Brain Surface Cortex Registration

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Brain Surface (Cortex) Registration

• Dr. Georgios Stylianou
• Computer Science and Engineering
• Cyprus College

This work was supported in part by the Arizona
Alzheimers Research Center
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Motivation

• Warping algorithms can
• Track temporal change and classify age-related,
  developmental and pathologic alterations in
  anatomy. Toga 99
• Measures of dilation, contraction, shearing and
  divergence of the cellular architecture may be
  computed locally from the warping field.
  Thompson 99

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Approaches

• Surface based
• Require segmentation and
• Reconstruction of the 3D surface
• Easier to validate
• Intensity based
• Directly on raw data
• Very hard to validate

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Brain mapping

• Problem
• Inter-subject non-rigid registration of the
  cortex with anatomical and biological validity.
• Input Two 3D surfaces (cortex) represented by
  triangulated mesh
• Output A warping field

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Methodology

• Use anatomical landmarks crest lines
• Partition the brain surface into meaningful
  regions
• Match (Coarse to fine) corresponding regions to
  create point pairs
• Use multilevel B-splines to iteratively compute a
  C2 continuous warping field.

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Crest Line - Example
Largest Curvature is maximum
Crest point
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Crest Lines- Examples
central sulcus
post-central sulcus
inf. frontal sulcus
sylvian fissure
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Which crest lines are used?

• We use only 3 crest lines corresponding to
• Central sulcus
• Post-central sulcus
• Inter-hemisphere fissure
• Why?
• Their position orientation guarantees unique
  partitioning

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2. Surface PartitionDiscrete Geodesic Voronoi
diagram

• Voronoi diagram (of points)
• Suppose we are given a set Sp1,p2,,pn of n
  points in space Rd. For each pi, the region
  R(Spi) contains all the points closer to pi than
  any other point in S and is called the Voronoi
  region of pi. This partition is called the
  Voronoi diagram of S.
• Geodesic Voronoi diagram (of curves)
• The geodesic Voronoi diagram of Sc1,c2,,cn,
  where ci are curves in R3 on a surface in R3,
  consists of regions R(Sci) that contain all
  points closer to curve ci than any other curve in
  S. The distance is the geodesic distance of a
  point p on the surface to the nearest point of ci.

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An Example of a Discrete Geodesic Voronoi Diagram
Boundary Line
Crest Line
Iso-Lines
A merely flat surface
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Create Pairs of Corresponding Regions
At this level We have only 3 regions
Corresponding Regions are Generated
by Corresponding Sulci
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Rigid Registration for Sulci Labeling

• Method Randomized Iterative Closest Curve
  (RICC)
• Registers 3D curves.
• Manually labeled on source brain
• Automatically labeled on target brains

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3. Region pairing
Overview
Flattening R3 -gt R2
R2 -gt R3
Generalized Barycentric Coordinates
Barycentric Search
R2-gt Rn-gtR2
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Flattening - Example 1
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Flattening - Example 2
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Optimization via Fine Matching
Matched Regions
Brain 2, Sentral Sulcus region
Brain 1, Sentral Sulcus region
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4. Warping usingMultilevel B-splines Lee et al.
95

• Uses uniform tri-cubic B-splines
• Coarse-to-fine deformation

. . .
4x4
5x5
7x7
i.e. (2i3) x (2i3) control points, i1,
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Evaluation
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Thank You!

• Questions?