1. Segmentation of Single-Figure Objects by Deformable M-reps
Stephen M. Pizer, Sarang Joshi, P. Thomas Fletcher, Martin Styner, Gregg Tracton, James Z. Chen, Edward L. Chaney
Medical Image Display & Analysis Group, University of North Carolina, Chapel Hill
M-reps Models and Segmentation Algorithm
Objective Function at Each Scale Level (stage) k
Object Modeling
via M-reps
Legend for objective function
m: deformed model candidate, m: medial atom
mk, bk: model & implied boundary for k+1th stage
a: geometric typicality weight (~spring constant)
Figure is represented by grid of medial atoms
= a  geometric typicality geometry to image match
(u2,v2,t2)
(u1,v1,t1)
Geometric typicality = vs model
(at last 2 stages)
vs neighbors in , where d/r is object-width-
proportional distance of implied boundary point to
figurally corresponding model boundary point
Hippocampus model and implied boundary
Internal atoms Crest (end) atoms Medial atoms
Figural boundary- point correspondence for geometric typicality
Tradeoff between geometric typicality and geometry to image match
Geometry to image match = within-mask normalized correlation with template at figurally corresponding points along boundary profiles
a) Gaussian derivative template for mostly high
contrast boundaries
b) Gaussian weighted training image template for other boundaries
Kidney model and implied boundary
Is trained algorithmically from some tens of training segmentations [Styner 2001]
Mask for geometry to image match
Figural point correspondence within mask
Profile of Gaussian derivative template
Cross-section of training image template for hippocampus
Deformable M-reps Segmentation
Manually place, scale, and elongate model on target image to produce 1)
Stage
Axial, sagittal, and coronal target image slices
Grey curve: boundary implied by m1 on slice
White curve: boundary implied by m2 on slice
Grey curve: boundary b2 on slice
White curve: boundary b3 on slice 3)
Until convergence, pass through all medial atoms in , for each optimizing to produce and thus implied boundary
Until convergence, pass through all boundary tile vertices in , for each optimizing to produce
Axial, sagittal, and coronal target image slices
Grey curve: boundary implied by m0 on slice
White curve: boundary implied by m1 on slice 2)
Find similarity transform plus elongation of that optimizes F to produce 4)
Results: On Kidneys in CT: ~ human in robustness and accuracy
Other results
Kidney results from CT
Median case, right kidney
Among best cases, left kidney
Stage 1 hippocampus results from MRI via training image template Top: vs MR image. Bottom: vs manual segmentation
Cerebral ventricle from MRI
Sagittal Coronal
Sagittal Axial Coronal
Sagittal
Coronal
Robust over all 12 kidney pairs. Speed: 2-3 minutes on PC
Average distance to human segmentation’s boundary (over boundary
and over all cases)
From another human: 1.1 mm
From m-rep boundary: 1.8 mm (measured),
but less due to biases of measurement process
Conclusion: Clinically acceptable agreement with humans
Additional Conclusions
No significant difference between segmentations of left and right kidneys
Locations where m-rep disagrees with humans are locations where humans
disagree with each other
Quantitative comparison to human performance
Performance for selected cases: interboundary distances in mm
avg, m-reps vs human avg, human vs human 3rd quartile, m-reps vs human 3rd quartile, human vs human
Among best cases
Median case
Among worst cases
The Critical Ideas
Coming Attractions, Well on Their Way
Multifigure cerebral ventricle m-rep
Male pelvis object complex m-rep
Object complex
Object , then figures
Medial atom (figural section)
Boundary section
Spatial correspondence through figural coordinates
Segmentation of multifigure objects
Segmentation of multi-object complexes
Statistical geometric models
Statistical intensity templates
Multimodality intensity templates
Penalty against implied boundary folding
Multiscale, figure-based operation
Acknowledgments: Brain image data provided by Guido Gerig. This work was carried out under the partial support of NIH grant P01 CA Some of the equipment was provided under a gift from the Intel Corporation.