MULTISCALE MORPHOLOGICAL SEGMENTATION OF GRAY-SCALE

IMAGES

PRESENTED BY :-ASTHA SHARMA

09302261

Segmentation +Morphological+Multiscale

• Segmentation : Decompose an image domain into a number of disjoint regions so that the features within each region have visual similarity , strong statistical correlation

and reasonably good homogeneity. • Morphology : It is set theoretic, shape oriented

approach which treats the image as a set and the kernel of operations, commonly called as Structuring Element (SE) as another set .

• Multiscale Techniques: They extract scale specific information from the image and integrate them to produce desired output.

Gray-scale Morphology Operation• Dilation of a gray-level image g(r,c) by a two dimensional point

set B is defined as:

• Erosion of a gray-level image g(r,c) by a two dimensional point set B is defined as:

• Opening (closing) is sequential combination of erosion (dilation) and dilation (erosion).

Multiscale Opening and Closing• Structuring element B takes care of the shape of the features

while processing the image but cannot treat objects of same shape but of different size equally.

• Thus, for processing objects based on their shape as well as size , a second attribute is incorporated to structuring element , which is its scale.

• Multiscale opening and closing is defined as:

where ‘n’ is an integer representing the scale factor of the structuring element B

Multiscale Morphological Operation

• Multiscale Morphological Operation decompose the given image into a set of filtered images.

• The multiscale opening produces flat regions by removing bright objects or its parts smaller than the SE. The properties:

• No new bright feature is generated at higher scales due to opening. Similarly is for closing i.e no new dark feature is formed.

• The SE leaves the features larger than it unaffected.• However removal of parts of an object introduces new edges

or causes drifts of the existing edges. Therefore , we use filters termed as morphological multiscale opening and closing by reconstruction filters to avoid this problem.

Basic Idea

• A gray level image consists of both bright and dark object features , which in general, have a distribution wrt to size or scale.

• Basic objective of Segmentation algorithm is to isolate or sketch out the most optimal contours of these bright and dark features.

Fig (a): image of bright and dark balls of varying radii

Fig (b): multiscale morphologic-alSegmentatio-n

Theoretical Formulation

• A digital gray-tone image can be viewed as a intensity surface over a spatial coordinate system.

• If L = and • S = be the spatial coordinates of the pixels be the spatial coordinates of the pixels of the image. Then , digital image is

represented as a function ‘g’ defined by :

where size of image is r cN N

-(5)

• In the paper, they have used multiscale bright and dark top-hat transformation to extract scale specific bright and dark features.

• The bright top-hat image obtained by filtering by an SE of size ‘i’ contains all bright features smaller than ‘i‘ as:

• Similarly a dark top-hat or a bottom-hat transformation at scale ‘i‘

sieves out the dark features smaller than ‘i‘ as:

• the section of the bright and dark top-hat images at a threshold t are given by

Different types of similar components at two successive scale ‘i‘ and ‘i+1’.

• The proposed algorithm treats the subsets of all three categories at various scales. Accordingly, it constructs the following four point sets, corresponding to both bright and dark features:

Implementation• Segmentation Scheme is divided into 2 passes : 1) multiscale region extraction 2) selection of valid regions that contribute to final

segmentation .

Fig. The stages of proposed multiscale image segmentation algorithm.

1. PREPROCESSING• Here noise smoothing is done to reduce the

effect of undesired perturbations which might cause over- and under-segmentation.

• Very small scale details are usually considered as noise. So morphological method is used to smooths out noise .

• Main problem is to determine the size of SE.

2) PASS-1:MULTISCALE REGION EXTRACTION

2) PASS-1:MULTISCALE REGION EXTRACTION

3) PASS-2 : SELECTION OF VALID REGIONS THAT CONTRIBUTE TO FINAL SEGMENTS

(a) (input) image of skin lesions, (b) multiscale morphological segmentation

THANKYOU

APPENDIX:Morphological Multiscale Opening and Closing by Reconstruction

For i=1,2,3,………

• for all practical purposes iteration is terminated at an integer ‘n’ such that

• This stable output is termed as reconstruction by dilation and is denoted by