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Efficient Sparse Shape Composition with its Applications in Biomedical Image Analysis: An Overview Shaoting Zhang, Yiqiang Zhan, Yan Zhou, and Dimitris N. Metaxas

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Outline Introduction Our methods Experiments Future work 2

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Introduction Motivations Segmentation (i.e., finding 2D/3D ROI) is a fundamental problem in medical image analysis. We use deformable models and shape prior. Shape representation is based on landmarks. Chest X-ray Lung CAD Liver in low-dose whole-body CT Rat brain structure in MR Microscopy 3

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Introduction Motivations Shape prior is important: – Automatic, accuracy, efficiency, robustness. – Handle weak or misleading appearance cues from image information. – Discover or preserve complex shape details. Segmentation system 4

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Introduction Challenges – shape prior modeling Good shape prior method needs to: – Handle gross errors of the input data. – Model complex shape variations. – Preserve local shape details. 5

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Introduction Relevant work – shape prior methods Handling gross errors. – RANSAC + ASM [M. Rogers, ECCV02] – Robust Point Matching [J. Nahed, MICCAI06] Complex shape variation (multimodal distribution). – Mixture of Gaussians [T. F. Cootes, IVC97] – Patient-specific shape [Y. Zhu, MICCAI09] Recovering local details. – Sparse PCA [K. Sjostrand, TMI07] – Hierarchical ASM [D. Shen, TMI03] 6

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Our Approach Shape prior using sparse shape composition Our method is based on two observations: – An input shape can be approximately represented by a sparse linear combination of training shapes. – The given shape information may contain gross errors, but such errors are often sparse.... 7

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Our Approach Shape prior using sparse shape composition Formulation: – Sparse linear combination: – Dense x Sparse x Aligned data matrix D Weight x Input y Global transformation parameter Number of nonzero elements 8 Global transformation operator

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Our Approach Shape prior using sparse shape composition Non-Gaussian errors: – 9

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Our Approach Shape prior using sparse shape composition Why it works? – Robust: Explicitly modeling e with L0 norm constraint. Thus it can detect gross (sparse) errors. – General: No assumption of a parametric distribution model (e.g., a unimodal distribution assumption in ASM). Thus it can model complex shape statistics. – Lossless: It uses all training shapes. Thus it is able to recover detail information even if the detail is not statistically significant in training data. Zhang, Metaxas, et.al.: MedIA11 10

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Experiments 2D lung localization in X-ray Setting : –Manually select landmarks for training purpose. –200 training and 167 testing. –To locate the lung, detect landmarks, then predict a shape to fit them. –Sensitivity (P), Specificity (Q), Dice Similarity Coefficient. 11

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Experiments 2D lung localization in X-ray Handling gross errors Detection PA ASM RASM NN TPS Sparse1 Sparse2 Procrustes analysis Active Shape Model Robust ASMNearest Neighbors Thin-plate-spline Without modeling e 12 Proposed method

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Experiments 2D lung localization in X-ray Multimodal distribution Detection PA ASM/RASM NN TPS Sparse1 Sparse2 13

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Experiments 2D lung localization in X-ray Recover local detail information Detection PA ASM/RASM NN TPS Sparse1 Sparse2 14

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Experiments 2D lung localization in X-ray Sparse shape components ASM modes:

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Experiments 2D lung localization in X-ray Mean values (µ) and standard deviations (σ). Left lung Right lung 1)PA, 2)ASM, 3)RASM, 4)NN, 5)TPS, 6)Sparse1, 7)Sparse2 µ σ 16

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Future Work Dictionary Learning Dictionary size = 128#Coefficients = 800#Input samples = 800

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18 D Initialize D Sparse Coding Use MP or BP Dictionary Update Column-by-Column by SVD computation Use K-SVD to learn a compact dictionary Aharon, Elad, & Bruckstein (04) YTYT * The slides are from Future Work Dictionary Learning

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Future Work Online Update Dictionary

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Future Work Mesh Partitioning for Local Shape Priors 20 Segmentation system Lung Heart Rib Colon Abdomen

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Thanks! Questions and comments 21

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