Efficient Sparse Shape Composition with its Applications in Biomedical Image Analysis: An Overview...
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Transcript of Efficient Sparse Shape Composition with its Applications in Biomedical Image Analysis: An Overview...
Efficient Sparse Shape Composition with its Applications in Biomedical Image Analysis:
An Overview
Shaoting Zhang, Yiqiang Zhan, Yan Zhou, andDimitris N. Metaxas
Outline• Introduction• Our methods• Experiments• Future work
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IntroductionMotivations
• 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 CADLiver in low-dose whole-body CT
Rat brain structure in MR Microscopy
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IntroductionMotivations
• 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
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IntroductionChallenges – shape prior modeling
• Good shape prior method needs to:– Handle gross errors of the input data.– Model complex shape variations.– Preserve local shape details.
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IntroductionRelevant work – shape prior methods
• Handling gross errors. – RANSAC + ASM [M. Rogers, ECCV’02]– Robust Point Matching [J. Nahed, MICCAI’06]
• Complex shape variation (multimodal distribution).– Mixture of Gaussians [T. F. Cootes, IVC’97]– Patient-specific shape [Y. Zhu, MICCAI’09]
• Recovering local details.– Sparse PCA [K. Sjostrand, TMI’07]– Hierarchical ASM [D. Shen, TMI’03]
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Our ApproachShape 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....
≈
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Our ApproachShape prior using sparse shape composition
• Formulation:–
• Sparse linear combination:–
...≈
...≈
Dense xSparse xAligned data matrix D
Weight x
Input y
Global transformationparameter
Number of nonzero elements
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Global transformationoperator
Our ApproachShape prior using sparse shape composition
• Non-Gaussian errors:–
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Our ApproachShape 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.: MedIA’11
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Experiments2D 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.
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Experiments 2D lung localization in X-ray
• Handling gross errors
Detection PA ASM RASM NN TPS Sparse1 Sparse2
Procrustes analysisActive Shape ModelRobust ASMNearest NeighborsThin-plate-splineWithout modeling “e”
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Proposed method
Experiments2D lung localization in X-ray
• Multimodal distribution
Detection PA ASM/RASM NN TPS Sparse1 Sparse2
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Experiments2D lung localization in X-ray
• Recover local detail information
Detection PA ASM/RASM NN TPS Sparse1 Sparse2
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Experiments2D lung localization in X-ray
• Sparse shape components
• ASM modes:
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≈
0.5760
+ +
0.2156 0.0982
Experiments2D 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
µσ
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Future WorkDictionary Learning
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... ≈... ...
Dictionary size = 128 #Coefficients = 800 #Input samples = 800
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DInitialize D
Sparse CodingUse MP or BP
Dictionary UpdateColumn-by-Column by SVD computation
Use K-SVD to learn a compact dictionary Aharon, Elad, & Bruckstein (‘04)
YT
* The slides are from http://www.cs.technion.ac.il/~elad/talks/
Future WorkDictionary Learning
Future WorkOnline Update Dictionary
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...≈
...
Future WorkMesh Partitioning for Local Shape Priors
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Segmentation system
Lung Heart
Rib
Colon
Abdomen
Thanks!Questions and comments
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