Where:
A12 22
B2(112 222)
C1222
2212
21222
ln(2P1) 1P2
One can solve for T
In the case 12 22 2
We can get
T12 2 lnP(2) 2 12 P1
5) Picture Tree: —— Emphasize region inclusion within another region. —— Recursively split an image into regions, and the process stops when no region can be further splitted (homogeneity predicate)
b) Split the region into 4 subregions, and represent them in 4 child nodes.
c) Check the color of each child node:
——if color is black or white, set node as “leaf node”, no further splitting.
S
1
2
3
4
1
2
3
4
Color of node:
wh.ia tellpixealrse"0" intheregi colo brla. cakllpixealrse"1" intheregi
gr.ayhavbeot"h0" and"1" pixels
Algorithm:
a) Set an image as a region, and represents it as a node in quad tree (0-level)
not want.
• Merge operation combines regions that are considered similar.
Algorithm:
a) Form initial regions in the image using thresholding, followed by clustering labeling (find connected components).
1. Region Representation
1) Array representation:
Given a region R in image S,
Its array representation A is:
A a[i,j]
[i,j]S, a[i,j] 1 0 io[fi,tj]hR e rw
In most application, we just simply threshold an image at intensity T where histograph has a valley, which can approximate optimal thresholding.
(3) Adaptive Thresholding
Course 4 Regions
Course 4. Regions
Def. of Region: A set of connected image pixels,
with similar properties. • similar gray level • similar color • similar texture so on ……
E (T ) P 2 E 1 (T ) P 1 E 2 (T )
T should be chosen such that
E(T)min
From
E(T) 0, T
Get
P 1p1(T)P 2p2(T)
Applying Gaussian distributions, get:
A2T B TC0
5)
by T
P=S/A.
Thus, wTe
P
set the value
p()d
of
threshold
at
0
ቤተ መጻሕፍቲ ባይዱ
6) such that
p( )
L
0 p( ) 1
(2) Optimal thresholding:
Suppose an image contain only two principal brightness regions and both obey Gaussian distribution in intensity.
3) Quad Tree (Quad =4)
nod e— s proo pfe re rtgyion Tr lein e ks — relabte io tw tnw s en o eon
Children: if a region S is partitioned into 4 sub region, in quad tree, each sub region node is call a child of the node of the original region.
2. Region Segmentation Suppose an image A is well segmented into n regions Ri, i=1,2,…,n, there must be:
n
Ri A
i 1
P ( R i ) True P ( R i R j ) False
they are similar. —— For the region that are similar, merge them and
modify the adjacency graph. d) Repeat step c) until no region are merged. Criteria for merge:
N N N N N N 1 1 22 44
Pixels value of upper layer image can be obtained by ——averaging the corresponding pixels of lower layer image, or ——subsampling (e.g. choose upper-left pixel value)
— same as binary image representation
— often be used as a mask over intensity image to select the region for proper processing.
2) Pyramids representation
s— common edge length
T — threshold, e.g. T=0.75
How to measure the weakness of an edge?
I —preset value
i.e., the gradient of image intensity.
3) Region Spliting:
b) Make an adjacency graph for the image .
c) For each region in the image, do the following steps: —— Consider it adjacent regions, and check whether
• Perform thresholding relating to the base level of intensity at the surface.
2) Region Merging
• Thresholding generates to many extra regions that we do
Where P(.) is homogeneity predicate measurement.
1) Thresholding:
2) (1) P-Tile Thresholing
3) If a pre-knowledge of object size S is given, the
4) area percentage of the object in image A can be got
The basic concept is to choose threshold T locally to against uneven distribution of image intensity (caused by uneven illumination in scene). • Partition an image into several regions . • In each region, choose threshold T at major valley of it histograph, and perform threholding in each region.
——if color is gray, go to step b). d) Stop if all nodes are either black or white.
4) Region Adjacency Graph: —— Emphasize the adjacency of regions —— node: region —— link: common boundary between regions.
Dark region: Bright region:
p1(Z)
1
(Zμ1)2
e 2σ12
2πσ1
p2(Z)