perceptual organization a mathematical approach based on scale, orientation and curvature remco...
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Perceptual Organization
A Mathematical Approach Based on scale, orientation and
curvature
Remco Duits
Perceptual Organization
:
The organization of
local image image
fragments into the global structure
3
Outline1. Scale Space
Repr.
2. Orientation Score
4
Part 1. Scale Space
The notion of scale :
5
Scale Space Theory
Axioms Gaussian scale space ? - NO !
Axioms
6
Scale Space Theory
Generator:
Gaussian SS:
Poisson SS:
7
Scale Space Theory
8
Deep Structure:Top-points:
9
Top-point Reconstruction
Gelfand TriplesSobolev/Traj. SpacesReproducing Kernels
10
If energy is norm on Hilbert space exact
solution is obtained by orthogonal projection :
11
Fast Top-point Reconstruction on large images,
cooperation with Frans Kanters, Bart Janssen :
Cooperation with Frans Kanters, Bart Janssen
12
Part 2. Orientation Scores
13
Reducible Generalization wavelet theory :
Stability Transformations :
14
Perceptual organization via orientation scores:
15
Processing on Orientation Scores
image score
processed score
processed image
Euclidean-invariant iff Left-invariant
16
Left-invariant Evolutions on :
17
Application Automatic Closure of Gaps:
Collision probability of forward and backward proces:
18
Orientation scores of 3D images
(Euler angles)
image orientation score
19
3D Proper Wavelets allowing stable inverse transform :
20
Line enhancement in 3D via invertible orientation scores
Application: Enhancement Adam-Kiewitz vessel
21
Robust orientation estimation
• (steerable) Tensor voting :
• Channel representations: