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Diffusion-geometric maximally stable component detection in deformable shapes. Roee Litman , Dr. Alexander Bronstein, Dr. Michael Bronstein. The “Feature Approach” to Image Analysis. Video tracking Panorama alignment 3D reconstruction Content-based image retrieval. Non-rigid Shapes.

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diffusion geometric maximally stable component detection in deformable shapes

Diffusion-geometricmaximally stable component detection in deformable shapes

Roee Litman, Dr. Alexander Bronstein, Dr. Michael Bronstein

the feature approach to image analysis
The “Feature Approach”to Image Analysis
  • Video tracking
  • Panorama alignment
  • 3D reconstruction
  • Content-based image retrieval
problem formulation
Problem formulation
  • Find a semi-local feature detector
    • High repeatability
    • Invariance to (non-stretching) deformation
    • Robustness to noise, sampling, etc.
  • Add informative descriptor
the goal
The Goal

“Head+Arm”

take a shape

Detect (stable) regions

“Head”

“Arm”

“Upper Body”

“Leg”

“Leg”

more results
More Results

(Taken from the TOSCA dataset)

Horse regions +

Human regions

region description
Region Description

Distance = 0.44

Distance

= 0.34

Distance

= 0.02

Distance

= 0.08

Distance= 0.17

Distance = 0.25

region matching
Region Matching

Query

1st, 2nd, 4th, 10th, and 15th matches

3d human scans
3D Human Scans

Taken from the SCAPE dataset

scanned region matching
Scanned Region Matching

Query

1st, 2nd, 4th, 10th, and 15th matches

in a nutshell
In a nutshell…

The Feature Approach

for Images

Deformable Shape Analysis

Shape

MSER

MSER

Maximally Stable ExtremalRegion

Diffusion Geometry

mser in a nutshell
MSER – In a nutshell
  • Threshold image at consecutive gray-levels
  • Search regions whose area stay nearly the same through a wide range of thresholds
algorithm overview1
Algorithm overview
  • Represent as weighted graph
  • Component tree
  • Stable component detection
algorithm overview2
Algorithm overview
  • Represent as weighted graph
weighting the graph
Weighting the graph

In images

  • Illumination (Gray-scale)
  • Color (RGB)

In Shapes

  • Mean Curvature (not deformation invariant)
  • Diffusion Geometry
weighting option
Weighting Option
  • For every point on the shape:
  • Calculate the prob. of a random walk to return to the same point.
  • Similar to Gaussian curvature
  • Intrinsic - i.e. deformation invariant
weight example
Weight example

Color-mapped

Level-set animation

diffusion geometry
Diffusion Geometry
  • Analysis of diffusion (random walk) processes
  • Governed by the heat equation
  • Solution is heat distributionat point at time
heat kernel
Heat-Kernel
  • Given
    • Initial condition
    • Boundary condition, if these’s a boundary
  • Solve using:
  • i.e. - find the “heat-kernel”
probabilistic interpretation
Probabilistic Interpretation

The probability density for a transition

by random walk of length ,

from to

spectral interpretation
Spectral Interpretation
  • How to calculate ?
  • Heat kernel can be calculated directly from eigen-decomposition of the Laplacain
  • By spectral decomposition theorem:
auto diffusivity
Auto-diffusivity
  • Special case -
  • The chance of returning to after time
  • Related to Gaussian curvature by
  • Now we can attach scalar value to shapes!
weight example1
Weight example

Color-mapped

Level-set animation

algorithm overview3
Algorithm overview
  • Represent as weighted graph
  • Component tree
  • Stable component detection
benchmarking the method
Benchmarking The Method
  • Method was tested on SHREC 2010 data-set:
    • 3 basic shapes (human, dog & horse)
    • 9 transformations, applied in 5 different strengths
    • 138 shapes in total

Scale

Original

Deformation

Holes

Noise

quantitative results
Quantitative Results
  • Regions were projected onto “original” shape,and overlap ratio was measured
    • Vertex-wise correspondences were given
  • Overlap ratio between a region and its projected counterpart is
  • Repeatability is the percent of regions with overlap above a threshold
repeatability
Repeatability

65% at 0.75

conclusion
Conclusion
  • Stable region detector for deformable shapes
  • Generic detection framework
    • Vertex- and edge-weighted graph representation
    • Surface and volume data
  • Partial matching & retrieval potential
  • Tested quantitatively (on SHREC10)
thank you

Thank You

Any Questions?