Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature...
Transcript of Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature...
![Page 1: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/1.jpg)
Multi-Scale Geometric Flow forSegmenting Vasculature in MRI:
Theory and Validation
Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi
Centre for Intelligent Machines
Montreal Neurological Institute
McGill University, Montréal, Canada
![Page 2: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/2.jpg)
Plan of the talk
• Problem and motivation• Previous work• Theory
– Extracting local shape information– Vesselness measure– Flux maximazing flow– Construction of the vector field– Multi-scale geometric flow
![Page 3: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/3.jpg)
Plan of the talk
• Experiment– Qualitative results and examples– Vessel extraction details– MRA and MRI image acquisition on the same
subject– Quantitative validation
• Discussions• Conclusions• Selected References
![Page 4: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/4.jpg)
Blood Vessel Segmentation
Input: 3D data sets (MRA, PD, GadoliniumMRI,…)
Output: Binary volume containing vascular tree
Useful?• Automatic (no manual slice by slice manipulation)• Image-guided neurosurgery• Pre-surgical planning• Clinical analysis
![Page 5: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/5.jpg)
What’s been done in the past
• Bullit – Aylward group• Frangi et. al.• Krissian et. al.• Lorigo – Westin et. al.• Vasilevskiy – Siddiqi
Work onangiographicdata sets ONLY(MRA and CTA)
![Page 6: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/6.jpg)
Problem
• These methods cannot be used on standard MRIvolumes such as PD
• Why?– Initialization based on thresholding original volume– No explicit tubular structure models– Not multi-scale– Based on the assumption that the gradient of the
original image is strong ONLY at vessel boundaries• FAILS for PD weighted volumes
![Page 7: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/7.jpg)
MRA vs PD
Phase-Contrast(PC)
Time-Of-Flight(TOF)
Proton Density(PD)
![Page 8: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/8.jpg)
Easier problem on MRA than PD
Consequence: Cannot base the segmentationonly on image intensity contrast
Needed: tubular shape model to constrain thesegmentation
Harder: Many dark->bright structures in PD otherthan vessels (white and gray matter)
Easier: Clear bright->dark contrast change inTOF and PC data sets
![Page 9: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/9.jpg)
Goal of our work
Propose a segmentation algorithm for standard MRIvolumes that overcomes limitations of existingmethods applied to MRA
If successful,• Vascular model available for surgical planning and
clinical analysis• Eliminates the need for an additional scan• Save time and burden on patient
![Page 10: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/10.jpg)
Extracting local shape information• We want to know the local behaviour of a 2D/3D image I• It is common to consider the Taylor expansion of an image
I in the neighborhood Δx of a pixel (2D) or a voxel (3D)x0
where
and
![Page 11: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/11.jpg)
Gradient operator
• Very very well-known and used everywhere• Its magnitude gives an edge detector• Its direction gives a normal to an implicitly
defined isosurface
![Page 12: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/12.jpg)
Hessian operator
• Usefulness is less known!• 2nd order derivatives encode the shape information
i.e. How the normal of an isosurface changes
![Page 13: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/13.jpg)
Eigen analysis of the Hessian
Finding e-values and e-vectors of the Hessian matrixis related to finding the direction with extremevalues of 2nd derivativesi.e. directions where there is extreme change in the
normal to the isosurface
e-vector corresponding to the smallest e-valueis the direction of the blood vessel locally
![Page 14: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/14.jpg)
Eigen analysis of the Hessian
![Page 15: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/15.jpg)
Eigen value classification
Key observations at locations centered withintubular structures:
1) smallest e-value (λ1) is close to zero
(low curvature along vessel)
2) other two e-values (λ2, λ3) are are high andvery close
(high curvature of the circular cross-section)
![Page 16: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/16.jpg)
Eigen value classification
![Page 17: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/17.jpg)
Frangi’s e-value ratios
• Three quantities are defined to differentiate bloodvessels from others:
![Page 18: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/18.jpg)
Frangi’s local structurediscrimination
max for blob-like max for vessel-like max for *-likezero for vessel-like zero for sheet-like zero for noise
![Page 19: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/19.jpg)
Multi-scale vesselness measure
max for blob-like max for vessel-like max for *-likezero for vessel-like zero for sheet-like zero for noise
![Page 20: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/20.jpg)
Multi-scale vesselness measure
• Designed to maximum along centerlines oftubular structures and close to zero outsidevessel-like regions
• Natural introduction of scale, σ. We computeentries of the Hessian matrix using derivatives ofLindeberg’s γ-parametrized normalized Gaussiankernels.
![Page 21: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/21.jpg)
After vesselness computation
We have:
• The local radius of the blood vessel whichcorresponds to the scale at which the maximumvesselness measure was computed
• The local orientation of the blood vessel givenby the e-vector corresponding to the smalleste-value
![Page 22: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/22.jpg)
Some Examples
![Page 23: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/23.jpg)
![Page 24: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/24.jpg)
![Page 25: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/25.jpg)
Vesselness map on PD
![Page 26: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/26.jpg)
Flux maximizing flowIdea:The inward flux of a vector field V through a closed curve (orsurface in 3D) S, given by an equation of the form
provides a measure of how well the normal vectors of thesurface are aligned with the vector field. A(t) is the surfacearea of the evolving surface.
![Page 27: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/27.jpg)
Flux maximizing flow (initial state)
![Page 28: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/28.jpg)
Flux maximizing flow (final state)
![Page 29: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/29.jpg)
Flux maximizing flow• It is used to direct the evolution of a curve so that the
normals of the curve are aligned with a given vector field.
Theorem (Vasilevskiy, Siddiqi PAMI 2002):if a closed surface S in 3D flows according to
then the inward flux through the boundary of the fixedvector field V increases as fast as possible. Here N is thenormal vector field of S.
![Page 30: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/30.jpg)
Choosing the vector field V
If we choose V to be1) Static (does not depend on evolving surface)2) Maximum along the surface of vessel boundaries
and zero outside vessel regions
Then we can use the flux maximizing flow to evolveseed points placed inside vessels.
• Seeds will evolve and cling to vessel boundaries
![Page 31: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/31.jpg)
Construction of vector field
• Natural choice: combination of vesselnessmeasure and gradient vector field
• Problem: vesselness measure is maximum oncenterline of vessels.
![Page 32: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/32.jpg)
Extending vesselness measure tovessel boundaries
We have local orientation and radius at every voxel
Distribute the vesselness to vessel boundaries => ϕ
![Page 33: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/33.jpg)
New vector field
1) The magnitude of ϕ is maximum at vesselboundaries and the ellipsoidal extensionperforms a type of local integration
2) The normalized gradient vector field of theoriginal image captures the direction informationwhich is expected to be high at boundaries ofvessels as well as orthogonal to them
![Page 34: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/34.jpg)
The multi-scale geometric flow
• The new vector field
• Expending the flux maximizing flow expression
![Page 35: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/35.jpg)
Properties of the flow
1) First term acts like a doublet term
2) Second term behave like a regularization term
3) No leaking because vector field is zero outsidevessel regions
![Page 36: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/36.jpg)
Implementation details
• Level set methods– Adaptive to topological change– Efficient, if original volume not too BIG!
• Use at most 3 MINC volumes at all time– MINC voxel loop is of great help!
• Obtain convergence in 5000 iterations in mostcases. Depends on initialization
![Page 37: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/37.jpg)
Some qualitative results
1) MRA (Anders Lassen)
2) Cropped portion of gadolinium enhanced MRI(Ingerid’s pre-operation scans)
3) Full PD weighted data set (ICBM subject 100)
4) Movie of segmentation on PD weighted volume
![Page 38: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/38.jpg)
MIP of MRA
![Page 39: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/39.jpg)
Initial seeds (t =0)
![Page 40: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/40.jpg)
t = 55
![Page 41: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/41.jpg)
t = 100
![Page 42: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/42.jpg)
t = 200
![Page 43: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/43.jpg)
t = 2000
![Page 44: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/44.jpg)
MIPs of gadolinium MRI
![Page 45: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/45.jpg)
Thresholding
![Page 46: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/46.jpg)
Our segmentations
![Page 47: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/47.jpg)
MIP of vesselness measure of thePD weighted MRI
![Page 48: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/48.jpg)
Blood vessel extractions
![Page 49: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/49.jpg)
Geometric flow in action
![Page 50: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/50.jpg)
Validation Experiment
• Image Acquisition of angiographic and non-angiographic on the same patient => ME!
• MRA• 3D axial Time-Of-Flight angiogram
(0.43mm x 0.43mm x 1.2mm)
• 3D axial Phase-Contrast angiogram(0.47mm x 0.47mm x 1.5mm)
• PD/T2-weighted dual turbo spin-echo (sagittal)(1 mm3)
![Page 51: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/51.jpg)
Image acquired
Phase-Contrast(PC)
Time-Of-Flight(TOF)
Proton Density(PD)
![Page 52: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/52.jpg)
Vessel extraction
• Registering and resampling all volumes in thesame space (0.5mm3 resolution)
volumes are HUGE!
• Crop common 259 x 217 x 170 region
• Run multi-scale geometric segmentation algorithm
![Page 53: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/53.jpg)
![Page 54: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/54.jpg)
Quantitative Validation
Alignment error: how well does the test dataexplains the ground truth data
• Take Euclidean DT of test data. Every voxelcontains the closest distance to vessel structure
• For every vessel label in ground truth, add up thetest data distances and compute the average
Results: average alignment error is 1mm!!!(PD is the test data and angiograms ground truth)
![Page 55: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/55.jpg)
![Page 56: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/56.jpg)
Kappa measure
Kappa coefficient: degree to which the agreementexceeds chance levels: 2a / (2a + b + c)
a = number of voxels agreeing in both volumei.e within 2 voxels each other (red labels)
b = number of vessel voxels only in ground truth(green labels)
c = number of vessel voxels only in test data(blue labels)
Results: kappa ~= 75%
![Page 57: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/57.jpg)
Ratio
a / (a + b)measures the degree to which the ground truth datais accounted by the test data.
Results:1) PD data accounts ~90% of the vasculature
segmented from either angiograms
2) ~30% of the vasculature obtained from PDdata are recovered from either angiograms
![Page 58: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/58.jpg)
Table of results
![Page 59: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/59.jpg)
Expected results???
• Resolution is higher in angiographic volumes• Should pick up smaller vessels
• MRA is designed to image blood vessels• Are the angiographic acquisition optimal?
• Visual examination of the PD data in fact showsstronger evidence for vessel of small size
![Page 60: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/60.jpg)
Phase-Contrast(PC)
Time-Of-Flight(TOF)
Proton Density(PD)
![Page 61: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/61.jpg)
Conclusions
• Our results suggest that the algorithm can beused to improve upon the results obtained fromangiographic data
• Promising alternative when MRA is not available.The PD-weighted MRI data are usuallly availablewhen planning brain tumor surgery
![Page 62: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/62.jpg)
What’s next
• Would be nice to go back in the scan andcompare GADO vs MRA vs PD
• Use this for other medical imaging problems– Ingerid’s vessel driven correction of brain shift– Other tubular structure detection… bone?– Suggestions?
![Page 63: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/63.jpg)
Selected references1) A. Vasilevskiy, K. Siddiqi. Flux maximizing geometric flows.
IEEE Transactions PAMI, vol. 24, 2002.
2) A. Frangi, W. Niessen, K.L. Vincken, M.A. Viergever. Multi-scale vessel enhancement filtering. Proc. MICCAI'98,pp.130-137, 1998.
3) K. Krissian, G. Malandain, N. Ayache. Model-baseddetection of tubular structures in 3D images. ComputerVision and Image Understanding, 80:2, pp. 130-171, Nov. 2000
THANK YOU!
![Page 64: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/64.jpg)
![Page 65: Multi-Scale Geometric Flow for Segmenting …Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: Theory and Validation Maxime Descoteaux, Louis Collins, and Kaleem Siddiqi](https://reader034.fdocuments.us/reader034/viewer/2022042110/5e8b6823db2e4c68927b6c1e/html5/thumbnails/65.jpg)
ϕ-distribution• We distribute vesselness measure at (x,y,z) to
every (x_e, y_e, z_e) on ellipsoid surface byscaling it with the projection on the cross-sectional plane.
• We define the superposition of the extensionscarried out independently at all voxels to be thescalar function ϕ.