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UMD CMSC 828 - An Integrated Pose and Correspondence Approach to Image Matching

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An Integrated Pose and Correspondence Approach to Image MatchingMotivation IMotivation IIResults Interactive 3D Sulcal TracingOverviewOverview IIOutlineOther Work in Brain RegistrationApproach RationaleOur Approach Point-based RepresentationOur Approach Robust Point Matching (RPM)Robust Point Matching Alternating OptimizationRobust Point Matching Energy FunctionRobust Point Matching Step I. Solve Spatial MappingRobust Point Matching Part II. SoftassignPowerPoint PresentationSlide 17Robust Point Matching Algorithm SummaryExperiment on Brain SectionsResults of MethodSlide 21Results RPM ExampleSlide 23Results Visual Matching ComparisonResults Visual Matching ComparisonQuantitative ComparisonQuantitative ComparisonFuture WorkThe EndThin-plate-spline ImplementationSlide 31Slide 32An Integrated Pose and Correspondence Approach to Image MatchingAnand RangarajanImage Processing and Analysis GroupDepartments of Electrical Engineering and Diagnostic RadiologyYale UniversityMotivation I•Human Brain Mapping:–Different subjects.•Statistical analysis.•Normal vs. abnormal.–Different times.•Detect significant change, help diagnosis.–Different modalities.•Combine complementary information.Motivation II•Difficulty : –Variability in pose, size, shape and acquisition.•Brain registration : –Common coordinate frame.–Data comparable.–Quantitative analysis.ResultsInteractive 3D Sulcal TracingOverview•Extract features: –Sulcal traces represented as point sets.–Labeling, ordering information [optional].•Jointly solve feature correspondence and spatial mapping.Overview II•Part II: Information Analysis: –Measurements. –Learn from the data, construct statistical models.•e.g., probabilistic atlas for structures / functions.–Make inference for new data based on the learned models.•e.g., automated sulcal labeling, segmentation, computer aided diagnosis.Outline•Related work.•The approach.–Point-based representation of sulci.–Robust point matching algorithm.•Results and examples.•Future work.Other Work in Brain Registration•Voxel-based methods:–Volumetric Warping: Christensen et al., Gee et al., Collins et al.•Feature-based methods: –Landmarks: Bookstein.–Curves: Sandor and Leahy, Collins et al.–Surfaces: Thompson et al., Davatzikos et al. –Sulcal Graphs: Lohmann and von Cramon.Approach Rationale•Voxel intensity matching does not ensure that corresponding sulci indeed match.•Landmarks hard to define.•Extraction, representation and matching of cortical curves / surfaces / graphs is difficult.Our ApproachPoint-based Representation•Hundreds of points, statistically more robust than just a few landmarks.•Additional information can be used:–Major sulcal labels.•Further analyses made easy:–Procrustes mean. –Eigen-analysis of the error covariance matrix.Our ApproachRobust Point Matching (RPM)•Estimation : –Correspondence and spatial mapping.•Softassign:–Soft correspondence.–Allows partial matching, noise.–Less sensitive to local minima.•Handles outliers.Robust Point Matching Alternating Optimization•When correspondence M is known, standard least squares solution for spatial mapping A.•When spatial mapping A is fixed, assignment solution for correspondence M.–Softassign - soft correspondence.–Deterministic Annealing - temperature T.Robust Point Matching Energy Function iijjjjijiiMM)()(11)()(),(||||2,AATraceYIAXMMAETjijiijjiijijMMT,logRobust Point Matching Step I. Solve Spatial Mapping•Given correspondence M, find the optimal spatial mapping A (affine):•Standard least-squares solution.•Gradually relaxed regularization on )()()|(||||2,AATraceYIAXMMAETjijiij1,,][)]([IYYMYYYXMATjjjiijTjjTjijiijRobust Point Matching Part II. Softassign•Given spatial mapping A, solve the Linear Assignment Problem: |||||2,)(min)(minYIAXMAMEjijiijMassignM1,1jijiijMMsubject tojiijijMQM,minRobust Point MatchingStep II. SoftassignTwo-way constraintsMijMijMijiRow NormalizationMijMijMijjCol. NormalizationPositivity=exp()QijMij•Step I: Mij = exp ( - Qij/T).•Step II: Double Normalization. Sinkhorn’s Algorithm.Outlier rejection using slack variables.Robust Point Matching Part II. Softassign•Deterministic Annealing :–T as an extra parameter.–F = Eassign - TS = •Gibbs Distribution :–Positivity ganranteed.–High T, insensitive to Q, uniform M .–Low T, sensitive to Q, binary M .jiijijjiijijMMTQM,,log)/exp(TQMijijRobust Point Matching Algorithm Summary•Start: uniform M, high temperature T.•Do until final temperature is reached.–Given M, solve for spatial mapping A.–Given A, use Softassign to update M.•Decrease temperature.Experiment on Brain SectionsResults of MethodResultsInteractive 3D Sulcal TracingResultsRPM ExampleTwo labeled sulcal point sets, initial position.RPM without label informationResultsVisual Matching ComparisonResultsVisual Matching ComparisonQuantitative ComparisonQuantitative ComparisonFuture Work•Error measure on the entire volume.•Fully non-rigid 3D spatial mapping.–Thin-plate spline and correspondence.•Automated sulcal extraction, Zeng et al.•Investigate partially labeled case.•Automated labeling.•Atlas construction.The EndThin-plate-spline ImplementationThin-plate-spline ImplementationResultsVisual Matching


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UMD CMSC 828 - An Integrated Pose and Correspondence Approach to Image Matching

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