Perspectives
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attention!
- Other connected operators, hierarchical partitions and viscous propagations.
- Faster computational implementation.
- Extension to color images.
An attribute or combination of several attributes can be used as well.
Multi-scale: lambda-flat zones and shape attributes do not depend on the object size.
Connected operator: lambda-flat zones do not create new contours on the image.
disadvantages
- Chaining effect due to transition regions.
- Prior knowledge to select attribute and stopping strategy.
Attribute controlled reconstruction and
adaptive mathematical morphology
Slow:
On a centrino 2.4GHz laptop:
- For a 255x255 image
- Approx. 5 seconds to compute SE.
- Approx. 300 ms to compute an opening .
No size parameter is required in order to determine the adaptive region.
Auto-dual: bright, dark and intermediate gray level regions are processed at the same time.
Disadvantages
Advantages
Andrés Serna and Beatriz Marcotegui
State of the Art
Introduction
Morphological Amoebas
(Lerallut, Decencière and Meyer)
(Gordon and Rangayyan, 1984)
- Perspective-adaptive SE (Beucher, 1987)
- Structuring functions
(Serra, 1988)
- Morpho bilateral filtering and Adaptive MM (Angulo and Velasco-Forero)
- Region growing SE (Morard, Decencière and Dokladal)
Using adaptive-SE shape to characterize the image
CMM - Center for Mathematical Morphology
MINES ParisTech, France
A simple threshold can be used to extract objects of a given shape.
80s
90s
Conclusions
2007
2009
2011
- 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.
ISMM2013
- Anisotropic diffusion theory (Perona and Malik, 1990)
- Adaptive SE in range imagery (Verly and Delannoy, 1993)
Angulo, Velasco-Forero, Curic, Luengo, and others...
- General approach of adaptive MM (Pinoli and Debayle)
- Important remarks (Roerdink)
- An overview (Maragos and Vachier)
Introduction
Conclusions
&
Perspectives
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.
Our contribution
Using adaptive-SE shape to characterize the image
Other works
- 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.
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.
Feature image (elongation)
Applications
Background
3. Feature Extraction
Flat zones
- Connectivity relation induced by the equality of gray-level.
- Maximal connected components of constant gray-level, called flat-zones
Lambda-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.
Computing attributes on those regions...
Non-increasing
attributes
Increasing
attributes
Attribute controlled
reconstruction
- Perimeter
- Circularity
- Geodesic diameter
- Geodesic elongation...
Quasi-flat zones (lambda=15)
- Area of the object.
- Volume of the object.
- Perimeter of the convex hull...
Geodesic Elongation E(X):
Geodesic diameter L(X):
2. Adaptive Mathematical Morphology
Input-adaptive MM:
ISMM2013 - 11th International Symposium on Mathematical Morphology
May 27–29 2013, Uppsala, Sweden
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.
Pilot image Ip
Erosion
- Original or filtered image.
- SE computed on this image.
- SE must be the same for successive operators.
- Idempotence property of morphological filters.
Adjunct dilation
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
Opening
- Using these algorithms, it consists in applying an erosion followed by a dilation using the same SEs in both cases.
Attribute controlled reconstruction
1. Image Segmentation
Propagation on lambda-flat zones
- Our idea comes from the reconstruction of an object from a marker
- Propagation by lambda-flat zones:
Input (Pilot)
image
Input image
Maximum attribute (Elongation)
Controlled propagation from each pixel
lambda=1
lambda=4
lambda=8
lambda=14
Classic opening (size 1):
Our adaptive opening
(Maximum attribute: Elongation):
Defining adaptive SE (maximum attribute: elongation)
Segmentation of connected objects:
3D urban analysis
Input (Pilot)
image
When should propagation be stopped?
Attribute rupture: Elongation
Advantages of an attribute controlled propagation?
attribute rupture mean gray-level
Attribute evolution
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
Defining adaptive SE (attribute rupture: mean gray-level)
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!