Date post: | 13-Jul-2015 |
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Semi-Automatic Vortex Extraction in 4D PC-MRI Cardiac Blood Flow Data Using Line Predicates
Authors: Benjamin Kohler Rocco Gasteiger Uta Preim Holger Theisel Matthias Gutberlet Bernhard Preim
Presented by: Subhashis Hazarika,
Ohio State University
Motivation
• Many Cardiovascular Diseases (CVD) can be detected based on the blood flow characteristics of the patients.
• The data collected by the 4D PC-MRI allows the quantitative and qualitative analysis of hemodynamics.
• This paper focuses on detection of vortex flow on the human aorta and pulmonary artery.
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Workflow
Data Acquisition & Pre-processing
Vortex Extraction (via local criteria)
Extended Line Predicates
Post-processing
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Workflow(1)
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Line Predicates
• Line predicate P is a boolean function mapping a point p of a pathline to true or false. [Salzbrunn et al.]
• Predicate filters out points that don’t lie within a certain interval. All remaining points (for which value was true) are called characteristic set.
• D is the domain of the flow field . I is the set of all temporal positions.
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Line Predicates(1)
• Basic Intuition : We can apply different set operation on CS to come up with hybrid line predicates.
• Classification of line predicates[Born et al.]:
Line based or Geometry Predicates :
• Depends solely on pathlines’ geometry e.g curvature
Derived or Flow Field Predicates :
• Depends on the underlying flow field parameters e.g velocity, local vortex criteria.
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Line Predicates(2)
• Mesh Predicate : e.g minimal distance of a point to the surface.
• Stream Predicate : depends on surrounding pathlines. E.g no. of pathlines weighted by their distance to each other can be used as density value.
• Sum Predicate :
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Line Predicates(3)
• Mean Predicate : assigns the avg value to each point. i.e, sum predicate divided by N.
• Smoothing Predicate : one- dimensional binomial filter with kernel size 3 in n iterations to the values along an integral line.
• Representation:
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Line Predicates(4)
• Threshold:
• Example:
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Pathline Integration and Vortex Extraction
• Initialization : Put the whole dataset in a segmentation mask with uniformly distributed seed positions.
• Vector Interpolation and Pathline Integration: Trilinear interpolation to get a vector in 3D flow field in one particular temporal position.
Quadrilinear interpolation for vectors in spatio-temporal domain.
• Jacobian Matrix Estimation: Calculation of a Jacobian Matrix for a whole voxel will deliver discontinuities at voxel
boundaries.
Hence use central differences of interpolated vectors, with offset corresponding to one voxel dimension.
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Pathline Integration and Vortex Extraction(1)
• Line Predicate 1 – Finding Vortices:
Leaves behind longer line segment.
Reduces non-swirling regions within a segment.
Fragmentation problem remains to an extent.
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Pathline Integration and Vortex Extraction(2)
• Line Predicate 2 – Refining the Vortex Shapes: Csdc
• Line Predicate 3 – Postprocessing: Cv
This the sum predicate of curvature values.
Proper threshold preserves long curved pathlines.
• Visualization:
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Comparison of Local Vortex Criteria
• Investigate which vortex criterion provides the best results.
• Quality Criteria: Fixed Minimum and Maximum.
Implicit Threshold.
Constant Vortex Core Values.
Correctness.
Helical and Vortical Flow.
Vortex Shape.
Pathline Quality.
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Comparison of Local Vortex Criteria(1)
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Comparison of Local Vortex Criteria(2)
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Comparison of Local Vortex Criteria(3)
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Comparison of Local Vortex Criteria(4)
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Summary
• Final parameters of the model used.
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Thank You
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