1. Chap.8 Image Analysis
숙명여자대학교 컴퓨터과학과
최 영 우
2005년 2학기

2. Signal-to-symbol transformation/ Symbol-to-symbol transformation/
Image Analysis
Abstract
Extract usable global information from the image.
The image analysis operators extract useful information
Pixel value distribution
Classified pixels
Connected components
This is part of the middle level image interpretation and used for the high level image interpretation.
Signal-to-symbol transformation/
feature extraction
Symbol-to-symbol transformation/

3. Intensity Histogram (I)
Brief Description
A graph showing the number of pixels in an image at each different intensity value
This shows the distribution of pixels graphically.
Intensity
Count

4. Intensity Histogram (II)
How It Works
The image is scanned in a single pass and a running count of the number of pixels found at each intensity value is kept.
Guideline for Use
One of the common uses is to decide what value of threshold to use when converting a grayscale image to a binary one.
Original Image
Histogram
Thresholded Image

5. Intensity Histogram (III)
Example: Thresholding
There is a significant illumination gradient across the image (a), and it blurs out the histogram.
No longer possible to select a single global threshold that will neatly segment the object from its background.
Two failed thresholding segmentations are shown in (c) and (d).
(c) Threshold 80
(a) Illuminated
Image
(b) Histogram
(d) Threshold 120

6. Intensity Histogram (IV)
Example: Contrast Stretching
Contrast stretching takes an image in which the intensity values do not span the full intensity range and stretches its values linearly.
Histogram of (a) shows that most of the pixels have rather high intensity values.
Contrast stretching the image yields (b) which has a clearly improved contrast .
(a) Original Image
(b) Result of Contrast Stretching

7. Intensity Histogram (V)
Example: Histogram Equalization
The idea is that the pixels should be distributed evenly over the whole intensity range.
i.e. The aim is to transform the image so that the output image
has a flat histogram.
The values are much more distributed than in the original histogram and the contrast in the image was essentially increased.
(A) Original Image
(B) Result of Histogram Equalization

8. Classification (I) Brief Description
Analyze the numerical properties of various image features and organize data into categories.
Methods
Supervised classification
The example classes are specified by an analyst.
Unsupervised classification
The example is automatically clustered.
Analyst merely specifies the number of desired categories.

9. Classification (II) How It Works Two phases of processing
Training phase
Isolate characteristic properties of typical image features.
And, create a unique description of each classification category.
Testing phase
Classifies image features.
Classification method
Supervised classification
Statistical processes
Distribution-free processes
Unsupervised classification
K-means clustering

10. Classification (III)
The motivating criteria for constructing training classes
Independent
A change in the description should not change the value of another.
Discriminatory
Different image features should have significantly different description.
Reliable
All image features in a group should share the common description.
Example: Classification of bolts and sewing needles
using head diameter and length

11. Classification (IV) Minimum (mean) distance classifier
Suppose that each training class is represented by a prototype (or mean) vector:
where Nj is the number of training patterns from class wj.
M is the number of classes.
If Euclidean distance is used for proximity measure, the distance to the prototype is x2
Cluster
Centers
For j=1,2,…,M
mneedle = [ ]T
mbolt = [ ]T x1

12. Classification (V)
Decision function, dj(x), based on the Euclidean distance is:
Thus, the decision functions in this example are: x1 x2

13. Classification (VI)
The decision boundary that separates two classes is:
Thus, the decision boundary(or surface) is:
In practice, the minimum distance classifier works well, when the distance between means is large compared to the spread of each class. x1 x2

14. Classification (VII) Guidelines for Use
Example: Remote sensing application
Classify each image pixel into one of the several classes (e.g. water, city, wheat field, pine forest, cloud, etc.) based on the spectral measurement of the pixel.
Visual Image
of Globe
Infrared band Image

15. Classification (VIII)
Example: (continued)
Difficult to find a threshold or a decision boundary that segments the images into training classes (e.g. spectral classes that correspond to physical phenomena such as cloud, ground, water, etc.).
Having a higher dimensional
representation of this information
can provide segmentation of
regions which might overlap
when projected onto a single axis.
(i.e. using one 2-D histogram
instead of two 1-D histograms)

16. Visual Intensity levels
Classification (IX)
Example: (continued)
Combine them into a single two-band image and find a decision surface which divides the data into distinct class regions.
To this aim, use a K-means algorithm to find the training classes of the 2-D spectral images.
Infrared
Intensity
levels
Visual Intensity levels
Its result (K=2)

17. Classification (X) Example: (continued)
We can see the classified regions that correspond to the distinct physical phenomena.
Following images show the color-assigned classification results using K=4 and K=6 training classes.
c.f. Classification accuracy using the minimum (mean) distance classifier improves as the number of training classes are increased.
K=4
K=6

18. :value of the jth cluster center at the lth iteration
Classification (XI)
K-Means Classification
Unsupervised classification
Assumption
The number of cluster centers is known a priori.
Steps
1) Initialize
Choose the number of clusters K.
For each cluster, choose an initial cluster center.
Starting values can be arbitrary.
:value of the jth cluster center at the lth iteration

19. Classification (XII) 2) Distribute samples.
Distribute all sample vectors ( ).
3) Calculate the new cluster centers.
Recalculate the position of each cluster.
4) Check for convergence
If no cluster center has changed, then convergence has occurred and stop. Otherwise, iterate by going to step 2.
for all i =1,2,…,K, i j.
represents the population of cluster j at iteration l.
Nj is the number of sample vectors attached to Sj.

20. Classification (XIII)
Example 1 2 3 4 5 6 7 8 9 10
initial cluster centers
: (0, 0)
: (1, 0)

21. Classification (XIV) : (0, 1) : (5.9, 5.3) 1st iteration 1 2 3 4 5 6 71 2 3 4 5 6 7 8 9 10
1st iteration
: (0, 1)
: (5.9, 5.3)

22. Classification (XV) : (1, 1) : (8, 7.5) 2nd iteration 1 2 3 4 5 6 7 81 2 3 4 5 6 7 8 9 10
2nd iteration
: (1, 1)
: (8, 7.5)

23. Cluster centers not changed.
Classification (XVI) 1 2 3 4 5 6 7 8 9 10
3rd iteration
: (1, 1)
: (8, 7.5)
Cluster centers not changed.

24. Connected Components Labeling (I)
Brief Description
Scans an image and groups its pixels into component based on the pixel connectivity.
Used in many automated image analysis application.

25. Connected Components Labeling (II)
Assume a binary image with 8-connectivity.
When we arrived at a point p for which V={1},
examine the four neighbors of p already scanned:
Left(i), above(ii), and
two upper diagonal terms(iii & iv) P
(i)
(ii)
(iii)
(iv) ?
Already scanned pixels
Pixels that should be scanned.

26. Connected Components Labeling (III)
If all four neighbors are 0, assign a new label to p,
else if only one neighbor has V={1}, assign its label to p,
else if one or more have V={1}, assign one of labels to p, and make a note of the equivalence.
Then, a second scan is made through the image for replacing labels according to the equivalence classes.

27. Connected Components Labeling (IV)
Example
Same label assigned. 1 A
New label assigned.

28. Connected Components Labeling (V)
New label assigned. 1 A B
Also,
same label assigned.

29. Connected Components Labeling (VI)
Third Case:
A & B must be the
same labels. 1 A B ?

30. Connected Components Labeling (VI)
Guidelines for Use
Example 1
After scanning this image and labeling the distinct pixel classes with a different gray-value, we obtain the labeled output image (b).
If we assign a distinct color to each gray-level, we obtain (c).
(a) Original Image
(b) Labeling in Graylevel
(c) Labeling in Color

31. Connected Components Labeling (VII)
Example 2
If we want to count the objects in a real world scene like (a), we first have to threshold the image to produce a binary image (b).
The connected components of the binary image are in (c).
(a) Original Image
(b) Thresholded Image
(c) Labeled Image

32. Connected Components Labeling (VIII)
Example 2: (continued)
In order to see the result better, assign a color to each component. But, the problem is that we cannot find 163 colors where each of them is different enough from all others to be distinguished by the human eye.
Two possible ways
Use only a few colors (e.g. 8)
which are clearly different
from each other and assign
each gray-level of the CC image
to one of these colors. (d)
Assign a different color
to each gray-value, many of
them being quite similar. (e)
(d)
(e)

33. Connected Components Labeling (IX)
Example 3
Big problems when we count the number of turkeys in (a).
Although we assigned one connected component to each turkey, the total number of components (196) does not correspond to the number of turkeys.
The last two examples showed that the CC labeling is the easy part of the automated analysis process, whereas the major task is to obtain a good binary image which separates the objects(turkeys) from the background(other objects).
(a) Original Image
(b) Thresholded Image
(d) Labeled in color
(c) Labeled in Grayscale