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 1.24 1.17 2.0 2.0 Median case 1.82 1.03 2.0 2.0 Among worst cases 2.72 0.79 2.0 4.0 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 CA47982. Some of the equipment was provided under a gift from the Intel Corporation.