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ISMM2013

Attribute controlled reconstruction and adaptive mathematical morphology
by

Andres Serna

on 12 December 2014

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Transcript of ISMM2013

Introduction
Attribute controlled reconstruction and
adaptive mathematical morphology

Background
Attribute controlled
reconstruction

CMM - Center for Mathematical Morphology
MINES ParisTech, France

Andrés Serna and Beatriz Marcotegui
State of the Art
First adaptive SE
(Gordon and Rangayyan, 1984)
Perspective-adaptive SE (Beucher, 1987)
Structuring functions
(Serra, 1988)
80s
2007
Anisotropic diffusion theory (Perona and Malik, 1990)
Adaptive SE in range imagery (Verly and Delannoy, 1993)
Morphological Amoebas
(Lerallut, Decencière and Meyer)
90s
General approach of adaptive MM (Pinoli and Debayle)
Important remarks (Roerdink)
An overview (Maragos and Vachier)
2009
Morpho bilateral filtering and Adaptive MM (Angulo and Velasco-Forero)
Region growing SE (Morard, Decencière and Dokladal)
2011
Angulo, Velasco-Forero, Curic, Luengo, and others...
ISMM2013
ISMM2013 - 11th International Symposium on Mathematical Morphology

May 27–29 2013, Uppsala, Sweden

Applications
Introduction
In MM, SE are used to define relations between pixels.
Powerful non-linear algorithms.
Square and Hexagonal SE are preferred.
How to adapt these algorithms according to intrinsic variability and a priori knowledge of the data?
Adaptive SE is an elegant solution using non-fixed kernels.
Lambda-flat zones
Connectivity relation induced by the equality of gray-level.
Maximal connected components of constant gray-level, called
flat-zones
Flat zones
A less restrictive connectivity relation can be defined adding a
threshold lambda
.
It allows to connect adjacent pixels if their gray-level difference does not exceed lambda.
Original
Flat zones
Quasi-flat zones (lambda=15)
Area of the object.
Volume of the object.
Perimeter of the convex hull...
Perimeter
Circularity
Geodesic diameter
Geodesic elongation...
Geodesic diameter L(X):
Geodesic Elongation E(X):
Attribute controlled reconstruction
Propagation on lambda-flat zones
lambda=1
lambda=4
lambda=8
lambda=14
Conclusions
&
Perspectives

When should propagation be stopped?
Advantages of an attribute controlled propagation?
No size parameter is required in order to determine the adaptive region.

An attribute or combination of several attributes can be used as well.

This is useful when reconstructing objects with similar attributes on large databases
1. Image Segmentation
3. Feature Extraction
2. Adaptive Mathematical Morphology
Segmentation of connected objects:
3D urban analysis
Urban Scene
3D analysis
Propagation from markers
Range image: 2.5-D image
Maximum attribute (Elongation)
Input (Pilot)
image
Defining adaptive SE
(maximum attribute: elongation)
Controlled propagation from each pixel
Our adaptive opening
(Maximum attribute: Elongation)
:
Classic opening (size 1):
Input image
attribute rupture
mean gray-level
Input (Pilot)
image
Defining adaptive SE
(attribute rupture: mean gray-level)
Controlled propagation
Our adaptive median filter
(attribute rupture : mean gray level)
:
Input image
Using adaptive-SE shape to characterize the image
For
each pixel x on the input image
do
:
Compute
the SE shape using the attribute controlled propagation starting from x
Set
the output pixel x to the attribute value at which the propagation has been stopped.
Using adaptive-SE shape to characterize the image
A simple threshold can be used to extract objects of a given shape.
Input image
Feature image
(elongation)
Chaining effect due to transition regions.
Prior knowledge to select attribute and stopping strategy.
Auto-dual:
bright, dark and intermediate gray level regions are processed at the same time.
No size parameter is required
in order to determine the adaptive region.
Connected operator:
lambda-flat zones do not create new contours on the image.
An attribute or
combination of several attributes
can be used as well.
Advantages
We present a reconstruction controlled by the evolution of a given attribute during propagation from markers.
Three applications are presented:
Image segmentation
Input-adaptive mathematical morphology
Feature extraction.
Disadvantages
Conclusions
Slow:
On a centrino 2.4GHz laptop:
For a 255x255 image
Approx. 5 seconds to
compute SE
.
Approx. 300 ms to
compute an opening
.
disadvantages
disadvantages
Our idea comes from the reconstruction of an object from a marker
Propagation by lambda-flat zones:

Intuitively, the evolution of an attribute could be useful to make the decision.
Maximum attribute:
to select the propagation such that the attribute is maximum.


Attribute rupture:
to select the propagation such that the attribute change between two consecutive lambda is maximum.
DO NOT use for increasing attributes!
Attribute rupture: Elongation
For
each pixel on Ip
do
:
Compute
the SE shape using the attribute controlled propagation starting from
Compute
the minimum M of the pixels in
Set
the output pixel to the value M
Input-adaptive MM:
Pilot image Ip
Using these algorithms, it consists in applying
an erosion followed by a dilation
using the same SEs in both cases.
Original or filtered image.
SE computed on this image.
SE must be the same for successive operators.
Idempotence property
of morphological filters.
Erosion
For
each pixel on Ip
do
:

Compute
the SE shape
For
each pixel y in
do
:
Set
:
Adjunct dilation
Opening
I_out(y)=max(I_in(y), I_in( ))
Attribute evolution
Geodesic paths
Geodesic arc
Geodesic Diameter
3D point cloud
Perspectives
Other connected operators, hierarchical partitions and viscous propagations.
Faster computational implementation.
Extension to color images.
Thank you for your
attention!
Our contribution
Other works
Our work
Require to select one or several parameters:
sizes, attributes, probability distributions,...
Only requires to select an
appropriate attribute
according to structures in the image.
Computing attributes on those regions...
Increasing
attributes
Non-increasing
attributes
Amoeba median
(lambda=2, radius=20)
Multi-scale:
lambda-flat zones and shape attributes do not depend on the object size.
Our attribute controlled propagation is computed for each pixel on an pilot image.
These regions are used as adaptive SE for morphological or other non-linear operators.
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