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Segmentation of Tree like Structures as Minimisation Problem applied to Lung
Vasculature
Pieter Bruyninckx
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Overview
• Introduction– What is vessel segmentation– Lung anatomy and pathology
• State of the Art• Minimisation Approach• Discussion
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Introduction
• Vessel segmentation– Extracting vessels from an image (3D)– Multiple representations possible
• Hard: Centerline, border
• Soft: Probability
• Use general properties– Intensity range– Tubular shape– Tree like structure
• Connectedness
• Bifurcations
Pathological cases?
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Lung anatomy and pathology
• General Structure– Vessels
– Bronchi
• Common pathology– Mosaic Perfusion
• Pulmonary embolism
• Small airways disease
• Emphysema
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Overview
• Introduction• State of the Art
– Top-down (initialisation)• Single Vessel
• Tracking
– Bottom-up (no initialisation)• Vessel Enhancement Filter
• Tschirren
• Minimisation Approach• Discussion
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Top-down: Single Vessel
• Initialisation– Start and end-point
• Iteration– Optimal path
– Minimal energy
– Intensity, smoothness
• Challenges– Whole vessel tree?
[Wink2002]
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Top-down: Tracking
• Initialisation– Start point (tree root)
• Iteration– Centerline tracking
– More advanced• Region growing• Wave front propagation• Level sets
• Challenges– Handling bifurcations
– Mathematical framework
[Wink2000]
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Bottom-up: Vessel Enhancement Filters
• Soft segmentation =vessel enhancement:
– Improve hard segmentation– Improve visualization
• No initialisation• Single iteration
– Eigenvalues/vectors Hessian• Vesselness and orientation
– Multiresolution approach– Anisotropic filtering
• Challenges– Physical units?– Sensitive to noise (second
derivatives)[Frangi1998]
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Bottom-up: Tschirren
• Initialisation– Detection of probably-
vessel voxels (intensity)
– Compute orientation
– Classify: • vessel, junction, nodule
• Iteration– Join points into a tree
• Challenge– Rather ad hoc method
[Tschirren2005]
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Overview
• Introduction• State of the Art• Minimisation Approach
– Pre-processing– Initialisation– Iteration– Results
• Discussion
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Minimisation Approach
Initial vesselness
(intensity only)
Patient scan
Initial vessel orientation
(with uncertainty)
Final vesselness and orientation through energy optimization
Energy: function ofneighbourhood and
local vessel orientation and vesselness
Lung Segmentation
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Lung Segmentation
• Goal– Separate lung from other tissue
– Allow for intensity-based vessel segmentation
– Increased efficiency
• Implementation– Simple ad hoc algorithm
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Minimisation Approach
Initial vesselness
(intensity only)
Patient scan
Initial vessel orientation
(with uncertainty)
Final vesselness and orientation through energy optimization
Energy: function ofneighbourhood and
local vessel orientation and vesselness
Lung Segmentation
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Vesselness Initialisation
• Based on intensities only• First step
– Determine average and standard deviationof local background(10x10x10 mm³)
• Second step– Express vesselness as a ‘probability’ [0,1]
(function of background , and intensity)
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Vesselness Initalisation
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Vesselness Initialisation
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Minimisation Approach
Initial vesselness
(intensity only)
Patient scan
Initial vessel orientation
(with uncertainty)
Final vesselness and orientation through energy optimization
Energy: function ofneighbourhood and
local vessel orientation and vesselness
Lung Segmentation
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Initial Vessel Orientation
• Estimate– Orientation
– Uncertainty
• Method– Compute gradients
perpendicular orientation
– Hessian approach also possible
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Minimisation Approach
Initial vesselness
(intensity only)
Patient scan
Initial vessel orientation
(with uncertainty)
Final vesselness and orientation through energy optimization
Energy: function ofneighbourhood and
local vessel orientation and vesselness
Lung Segmentation
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Iteration: Energy Function
• Energy Function f– Energy ~ Vessel-likeness
internal energy EE( ) < E( )
– Energy ~ ‘distance’ to original distance DD( , ) < D( , )
1,0,1 DEf
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Iteration: Energy Function
Vv i
ii uvdwE 2,
2
vn
vnw
i
Ti
i
1,0,1 DEf
ni v
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Iteration: Energy Function
Vv i
ii uvdwE 2,
2
vn
vnw
i
Ti
i
1,0,1 DEf
2
2
2, m Tm T vvuuvud
d( , )
d( , )
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Iteration: Energy Function
• Distance function D– Extension of d
– gn: main directions (orthogonal) ( )
1,0,1 DEf
TTTv ggggggG 332211
Vv
vTjj GvvD
2
2
2
2
2, m Tm T vvuuvud
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Iteration: Energy Function
Vv
vTjj GvvD
2
2
1,0,1 DEf
No uncertainty
No certainty
Some uncertainty
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Optimisation: Method
• Possible approaches– Simulated annealing (SA)
• Slow
– Local alignment• Fast
• Global optimum?
• Proposed solution– Local everywhere– SA at ‘difficult’ locations
Best of both worldsIf difficult locations can be found
(high local energy)
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Results: 2D
original α = 0.1α = 0.4α = 0.6α = 0.8α = 0.9α = 0.95α = 0.99
1,0,1 DEf
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Results: 2D (detail)
original α = 0.99
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Visualisation: 3D
• Result: soft segmentation• Visualisation
– Volume rendering (Voxar3D)– Intensity = vesselness– (no orientation information)– Window/level
(can't see the wood for the trees)
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Results: 3D (Overview)
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Results: 3D (Detail)
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Overview
• Introduction• State of the Art• Minimisation Approach• Discussion
– Current challenges– Future Work
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Current Problems
• Bronchi– Tubular structures– Walls are likely
to be enhanced– Multiresolution needed?
• Speed– Processing time > 24 h
• Rewrite code partially in C• More efficient optimisation
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Current Problem: Discrete weights
• Current weights
– Influence of all neighbours Vessels get wider
• Discrete weights– Look at two neighbors– Smaller vessels possible– Better delineation– Efficient local alignment?
2
vn
vnw
i
Ti
i
1,0,1 DEf
Vv i
ii uvdwE 2,
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Future Work: Liver and Bronchi
• Liver vasculature– Complex tree like structure
• Arterial and venous
– More ‘noisy’ background
• Bronchi– Complex tree like structure– Intensity based classification difficult
• Low intense centre surrounded by high intense wall (partial volume artefacts)
– Multiresolution?
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Future work
• Multiresolution– Separation:
• Vessel wall Vessel
– Improve speed?
• Model extensions– Synchronous segmentation:
• Vessels and Bronchi
– Bifurcation detection
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Future Work
• Post processing– Multitude of information
• Vesselness
• Orientation
• (3 degrees of freedom / voxel)
– Advanced visualisation– Improved hard segmentation algorithms
• Validation
•
Minimisation Approach
State of the Art
Introduction
Discussion
Vessel segmentation Thank you for your attention
Questions ?
