Diffusion geometric maximally stable component detection in deformable shapes
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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

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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


Non rigid shapes

Non-rigid Shapes


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”


Deformation invariant

Deformation Invariant


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


Methodology

(The “how”)

Methodology


In a nutshell

In a nutshell…

The Feature Approach

for Images

Deformable Shape Analysis

Shape

MSER

MSER

Maximally Stable ExtremalRegion

Diffusion Geometry


Original mser matas et al

Original MSER (Matas et-al)


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


Mser in a nutshell1

MSER – In a nutshell


Algorithm overview

Algorithm overview


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:


Laplace beltrami eigenfunctions

Laplace-Beltrami Eigenfunctions


Deformation invariance

Deformation Invariance


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


Performance

Performance


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


Results

Results


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?


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