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 Cine-CT
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. Gradient Based Boundary 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. Fitting the Profile cont.’d
Image Acquisition
Real Boundary
Image Boundary

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 *

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 I1 and I2

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

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

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

42. > 1.5 results in m error < 1

43. A threshold of
guarantees

44. guarantees
A threshold of

45. Boundary profiles with high-confidence m estimates

46. 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, : p

47. Core Atom Computationally efficient1 b 2
center
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

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

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

50. Medial Requirements Boundary profiles have high-confidence estimates1. 2. 3.
where is an intensity tolerance
Constraint 3 is for homogeneous core profiles

51. Medial Requirements Solid lines are homogeneous
Dashed lines are heterogeneous exhibiting lateralness

52. Basic Core Configurations

53. Measuring Medial Properties
Population of core profiles analyzed
Eigenvalues define dimensionality of the core
Eigenvectors define population orientation

54. Lambda Triangle
Constraints: 1. 2.

55. Hollow Sphere Models cardiac data To calculate volumes 3D data set
Left Ventricle
Myocardium
Epicardium
Endocardium
Hollow Sphere
Models cardiac data
To calculate volumes
3D data set
8-bit voxels
100x100x100
Hollow sphere
inner radius of 15 voxels (intensity of 32)
outer radius of 30 voxels (intensity of 128)
background of intensity 64

56. Hollow Sphere - Boundariesas
DoG Boundary Points
Boundary Profiles

57. Hollow Sphere – Core Profiles

58. Hollow Sphere - Medialness

60. Hollow Sphere – Core Profile Radii
The center of the sphere is at 0 and the center of the slab between the spheres is at 22.5

61. Hollow Sphere – Radius Errors
96% of the total profiles vs. 29% of the total DoG points estimated a boundary location within one voxel

62. Hollow Sphere – Core Profile Scale

63. Hollow Sphere – Volume Measures
Core atoms applied twice
Volume measures are both fairly accurate
Standard deviation of scales shows consistency

64. Concentric Ellipsoids
Models RT3D phantom
Determines expected
medialness
Illustrate non-parametric
volume measure
techniques

65. Concentric Ellipsoids – Profiles
Homogeneous Boundary Profiles

66. Concentric Ellipsoids – Medialness
Cylindricalness and slabness of concentric ellipsoids

67. Concentric Ellipsoids – Volume
2 proposed techniques
Rely on dense core profiles or medial node population

68. Search and Count Method
Construct ellipsoids around core profiles
Average intensity of core profile
Add voxel to volume count if within tolerance of average
Requires dense core profile population

69. Medial Region Fill Construct spheres around each medial node
Deform sphere to an ellipsoid in direction orthogonal to pop.
Expand ellipsoid until they collide with object boundaries
Count voxels within ellipsoid for volume measure

70. Real-Time 3D Ultrasound
Developed in the early 90’s at Duke University
Matrix array of transducer elements
Captures pyramid of data at approximately 22 frames per second
Rapid enough to acquire cardiac data throughout its cycle

71. RT3D Cardiac Phantom Phantom from OHSU Two latex balloons
Ultrasound Gel solution
between balloons
Water in inner balloon
Myocardium
C-mode slice
Left Ventricle
B-mode slices

72. RT3D Cardiac Phantom Homogeneous boundary profiles
Population of core profiles

73. RT3D Cardiac Phantom Two passes
Medial nodes found from long core profiles
Slabness found from short core profiles

74. RT3D Cardiac Phantom Single pass Applying constraints
Resulting medial nodes

75. Future Work Improve computational speed of profiles
Construct models from medial nodes
Compute volumes from models

76. Insight Toolkit (ITK) Sponsored by National Library of Medicine
Open-source registration and segmentation toolkit
Architecture for large datasets
Generic programming
Boundary profiles have been contributed

77. Conclusions Gradient-Oriented Boundary profiles:
accurately parameterize boundaries
improve the results of core atoms
can locate boundaries in noisy data
computationally expensive
Measures of confidence shown to eliminate low-confidence parameters

78. Acknowledgments Dr. Stetten Aaron Cois Damion Shelton Wilson Chang
Dr. Sclabassi
Dr. Li
And….

79. YOU!
YOU!