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Gradient-Oriented Boundary Profiles for Shape Analysis Using Medial Features

Gradient-Oriented Boundary Profiles for Shape Analysis Using Medial Features. Robert J. Tamburo, BS Bioengineering University of Pittsburgh Under the Advisement of: George D. Stetten, MD, PhD U. Pitt. Bioengineering CMU Robotics Institute. Overview. Background Part I

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Gradient-Oriented Boundary Profiles for Shape Analysis Using Medial Features

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  1. Gradient-Oriented Boundary Profiles for Shape Analysis Using Medial Features Robert J. Tamburo, BS Bioengineering University of Pittsburgh Under the Advisement of: George D. Stetten, MD, PhD U. Pitt. Bioengineering CMU Robotics Institute

  2. Overview • Background Part I • Gradient-Oriented Boundary Profiles • Validation of Boundary Profiles • Background Part II • Boundary Profiles and Shape Analysis • Results on Synthetic and RT3D Ultrasound Data • Future Work • Conclusion

  3. Clinical Motivation • In 1999: • Cardiovascular Disease (CVD) contributed to one-third of worldwide deaths • CVD ranks as the leading cause of death in the U.S. responsible for 40% of deaths per year • 62 million Americans live with some form of cardiovascular disease • Americans were expected to pay about $330 billion in CVD-related medical costs this year *CDC/NCHS and the American Heart Association Causes of Death for All Americans in the United States, 1999 Final Data

  4. Image Analysis • Left ventricular (LV) and myocardial volume to calculate cardiac function parameters: - cardiac output - stroke volume - ejection fraction • Myocardial thickness and motion can be monitored • Diagnoses of CVD, including cardiomyopathy, arrhythmia, ischemia, valve disease, myocardial infarction, and congestive heart failure

  5. Medical Imaging • 2D ultrasound • 3D ultrasound • Gating to the electrocardiogram • Mechanically scanned • Cine-CT • 50 ms/slice (400 ms for full volume) • Real-time three-dimensional (RT3D) ultrasound • 22 frames/sec (45 ms)

  6. Goals • Automatically identify and measure structures RT3D ultrasound data • Develop “intelligent” boundary points: Gradient-Oriented Boundary Profiles • Apply to Profiles to a shape analysis routine

  7. Boundary Detection • First step in most Image Analysis routines • Convolution with kernel in spatial domain • High-pass frequency filters in frequency domain • Spatial domain detection: • is computationally less expensive • often yields better results

  8. Gradient Based Detectors • Gradient magnitude is rotationally insensitive • Gradient magnitude sensitive to: • object intensity • background intensity • overall image contrast

  9. Common Gradient Based Detectors • Roberts Cross • 2x2 kernel • Very sensitive to noise • Very fast • Sobel • 3x3 kernel • Somewhat sensitive to noise • Slower than Roberts Cross • Both amplify high-frequency noise (derivative)

  10. GradientBasedBoundary Detectors With Smoothing • Marr • Gaussian Smoothing • Laplacian of Gaussian • Canny • Gaussian smoothing • Ridge tracking • Both require multiple applications • Some fine detail lost

  11. Algorithm for Classifying Boundaries • Find candidate boundary points • Create an intensity profile • Fit a cumulative Gaussian to the intensity profile • Eliminate blatantly “bad” profiles • Calculate measures of confidence • Classify the boundary

  12. Difference of Gaussian (DoG) Detector • Gradient magnitude • Gaussian smoothing • Difference between 3 same-scale Gaussian kernels • Measures gradient direction components in 3D

  13. Finding Candidate Boundary Points • Over sample with small sampling interval • Apply gradient detector (DoG) • Accept those above pre-determined threshold

  14. Algorithm for Classifying Boundaries • Find boundary candidates • Create an intensity profile • Fit a cumulative Gaussian to the intensity profile • Eliminate blatantly “bad” profiles • Calculate measures of confidence • Classify the boundary

  15. Generating an Intensity Profile • Sample voxels in a neighborhood • Partition sampling region • Project voxels (splat) to the major axis

  16. Sampling Voxels • Ellipsoidal or cylindrical • Centered at boundary point • Major axis in direction of gradient • Reduces the effect of image noise

  17. Splatting Voxel Intensity • Triangular or Gaussian footprint • Store weights of contribution • Profile of average voxel intensity

  18. The Intensity Profile

  19. Algorithm for Classifying Boundaries • Find boundary candidates • Create an intensity profile • Fit a cumulative Gaussian to the intensity profile • Eliminate blatantly “bad” profiles • Calculate measures of confidence • Classify the boundary

  20. Fitting the Profile • Choice of function • Should parameterize boundary • Should be intuitive • Image acquisition blurs boundaries • Convolution with a Gaussian kernel • Step function becomes a cumulative Gaussian

  21. Real Boundary Image Acquisition Image Boundary Fitting the Profile cont.’d

  22. Derivation of Cumulative Gaussian

  23. Cumulative Gaussian A function of 4 parameters • Mean, m • Standard deviation, s • Asymptotic value for one side, I1 • Asymptotic value for other side, I2

  24. Boundary Parameterization • m- boundary location • s- boundary width • I1 - intensity far inside boundary • I2 - intensity far outside boundary

  25. Curve Fitter • AD Model Builder from Otter Research, Inc.* • Quasi-Newton non-linear optimization • Auto-differentiation • Rapid and robust *http://otter-rsch.com/admodel.htm

  26. Algorithm for Classifying Boundaries • Find boundary candidates • Create an intensity profile • Fit a cumulative Gaussian to the intensity profile • Eliminate blatantly “bad” profiles • Calculate measures of confidence • Classify the boundary

  27. Eliminating “Bad” Profiles • “Bad” – profile for which parameters are unacceptible • I1 or I2 is outside range for the imaging modality  • m is outside of the ellipsoidal sample region • These profiles are rejected and no longer considered

  28. Algorithm for Classifying Boundaries • Find boundary candidates • Create an intensity profile • Fit a cumulative Gaussian to the intensity profile • Eliminate blatantly “bad” profiles • Calculate measures of confidence • Classify the boundary

  29. Establishing Intrinsic Measures of Confidence • Based on location and width of boundary within sampling region • Place thresholds on measures of confidence • Accept high-confidence parameters

  30. Measures of Confidence for I1and I2 and

  31. Measure of Confidence for m • zmin = min(z1, z2) • Sufficient samples exist on both sides of m

  32. Algorithm for Classifying Boundaries • Find boundary candidates • Create an intensity profile • Fit a cumulative Gaussian to the intensity profile • Eliminate blatantly “bad” profiles • Calculate measures of confidence • Classify the boundary

  33. Classify the Boundary • Classify boundary with high-confidence parameters • Boundary is classified by: • Intensity on both sides of boundary • Estimate of true boundary location

  34. Application to Test Data • 3D data set • 8-bit voxels • 100x100x100 • Generated sphere • radius of 30 voxels • interior value of 32 • exterior value of 64

  35. Validation on Sphere • Ellipsoidal vs. Cylindrical sampling regions • Triangle vs. Gaussian footprints • Measures of confidence determined • Validation of improved boundary location

  36. Neighborhood Type Splat Type RMS Cylindrical Gaussian 0.092 Cylindrical Triangle 0.104 Ellipsoidal Gaussian 0.086 Ellipsoidal Triangle 0.078 Radius RMS Errors

  37. 95% of profiles estimate radius to less than 1 voxel

  38. 23% of points estimate radius to less than 1 voxel

  39. Boundary Points and Profiles 90 secs DoG boundary points Boundary profiles

  40. The distribution of error in estimating the intensity values on either side of the boundary as a function of m

  41. > 1.5 results in m error < 1

  42. guarantees A threshold of

  43. guarantees A threshold of

  44. Boundary profiles with high-confidence m estimates

  45. Medial-Based Shape Analysis • Medial axis by Blum • Medialness by Pizer • Robust against image noise and shape variation* • Stetten automatically identified LV and measured volume *Morse, B.S., et al., Zoom-Invariant vision of figural shape: Effect on cores of image disturbances. Computer Vision and Image Understanding, 1998. 69: p. 72-86

  46. b b 1 2 center Core Atom • Computationally efficient • Statistically analyzed to extract medial properties of the core • Require a priori knowledge of object intensity • Can not differentiate between objects of different intensity

  47. Core Profiles • Form independent of background intensity • Multiple objects of differing intensities can be found • Better boundary location

  48. Face-to-faceness is close to 1 is the orientation of the ith boundary profile Medial Requirements • Distance between boundary profiles within range

  49. where is an intensity tolerance Medial Requirements • Boundary profiles have high-confidence estimates • 1. • 2. • 3. • Constraint 3 is for homogeneous core profiles

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