REGIONS INEL 6088 Computer Vision Ref. Jain et. al. Ch. 4 - - PowerPoint PPT Presentation

REGIONS

INEL 6088 Computer Vision

• Ref. Jain et. al. Ch. 4

SEGMENTATION BY
 REGION SPLITTING AND MERGING

Segmented image RAG Dual of RAG

RAG MATLAB EXAMPLE

Link to sample code

RAG MATLAB EXAMPLE

Link to sample code

distance function watershed

RAG MATLAB EXAMPLE

Link to sample code

How do we judge if two regions are similar?

• If the difference of their mean gray level is less than some

predetermined value

• If the regions are statistically similar. It is assumed that

H0: if the two regions belong to the same object, the intensities are drawn from a single Gaussian distribution with mean µ0 and variance σ02 H1: if the two regions belong to different objects, they belong to two different Gaussian distributions with parameters (µ1,σ12) and (µ2,σ22).

Normal distribution Normal distribution parameters: for n pixels Gray levels are represented by gi

Use previous definition to find σ using the m1+m2 pixels. Assumption H0: if the two regions belong to the same

• bject, the intensities are drawn from a single Gaussian

distribution with mean µ0 and variance σ02. If we assume H0, the joint probability density:

To determine if the two regions should merge, find the likelihood ratio Merge if L is below some threshold. Assumption H1: if the two regions belong to different

• bjects, they belong to two different Gaussian

distributions with parameters (µ1,σ12) and (µ2,σ22).

MERGING BY REMOVING WEAK EDGES

Combine regions if boundary between them is weak.

• Pixel intensities in the two sides of a weak boundary

differ by less than some amount T.

• Boundary length must also be taken into account.

Merge regions R1 and R2 if : W = length of weak part of the boundary S = minimum of the perimeters of the two regions τ = threshold (0.5 is a good heuristic value) Do not merge merge

Another method: redefine S as the common boundary Do not merge merge

Left: weak boundary is small compared to the total common boundary

REGION SPLITTING

Var = σ2 = Pn

i=1(xi − ¯

x)2 n

Possible ways of finding a boundary:

• Use edge strength
• Regular decomposition methods: divide

region into a fixed number of equal-sized regions.

• See quad-tree representation. Modify to

use in grayscale images (see text) Region splitting is usually more dificult that merging.

P(R) = { 1 if the variance is small 0 otherwise

REGION GROWING

REGION GROWING

REGION GROWING

REGION GROWING

REGION GROWING

Start with a set of “seed” regions, then expand the regions if they satisfy some constrain. Textbook example: homogeneity predicate is based on fitting a planar or biquadratic functions (m between 0 and 2, included) to the gray values: Homogeneity:

Algorithm 3.8: Region Growing Using Planar and Biquadratic Models (cont)

• Step 2 tries to avoid the effect of outliers – algorithm is

very sensitive to outliers

• One approach to find the seed regions is to use a

conservative threshold

• Another approach is to partition the image using domain

knowledge

REGION REPRESENTATION

Array representation

• Labeled images - use an array of the same size as the original

image to indicate the region to which each pixel belongs.

• Overlays - use binary masks to define each region

Other representations

• Hierarchical representation – use many different resolutions

to represent an image

• Symbolic representation – enclosing rectangle, moments, Euler

numbers

• Boundary coding – use region boundaries

ARRAY REPRESENTATION (LABELING)

(a) binary image (b) connected components

ARRAY REPRESENTATION
 (OVERLAYS)

HIERARCHICAL REPRESENTATIONS USING PYRAMIDS

Contains the n×n image plus k reduced versions (levels). Fits into a linear array of size 2(22×level).

• Emphasise inclusion of a

region inside another region.

• Constructed by recursively

splitting an image into component parts.

• Stops when regions have

constant characteristics.

BINARY TREES

Quad Trees Representation

• Obtained by recursively

splitting of an image into 4 subregions.

• If all points in a subregion are

either black or white then that subregion is not further split and the subregion is marked as black

• r white.
• Regions with both 0 & 1 are

considered “gray” and can be further split.

• Each node is either a leaf node
• r have four children.
• Process is stopped when there

are no further gray regions.