Statistical Shape Analysis of Multi-object Complexes

1
Statistical Shape Analysis of Multi-object
Complexes
Kevin Gorczowski1, Martin Styner1,2, Ja-Yeon
Jeong1, J.S. Marron3, Joseph Piven2, Heather Cody
Hazlett2, Stephen M. Pizer1, Guido Gerig1,2 1
Department of Computer Science, 2 Department of
Psychiatry, 3 Department of Statistics University
of North Carolina at Chapel Hill
Summary We studied the ability to discriminate
between two populations based on features
extracted from 10 subcortical structures. For
our data of autistic and typically-developing
brains, volume and the radius of the m-rep shape
description performed best.
Introduction

• Most studies of shape limited to single objects
  1,2
• Neuroimaging studies interested in group
  differences 3,4
• Mental illness processes likely not isolated to
  single structures
• Methodology required to analyze multiple
  structures jointly

Fig. 3 Left Data samples from two populations
with separating axis and normal vector to axis.
Right Data projected onto normal vector of
separating axis, used as classification score.
Statistical Discrimination

• From training set, calculated normal of
  separating axis using distance weighted
  discrimination (DWD) 5
• Projecting test samples onto DWD normal gives
  classification score
• Ran 100 times using training sets of 32 samples
  (16 autism, 16 control), 38 test samples
• Classification accuracy percentage of 38 test
  samples correctly classified
• Mean classification score average projection
  onto DWD normal for runs in which sample was in
  testing set

Fig. 1 Left Sheets of medial atoms describing
subcortical structures. Right Implied surfaces
of subcortical structures medial descriptions.
Data

• Subcortical structures amygdala, caudate,
  hippocampus, globus pallidus, putamen. Total of
  10 structures (left and right).
• 46 autism and 24 typically-developing samples
  from a longitudinal, pediatric autism study
• Scans at age 2 and age 4 (23 autism subjects, 10
  control)
• Corrected for uneven gender distributions (autism
  samples heavily weighted towards males) by
  subtracting gender-specific mean

Fig. 4 Average classification accuracy
(percentage of 38 test samples correctly
classified) over 100 runs using different
training and testing sets.
Fig. 2 Left Object set after global alignment
without scaling. Center Global alignment with
scaling, local pose differences remain. Right
Object set after global and local alignment.
Feature Extraction
Shape Used the medial representation (m-rep).
Deformed template model to fit manual
segmentations. Describes objects as a sheet of
medial atoms. Atoms have elements position,
radius, and normal vectors to surface
boundary. Pose Object sets first aligned jointly
(global) to remove image scan differences. Then
individual objects aligned (local) to extract
relative pose changes. Parameters of local
alignments (translation, rotation, scale) used as
pose features. Volume Volumes of individual
objects computed from m-rep shape description
before any alignment. Feature Dimensionality
Volume - 10, Pose - 70, Shape - 1890
Fig. 5 Left Distributions of mean
classification scores using volume. Right Using
only radii of m-rep shape description.
Conclusions

• Joint analysis of multiple objects using
  statistical discrimination
• Exploration of different features extracted from
  object sets
• Volume and local width (m-rep radii) give best
  performance for our application

Funding provided by NIH NIBIB grant P01EB002779
and NIH Conte Center MH064065. MRI images and
expert manual segmentations funded by NIH RO1
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June 2007, CVPR 2007