**Introduction**

**Attribute controlled reconstruction and**

adaptive mathematical morphology

adaptive mathematical morphology

**Background**

**Attribute controlled**

reconstruction

reconstruction

**CMM - Center for Mathematical Morphology**

MINES ParisTech, France

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

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

&

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.