Efficient sparse shape composition with its applications in biomedical image analysis an overview
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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. Outline. Introduction Our methods Experiments Future work. Introduction Motivations. Chest X-ray.

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Shaoting Zhang, Yiqiang Zhan, Yan Zhou, and Dimitris N. Metaxas

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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


Outline

  • Introduction

  • Our methods

  • Experiments

  • Future work


IntroductionMotivations

Chest X-ray

Rat brain structure in MR Microscopy

Lung CAD

Liver in low-dose whole-body CT

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.


IntroductionMotivations

Segmentation system

  • Shape prior is important:

    • Automatic, accuracy, efficiency, robustness.

    • Handle weak or misleading appearance cues from image information.

    • Discover or preserve complex shape details.


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.


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]


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.


Our ApproachShape prior using sparse shape composition

Number of nonzero elements

...

...

Global transformation

operator

Global transformation

parameter

Input y

Weight x

Aligned data matrix D

Dense x

Sparse x

  • Formulation:

  • Sparse linear combination:


Our ApproachShape prior using sparse shape composition

  • Non-Gaussian errors:


Our ApproachShape prior using sparse shape composition

Zhang, Metaxas, et.al.: MedIA’11

  • 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.


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.


Experiments 2D lung localization in X-ray

  • Handling gross errors

Detection PA ASM RASM NN TPS Sparse1 Sparse2

Procrustes analysis

Active Shape Model

Robust ASM

Nearest Neighbors

Thin-plate-spline

Without modeling “e”

Proposed method


Experiments2D lung localization in X-ray

  • Multimodal distribution

Detection PA ASM/RASM NN TPS Sparse1 Sparse2


Experiments2D lung localization in X-ray

  • Recover local detail information

Detection PA ASM/RASM NN TPS Sparse1 Sparse2


Experiments2D lung localization in X-ray

  • Sparse shape components

  • ASM modes:

+

+

0.5760

0.2156

0.0982


Experiments2D lung localization in X-ray

  • Mean values (µ) and standard deviations (σ).

σ

µ

Left lung

Right lung

1)PA, 2)ASM, 3)RASM, 4)NN, 5)TPS, 6)Sparse1, 7)Sparse2


Future WorkDictionary Learning

Dictionary size = 128

#Coefficients = 800

#Input samples = 800

...

...

...


D

Initialize D

Sparse Coding

Use MP or BP

YT

Dictionary Update

Column-by-Column by SVD computation

Future WorkDictionary Learning

Use K-SVD to learn a compact dictionary Aharon, Elad, & Bruckstein (‘04)

* The slides are from http://www.cs.technion.ac.il/~elad/talks/


Future WorkOnline Update Dictionary

...

...


Future WorkMesh Partitioning for Local Shape Priors

Heart

Lung

Rib

Abdomen

Segmentation system

Colon


Thanks!Questions and comments


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