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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

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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

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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

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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

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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)

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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

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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

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

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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)

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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

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Algorithm for Classifying Boundaries 1. Find candidate boundary points 2. Create an intensity profile 3. Fit a cumulative Gaussian to the intensity profile 4. Eliminate blatantly bad profiles 5. Calculate measures of confidence 6. Classify the boundary

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

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

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Algorithm for Classifying Boundaries 1. Find boundary candidates 2. Create an intensity profile 3. Fit a cumulative Gaussian to the intensity profile 4. Eliminate blatantly bad profiles 5. Calculate measures of confidence 6. Classify the boundary

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

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

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

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The Intensity Profile

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Algorithm for Classifying Boundaries 1. Find boundary candidates 2. Create an intensity profile 3. Fit a cumulative Gaussian to the intensity profile 4. Eliminate blatantly bad profiles 5. Calculate measures of confidence 6. Classify the boundary

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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

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

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Derivation of Cumulative Gaussian

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Cumulative Gaussian A function of 4 parameters 1. Mean, 2. Standard deviation, 3. Asymptotic value for one side, I 1 4. Asymptotic value for other side, I 2

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Boundary Parameterization - boundary location - boundary width I 1 - intensity far inside boundary I 2 - intensity far outside boundary

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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

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Algorithm for Classifying Boundaries 1. Find boundary candidates 2. Create an intensity profile 3. Fit a cumulative Gaussian to the intensity profile 4. Eliminate blatantly bad profiles 5. Calculate measures of confidence 6. Classify the boundary

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Eliminating Bad Profiles Bad – profile for which parameters are unacceptible – I 1 or I 2 is outside range for the imaging modality – is outside of the ellipsoidal sample region These profiles are rejected and no longer considered

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Algorithm for Classifying Boundaries 1. Find boundary candidates 2. Create an intensity profile 3. Fit a cumulative Gaussian to the intensity profile 4. Eliminate blatantly bad profiles 5. Calculate measures of confidence 6. Classify the boundary

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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

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Measures of Confidence for I 1 and I 2 and

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Measure of Confidence for z min = min(z 1, z 2 ) Sufficient samples exist on both sides of

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Algorithm for Classifying Boundaries 1. Find boundary candidates 2. Create an intensity profile 3. Fit a cumulative Gaussian to the intensity profile 4. Eliminate blatantly bad profiles 5. Calculate measures of confidence 6. Classify the boundary

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

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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

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

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Radius RMS Errors Neighborhood TypeSplat TypeRMS CylindricalGaussian0.092 CylindricalTriangle0.104 EllipsoidalGaussian0.086 EllipsoidalTriangle0.078

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95% of profiles estimate radius to less than 1 voxel

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23% of points estimate radius to less than 1 voxel

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Boundary Points and Profiles DoG boundary pointsBoundary profiles 90 secs

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

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> 1.5 results in error < 1

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A threshold of guarantees

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A threshold of guarantees

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Boundary profiles with high-confidence estimates

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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

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Core Atom 1 b 2 b 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

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

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Medial Requirements Face-to-faceness is close to 1 is the orientation of the i th boundary profile Distance between boundary profiles within range

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Medial Requirements Boundary profiles have high-confidence estimates where is an intensity tolerance Constraint 3 is for homogeneous core profiles

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

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Basic Core Configurations

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

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Lambda Triangle Constraints: 1. 2.

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Hollow Sphere Left Ventricle MyocardiumEpicardium Endocardium 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

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Hollow Sphere - Boundaries as Boundary ProfilesDoG Boundary Points

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Hollow Sphere – Core Profiles

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Hollow Sphere - Medialness

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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

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

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Hollow Sphere – Core Profile Scale

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

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

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Concentric Ellipsoids – Profiles Homogeneous Boundary Profiles

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Concentric Ellipsoids – Medialness Cylindricalness and slabness of concentric ellipsoids

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

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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

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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

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Real-Time 3D Ultrasound Developed in the early 90s 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

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

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RT3D Cardiac Phantom Homogeneous boundary profilesPopulation of core profiles

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

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RT3D Cardiac Phantom Resulting medial nodes Applying constraints Single pass

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

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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

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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

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

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YOU!

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