundaries in image data. We propose two primary algorithms, one which jointly estimates the underlying field and boundary in a static image and another which performs image segmentation across a temporal sequence. Some motivating applications come from the earth sciences and medical imaging. In particular, we examine the problems of oceanic front and sea surface temperature estimation in oceanography, soil boundary and moisture estimation in hydrology, and left ventricle boundary estimation across a cardiac cycle in medical imaging. To accomplish joint estimation in a static image, we introduce a variational technique that incorporates the spatial statistics of the underlying field to segment the boundary and estimate the field on either side of the boundary. For image segmentation across a sequence of frames, we propose a method for learning the dynamics of a deformable boundary that uses these learned dynamics to recursively estimate the boundary in each frame over time. In the recursive estimation algorithm, we extend the traditional particle filtering approach by applying sample-based methods to a complex shape space.(cont.) We find a low-dimensional representation for this shape-shape to make the learning of the dynamics tractable and then incorporate curve evolution into the state estimates to recursively estimate the boundaries. Experimental results are obtained on cardiac magnetic resonance images, sea surface temperature data, and soil moisture maps. Although we focus on these application areas, the underlying mathematical principles posed in the thesis are general enough that they can be applied to other applications as well. We analyze the algorithms on data of differing quality, with both high and low SNR data and also full and sparse observations.by Walter Sun.Ph.D

    Deformable shape matching

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    Deformable shape matching has become an important building block in academia as well as in industry. Given two three dimensional shapes A and B the deformation function f aligning A with B has to be found. The function is discretized by a set of corresponding point pairs. Unfortunately, the computation cost of a brute-force search of correspondences is exponential. Additionally, to be of any practical use the algorithm has to be able to deal with data coming directly from 3D scanner devices which suffers from acquisition problems like noise, holes as well as missing any information about topology. This dissertation presents novel solutions for solving shape matching: First, an algorithm estimating correspondences using a randomized search strategy is shown. Additionally, a planning step dramatically reducing the matching costs is incorporated. Using ideas of these both contributions, a method for matching multiple shapes at once is shown. The method facilitates the reconstruction of shape and motion from noisy data acquired with dynamic 3D scanners. Considering shape matching from another perspective a solution is shown using Markov Random Fields (MRF). Formulated as MRF, partial as well as full matches of a shape can be found. Here, belief propagation is utilized for inference computation in the MRF. Finally, an approach significantly reducing the space-time complexity of belief propagation for a wide spectrum of computer vision tasks is presented.Anpassung deformierbarer Formen ist zu einem wichtigen Baustein in der akademischen Welt sowie in der Industrie geworden. Gegeben zwei dreidimensionale Formen A und B, suchen wir nach einer Verformungsfunktion f, die die Deformation von A auf B abbildet. Die Funktion f wird durch eine Menge von korrespondierenden Punktepaaren diskretisiert. Leider sind die Berechnungskosten für eine Brute-Force-Suche dieser Korrespondenzen exponentiell. Um zusätzlich von einem praktischen Nutzen zu sein, muss der Suchalgorithmus in der Lage sein, mit Daten, die direkt aus 3D-Scanner kommen, umzugehen. Bedauerlicherweise leiden diese Daten unter Akquisitionsproblemen wie Rauschen, Löcher sowie fehlender Topologieinformation. In dieser Dissertation werden neue Lösungen für das Problem der Formanpassung präsentiert. Als erstes wird ein Algorithmus gezeigt, der die Korrespondenzen mittels einer randomisierten Suchstrategie schätzt. Zusätzlich wird anhand eines automatisch berechneten Schätzplanes die Geschwindigkeit der Suchstrategie verbessert. Danach wird ein Verfahren gezeigt, dass die Anpassung mehrerer Formen gleichzeitig bewerkstelligen kann. Diese Methode ermöglicht es, die Bewegung, sowie die eigentliche Struktur des Objektes aus verrauschten Daten, die mittels dynamischer 3D-Scanner aufgenommen wurden, zu rekonstruieren. Darauffolgend wird das Problem der Formanpassung aus einer anderen Perspektive betrachtet und als Markov-Netzwerk (MRF) reformuliert. Dieses ermöglicht es, die Formen auch stückweise aufeinander abzubilden. Die eigentliche Lösung wird mittels Belief Propagation berechnet. Schließlich wird ein Ansatz gezeigt, der die Speicher-Zeit-Komplexität von Belief Propagation für ein breites Spektrum von Computer-Vision Problemen erheblich reduziert

    Segmentation of the evolving left ventricle by learning the dynamics

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    We propose a method for recursive segmentation of the left ventricle (LV) across a temporal sequence of magnetic resonance (MR) images. The approach involves a technique for learning the LV boundary dynamics together with a particle-based inference algorithm on a loopy graphical model capturing the temporal periodicity of the heart. The dynamic system state is a low-dimensional representation of the boundary, and boundary estimation involves incorporating curve evolution into state estimation. By formulating the problem as one of state estimation, the segmentation at each particular time is based not only on the data observed at that instant, but also on predictions based on past and future boundary estimates. We assess and demonstrate the effectiveness of the proposed framework on a large data set of breath-hold cardiac MR image sequences
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