1 Skeletal Models Correspondence: Improved Interface, Organization, and Speed Clients: Prof. Stephen Pizer Comp. Sci. Grad Students University of North Carolina, Chapel Hill

2  Disease diagnosis based on shape  Neuroscience:  How do diseases change shapes of brain structures?  How does shape change with normal brain development?; how does that explain learning?  How to extract structures from medical images in treatment planning and delivery Importance of Statistics on Anatomic Shape A hippocampus, an important brain structure Shape differences between schizophrenic and typical hippocampus

3  One of the best model types for statistics is the skeletal model  S-reps  Sheet central to object, plus spokes covering object interior  Discrete spokes with spoke interpolation to yield “continuity” Statistics are done on object models Mean hippocampus, schizophrenics Mean hippocampus, controls Lateral cerebral ventricle

4  Input: a set of many s-reps (the object for different individuals)  Output: new s-reps with shifted spokes making variation tighter  Code exists for making this correspondence improvement Effective S-rep Statistics Requires Spoke Correspondence

5  Awkward to use  User must understand many subfunctions  Command line  Consists of many routines  Some in Matlab, some in C++, some in Python  Some from standard libraries, some within other programs, some for this special objective  Ridiculously slow  A week for a few tens of models as input  But real inputs have a few hundred models  Presently available data  30 cerebral ventricle s-reps  Simulated ellipsoid s-reps The Present Code’s Properties

6  Read s-reps (.m3D format) -- Python  Interpolator -- C++ within Pablo  Main control code producing objective function to be optimized – Matlab  2 optimizers – from standard packages  Statistics of s-reps modules  Our method for non-Euclidean statistics – many Matlab functions  Changing features back to s-reps after statistics – Matlab or C++  Principal Component Analysis: standard stats from std pkg  Spoke regularity calculators – Matlab  Display functions (extracted from Pablo) -- VTK The Present Code’s Components

7  Good user interface  Rationalize and document code  For users  For later developers  Speed up  Use better language  Parallelization  Use parallel computer The Project Objective

8  Not needed by most team members  High level mathematics and statistics  Geometric understanding  Needed  Understand multiple languages  One team member needs VTK (graphics pkg) knowledge  One team member needs some math and statistics understanding Background Needed and Not Needed

9  Your work will help patients ultimately  Your work will help neuroscience  Your work will help researchers in shape statistics  It is good practice in a common software task: turning first-try code into a usable package Why Choose This Project

10 For more information A paper by Liyun Tu, Jared Vicory et al. on this topic: Entropy-Based Correspondence Improvement of Interpolated Skeletal Models (submitted for publication) is available by to Many related papers (esp. one on s-rep fitting by Pizer et al. and ones on s-rep statistics by Jung) can be found at

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12 MIDAG Preprocessing for Fitting S-reps into Signed Distance Images Alignment of cases –Weighted Procrustes on skeletal and spoke end points Weights = # of incident spokes Getting correspondence of spokes –Shift spokes along skeleton to tighten p(s-rep) Requires function p(s-rep)! –Methods Now: fit from common initialization: population mean, and across common modes of variation; then refine spoke lengths In development: Optimal entropy on spokes Regularity of spokes (in volume) Tight probability distribution on features

13 Other Brain Structures than Hippocampus Lateral ventricles Under study Quasi-tubular structures Developing spoke-shifting correspondence via entropy [Tu] Finding whether present results repeatable on other structures and other diseases is needed