SIEMENS

1
Unitialized, Globally Optimal, Graph-Based
Rectilinear Shape Segmentation - The Opposing
Metrics Method
Computer Science Department Carnegie Mellon
University, Pittsburgh Department of Imaging and
Visualization Siemens Corporate Research,
Princeton
Ali Kemal Sinop and Leo Grady
SIEMENS
asinop_at_cmu.edu, Leo.Grady_at_siemens.com
Main Idea
Weak boundary completion
Optimization
Globally optimal variational segmentation
requires two propreties 1) Ability to measure
shapeness of a segmentation 2) Ability to find
a segmentation that optimizes the shapeness
measure
Rectilinearity measure
For a given boundary P, measure rectilinearity as
the ratio
x binary indicator vector on nodes L1
Laplacian matrix of L1 graph L2 Laplacian
matrix of L2 graph
Kaniza square
gen. eigenvector
segmentation
Relax binary formulation to allow real values for
x Generalized eigenvector problem!
Merged circle/square
gen. eigenvector
segmentation
Threshold solution x at value producing
maximal ratio
for an intrinsic parameterization in terms of u
and v
For a segmentation on lattice, L1 and L2 boundary
metrics representable as cuts on weighted graph
Natural image results
Effect of resolution on measure
Per2 (P) 13.9
Per1 (P) 16
Q(P) 1
Graph formulation allows us to measure exact
dependence of shape descriptor on the number of
pixels comprising object
Q(P) .8536
Per1 (P) 16
Per2 (P) 11.8
Correctness