Taylor Goodhart

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Presentation 2

• Taylor Goodhart

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Who am I?

• Taylor Goodhart
• Junior / 21 / Dallas, TX
• Rice University Houston
• Computer Science
• Geometric Modeling
• Electrical Engineering
• Computer Engineering - VLSI
• Mathematics
• Topology
• Graph Theory

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History Future

• Past Research Log. Canonical Threshold of plane
  curve singularities
• Equi-threshold deformation space
• Computation
• Difficult to compute
• Bound and criterion for exactness
• Future
• PhD
• AI, Compression
• Defense Industry
• DARPA, Raytheon, TI

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Examples
xy-x6-y6 0
X4 x6y x2y3 y6 x3y4 0
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Overview

• Recode SPREF framework in C
• SPREF calculation
• Octtree construction
• Split / Merge
• Adjacency Graph

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SPREF Calculation

• SPREF is spline approximation of minimal energy
  path through volume
• Spline is a piecewise polynomial curve
• Fit spline to average flow of a subvolume
• Number of spline coefficients is parameterized

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Octtree Construction

• Octtree is a way of dividing a volume
• Each volume is divided into 8 sub-volumes
• Tree structures in C are much easier and
  intuitive than in Matlab
• Whoever inherits my code will be grateful

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Split / Merge

• For each sub-volume, calculate error of SPREF
• If error is significantly greater than sum of
  error of all children, use children
• Else merge children into larger volume

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In progress Adjacency Graph

• Goal Convert tree structure of Octtree into
  weighted graph representing adjacent volumes
• Graph is a set of vertices and edges
• Weights to be calculated according to angle
  between SPREF curves
• Formula for converting Octtree to adjacency graph
  is elegant
• Can be constructed using simple bitwise
  operations
• Find adjacent nodes in O( log n)

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Future

• Using adjacency graph, segment volume according
  to similar SPREF curves
• Establish criterion for distinguishing background
  from foreground
• Calculate spatial features within volume