Lessons from Cardiac Ultrasound Image Analysis

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1 Lessons from Cardiac Ultrasound Image Analysis Hemant D. Tagare Dept. of Diagnostic Radiology Dept. of Biomedical Engineering Yale University

2 Cardiac vs. Tongue Image Processing Both organs are essentially muscle. The boundary of interest in both is a muscle-fluid boundary. Cardiac video sequence: order of 10 frames, 1 frame/sec, gated. Geometric parameters used in everyday diagnosis (cardiac). Automation desirable because of clinical setting (cardiac). Computational resources are not hard to come by (cardiac).

Cardiac video sequence: order of 10 frames, 1 frame/sec, gated.

3 Cardiac Ultrasound Image Analysis Image analysis in cardiac images: Segmentation (Endo- and Epicardium). Motion Analysis. Strain Analysis. Ultrasound segmentation research: Edge Detectors (early 80s). Connected boundaries, local algorithms. Snake + Template warping algorithms (late 80s - early 90s). Mildly-disconnected boundaries, local algorithms. Probabilistic (Bayesian) level-set algorithms (90s-00s). Ultrasound physics, region-based, non-local algorithms. Discriminative machine-learning algorithms. Spatial inhomogeneity, curse of dimensionality, drag-and-drop segmentation.

Snake + Template warping algorithms (late 80s - early 90s). Mildly-disconnected boundaries, local algorithms.

4 Overview Cardiac Anatomy Ultrasound physics and image formation. Ultrasound Segmentation. Challenges.

5 Cardiac Anatomy Thoracic Cavity Myocardium Fibers (Schematic) Fibers (Sample)

6 Cardiac Ultrasound Image Anatomy Image How do we understand image content?

7 Ultrasound Image Formation (1d)

8 Ultrasound Image Formation (Anisotropy) Holland M. R. et. al., Journ. Amer. Soc. of Echo. Volume 11, Issue 10, October 1998, Pages

9 Ultrasound Image Formation (2d) Artifacts: 1. Contrast inhomogeneity and data drop-out. 2. Spurious signal from side lobes.

10 Cardiac Ultrasound Image Anatomy Image

11 First-order Ultrasound Statistics Image Regions Blood Pool Mean and stdev. are proportional Tissue Tao Z., Tagare H. D., Beaty J. D., I. E. E. E. Trans. Medical Imaging, vol. 25, No. 11, pp , Nov

12 Summary of Ultrasound Image Statistics Images contains specular reflection and speckle. Specularity due to acoustic impedance change. Speckle due to scattering. Speckle inhomogeneity due to fiber-like structures. Side-lobe and total internal reflection.

13 Ultrasound Image Segmentation Exploit speckle statistics (mean, stdev. etc.) Machine/operator independence Handle dropout and inhomogeneity Model dropout and inhomogeneity Model boundary shape (generic or organ specific) Contain the computational complexity Non-local methods Automatic segmentation

dropout and inhomogeneity Model boundary shape (generic or organ specific)

14 Ultrasound Image Analysis Ultrasound segmentation research: Edge Detectors (early 80s). Connected boundaries, local algorithms. Snake + Template warping algorithms (late 80s - early 90s). Mildly-disconnected boundaries, local algorithms. Probabilistic (Bayesian) level-set algorithms (90s-00s). Ultrasound physics, region-based, non-local algorithms. Discriminative machine-learning algorithms. Spatial inhomogeneity, curse of dimensionality, drag-and-drop segmentation.

Mildly-disconnected boundaries, local algorithms. Probabilistic (Bayesian) level-set algorithms (90s-00s).

15 Edge-based methods Exploit difference in the local mean intensity Roberts, Canny, Marr-Hildreth, Wavelet-based etc. Image Smoothed Image Maximal Change

16 Edge-based methods (Example)

17 Snakes, Templates, Dynamic Programming Tagare H. D., Deformable 2-D Template Matching Using Orthogonal Curves, I.E.E.E. Trans. on Medical Imaging, vol. 16, No. 1, pp , Feb Image Smoothed Image Edge Image Base template Deformation along normals Optimal deformation: Deformation passing over most edges

18 Snakes, Templates, Dynamic Programming (contd.) Computationally expensive. Iterative solution Many methods (template optimization) Template Optimization Name Fixed Manual Grad. Desc. Snake Variable Manual Dyn. Prog. Live wire Fixed template Dyn. Prog. Templ. deformation Limitations Difficult to bridge large gaps and inhomogeneities Difficult to extend to 2d+time or 3d Difficult to control deformation, model Multiple shapes, model complex images Difficult to handle self-crossing

Snake Variable Manual Dyn. Prog. Live wire Fixed template Dyn. Prog. Templ.

19 Snakes, Templates, Dynamic Programming (Example.)

20 Segmentation and Probability Theory The New Approach Key recent developments (90s-00s) Probability as the theoretical basis for segmentation (Mumford, Geman, Grenander, Chellappa, Jain etc.) Replace ad-hoc objective functions with standard ones Learn from real-world examples Make all assumptions explicit Level sets for representing evolving curves (Tsitstiklis, Osher, Sethian, Vemuri etc.) Self crossing is not a problem any more Draws on mature numerical analysis for p.d.e. New optimization techniques Escape from local minima (Zabeh, Tagare etc.) Graph cuts

) Replace ad-hoc objective functions with standard ones Learn from real-world examples Make all assumptions explicit Level sets for

21 Likelihood of Segmentation p(curve Image) 2 Image Space (N dim) Segmentation Space (N 2 dim) Find the most probable segmentation. This is the best segmentation possible (given the model for p(curve Image) ).

22 Approach I: Generative (Bayesian) Generative Model p(image Curve) p(curve Image) 2 Image Space (N dim) Segmentation Space (N 2 dim) Bayes Theorem: p(c I) p(i C)p(C). Translation: p(i c) p(c) Generative model Shape prior

23 The Bayesian Approach Pros: Models the entire image (region-based rather than edge-based) The segmentation is optimal (minimum variance) if the generative model is correct No ad-hoc techniques Canonical introduction of prior shape information (can be weak) Cons: Can get trapped in spurious local maxima Spatially in-homogenous generative models are cumbersome Many extra parameters Optimization is difficult

24 The Bayesian Approach (Examples) Successful segmentation Homogenous myocardium (Movie) Inhomogenous myocardium (Movie) Leakage Tao Z., Tagare H. D., Tunneling Descent; A New Strategy for M. A. P. Active Contour Evolution and its Application to Ultrasound Segmentation, Medical Image Analysis,(11), pp , 2007.

25 The Discriminative Approach Training set p(curve Image) 2 Image Space (N dim) Segmentation Space (N 2 dim) Use a training set (learn spatial inhomogeneity) Penalized logisitic field Learn only what is needed for segmentation

26 The Discriminative Approach (contd.) Yue Y., Tagare H. D., Learning to Segment Using Machine-Learned Penalized Logistic Models, MMBIA, Computer Vision and Pattern Recognition Workshops, pp , Movies

27 Validation Mean Distance: 1.38 pixels. Ultrasound Phantom Prof. E. Madsen, Univ. Wisc. Phantom Segmentation Collaboration between Yale University, University of Florida, and University of Wisconsin

28 Why is this hard? High-dimensional spaces are very non-intuitive Optimization is difficult V sphere /V cube 0. Distance to nearest neighbor Distance to farthest neighbor. Most of the volume of the sphere is concentrated near the surface. All diagonals of the unit cube are almost perpendicular to the sides. All of these phenomenon are apparent between dim=10 & 20 Many local maxima to get trapped in.

29 But there is hope! Most image classes have low intrinsic dimension PCA ICA Manifold Learning Low dimensional support for image and the segmentation class: - PCA, ICA, Manifold Learning (Isomap etc.), Kernel-based approaches etc. Low dimensional approximation to the probability distribution: - Gaussian models, Mixture models, Markov random fields, Logistic models etc.

30 Shape-based Motion Analysis

Analysis of Correspondence Tagare H. D., OShea D., Groisser D., Shape Based Non-rigid Correspondence for Plane Curves, Journal of Mathematical Imaging and Vision, 16:57-68, 2002.

31 Analysis of Correspondence Tagare H. D., OShea D., Groisser D., Shape Based Non-rigid Correspondence for Plane Curves, Journal of Mathematical Imaging and Vision, 16:57-68, Tagare H. D., Groisser D., Skrinjar O., Symmetric Non-rigid Registration: A Geometric Theory and Some Numerical Techniques, Journal of Mathematical Imaging and Vision, 34, pp. 6188, 2009.

32 Tracking Tagare H. D., Shape-Based Non-rigid Correspondence with Applications to Heart Motion Analysis, I.E.E.E. Trans. Medical Imaging, vol. 18, no. 7, pp , July 1999.

33 Point Motion from Shape Change Khalil s comments: Shape change in the tongue during speech production is accompanied by the motion of fleshpoints on it. A major question is how analysis using fleshpoints relates to analysis using shape change. Several methods for tongue motion detection track the motion of these points. One area where success in cardiac imaging could inform tongue imaging is the estimation of point motion from contour change. If this can be done, these the two levels of analysis of tongue motion can be related to each other.

34 Final Comments Probabilistic approach gives principled solutions Generative approach works with simple models (no training) Discriminatory approach works with training sets Shape tracking is a proxy for motion of the endocardium Further work: Extend discriminatory approach to large heterogenous training sets Towards true drag and drop segmentation (speed) Dynamic shape analysis (shape grammar?) Shape motion vs. physical motion

35 Acknowledgements Yale: Students: Zhong Tao, Xiaoning Qian, James Beaty Post-docs: Yong Yue Faculty: Al Sinusas, Rob McNamara, Leslie Scoutt Univ. of Florida: Faculty: David Groisser, Yunmei Chen, Murali Rao Univ. Wisconsin: Faculty: Ernest Madsen Supported by grant R01 HL from NHLBI (NIH).

Level Set Evolution Without Re-initialization: A New Variational Formulation

Level Set Evolution Without Re-initialization: A New Variational Formulation Chunming Li 1, Chenyang Xu 2, Changfeng Gui 3, and Martin D. Fox 1 1 Department of Electrical and 2 Department of Imaging 3