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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