This is about Image segmenting.We will be using fuzzy logic & wavelet transformation for segmenting it.Fuzzy logic shall be used because of the inconsistencies that may occur during segementing or

1. For more than a decade people
have developed an interest for
PROJECT the researching in the domain
SEMINAR/GROUP
NO.-7 IMAGE PROCESSING and now
there’s more than a million
patents have been submitted
this year on this topic.And
now we bring you…
OUR PROJECT ON
IMAGE
PROCESSING

2. PART One
1
INTRO TO
IMAGE processing

3. Introduction
 Image processing is any form of signal processing
for which the input is an image, such as
photographs or frames of video; the output of
image processing can be either an image or a set of
characteristics or parameters related to the image.
 Most image-processing techniques involve treating
the image as a two-dimensional signal and
applying standard signal-processing techniques to
it.

4. Types
 Image processing usually refers to digital
image processing, but optical and analog
image processing are also possible.

5. Image Processing Operations
 Geometric transformations such as enlargement,
reduction, and rotation
 Color corrections such as brightness and contrast
adjustments, quantization, or conversion to a different
color space
 Digital compositing or optical compositing (combination
of two or more images). Used in filmmaking to make a
"matte"
 Interpolation, demosaicing, and recovery of a full image
from a raw image format using a Bayer filter pattern

6. Image Processing
Operations(Contd.)
 Image editing (e.g., to increase the quality of a digital
image)
 Image differencing
 Image registration (alignment of two or more images)
 Image stabilization
 Extending dynamic range by combining differently exposed
images

7. Image Processing Applications
 Computer vision
 Face recognition
 Feature detection
 Non-photorealistic rendering
 Medical image processing
 Microscope image processing
 Morphological image processing
 Remote sensing

8. IMAGE SEGMENTATION USING
WAVELET TRANSFORMATION
& FUZZY LOGIC

9. 2 PART
 IMAGE

10. The Definition…
 The purpose of image segmentation is to partition an
image into meaningful regions with respect to a particular
application .
 Image segmentation is the process of dividing an
image into different regions such that each region is
homogeneous.
 It basically identifies the pixels belonging to the
desired object that we may want to extract from an
input image.

11. More about segmentation…
• To humans, an image is not just a random
collection of pixels; it is a meaningful
arrangement of regions and objects.
• There also exits a variety of images: natural
scenes, paintings, etc. Despite the large
variations of these images, humans have no
problem to interpret them.

12. Segmentation can be
IN TERMS OF:
Grey level
 Colour
Texture,
 Depth or motion

13. Introduction to image
segmentation
 Example 1
 Segmentation based on greyscale
 Very simple ‘model’ of greyscale leads to inaccuracies in
object labelling
13

14. Introduction to image
segmentation
 Example 2
 Segmentation based on texture
 Enables object surfaces with varying patterns of grey
to be segmented
14

15. Introduction to image
segmentation
15

16. Introduction to image
segmentation
 Example 3
 Segmentation based on motion
 The main difficulty of motion segmentation is that an
intermediate step is required to (either implicitly or
explicitly) estimate an optical flow field
 The segmentation must be based on this estimate and
not, in general, the true flow
16

17. Introduction to image
segmentation
17

18. TYPES OF IMAGE SEGMENTATION
A) Supervised.- These methods require the interactivity in
which the pixels belonging to the same intensity range
pointed out manually and segmented.
B) Automatic.- This is also known as unsupervised methods,
where the algorithms need some prior information, so these
methods are more complex.
C) Semi-automatic.- That is the combination of manual and
automatic segmentation.

19. SEGMENTING CAN ALSO BE ON
DISCONTINUITY : Partitioning an image based
on abrupt change.
Edge detection in a image.
SIMILARITY : Partitioning an image into
regions that are similar according to a set of pre
defined criteria.
Thresholding , Region Growing , Clustering.

20. DISCONTINUITIES
LINES
POINTS
EDGES

21. Definition of edge
• Definition : Set of connected pixels that lie on the
boundary b/w 2 regions.
• Edge is a “local” concept & boundary is “global”
concept.
• Reasonable definition of edge requires ability to
measure gray level transition in a meaningful way.

22. EDGE DETECTION
• It is the most common approach for
detecting meaningful discontinuities in
gray level.
• Process: By implementing the 1st order
derivative 2nd order derivative ,edges in
an image can be detected.

23. DIFFERENCE B/W EDGE & PRACTICAL EDGE
 IDEAL : Set of pixels ,each of which is located at an
orthogonal step transition in gray level
 PRACTICAL : Used by optics sampling and other image
acquisition imperfections and yield blurred edges
where degree of blurring is determined by factors such
as
1. Quality of image acquisition system
2. Sampling rate
3. Illumination conditions under which image is acquired

24. EXAMPLE

25. Segmentation Techniques
 There are 2 very simple image segmentation techniques
that are based on the grey level histogram of an image
 Thresholding
 Clustering
 But in our project we will be using clustering so we will
look into the details of clustering.

26. Clustering….
• Similar data points
grouped together into
clusters.
• In this , centroid is used
to represent each cluster,
based on the similarity
with the centroid of
cluster we can classify
the patterns.

27. Clustering…
Most popular clustering algorithms suffer from two major
drawbacks
 First, the number of clusters is predefined, which makes
them inadequate for batch processing of huge image
databases
 Secondly, the clusters are represented by their centroid and
built using an Euclidean distance therefore inducing
generally an hyperspheric cluster shape, which makes them
unable to capture the real structure of the data.
 This is especially true in the case of color clustering where
clusters are arbitrarily shaped

28. Clustering Algorithms
 K-means
 K-medoids
 Hierarchical Clustering
 There are many other algorithms used for clustering.
Here we would look into 2 algorithms mainly K-means
And Hierarchical Clustering.

29. HIERARCHICAL CLUSTERING
 The concept of hierarchical clustering is to construct a
dendrogram representing the nested grouping of
patterns (for image, known as pixels) and the
similarity levels at which groupings change.
 We can apply the two-dimensional data set to interpret
the operation of the hierarchical clustering algorithm

30. CLUSTER & DENDOGRAM

31. K-means Clustering Algorithm
 Step1. Determine the number of clusters we want in the final
classified result and set the number as N. Randomly select N
patterns in the whole data bases as the N centroids of N clusters.
 Step2. Classify each pattern to the closest cluster centroid. The
closest usually represent the pixel value is similarity, but it still
can consider other features.
 Step3. Recompute the cluster centroids and then there have N
centroids of N clusters as we do after Step1.
 Step4. Repeat the iteration of Step 2 to 3 until a convergence
criterion is met.

32. APPLICATIONS OF IMAGE
SEGEMENTATION
 Medical Imaging Tasks (detecting tumors,etc)
 Object recognitions in images of remote sensing via
satellite on aerial platforms.
 Automated recognition systems to inspect the
electronic assemblies
 Biometrics
 Automated traffic control system.

33. MODULE
3
WAVELET TRANS

35. More Facts about Wavelets :
• Wavelets are localized in frequency as well as in space having an advantage
over the Fourier transform which is only localized in frequency
• As a result temporal-spatial information is maintained during the wavelet
transformation process which is extremely important for edge detection.
Two methods based on wavelets from the multiresolution point of view have
been introduced -
• The first method was based on the two-dimensional fast wavelet transform
using the Biorthogonal Mother Wavelet
• The second method was based on a new wavelet named “Contourlet”
which has been developed recently as an improvement of the classical
wavelets.

36. Some facts about Fourier To Wavelet Analysis
• The Fourier transform has been the mainstay of transform-based image
processing since the late 1950s but they have a serious drawback as only
frequency information remains while the local one is lost which means change
in Fourier coefficients has a global effect on the image.
• This means, that any modification of the Fourier coefficients has a global effect
on the image. In order to involve localization on the analysis, the Short Time
Fourier transform (STFT) is adapted.
• In this case, the image is windowed, and thus the information has a precision
relevant to the size of the window used.
The drawback is that the window is the same in all frequencies.
• Wavelet analysis allows the variation of the window based on the frequency
information. As a result, long time intervals are used in low-frequency
information and short time intervals in high-frequency information.

40. Fast Wavelet Transform using DWT :

43. 4 MODULE:
FUZZY LOGIC

44. Some Fuzzy Background
• Fuzzy logic is an approach to computing based on
"degrees of truth" rather than the usual "true or false" (1
or 0) Boolean logic on which the modern computer is
based. The idea of fuzzy logic was first advanced by Dr.
Lotfi Zadeh of the University of California at Berkeley in
the 1960’s.
• Fuzzy logic includes 0 and 1 as extreme cases of truth (or
"the state of matters" or "fact") but also includes the
various states of truth in between

45. Fuzzy Vs. Probability
The difference between probability and fuzzy logic is clear
when we consider the underlying concept that each attempts
to model. Probability is concerned with the undecidability in
the outcome of clearly defined and randomly occurring
events, while fuzzy logic is concerned with the ambiguity or
undecidability inherent in the description of the event itself.
Fuzziness is often expressed as ambiguity rather than
imprecision or uncertainty and remains a characteristic of
perception as well as concept.

46. Membership Functions (MFs)
 What is a MF?
 Linguistic Variable
 A Normal MF attains ‘1’ and ‘0’ for some input
x1 , x2 A x1 1, A x2 0
 How do we construct MFs?
 Heuristic
 Rank ordering
 Mathematical Models
 Adaptive (Neural Networks, Genetic Algorithms …)

47. Membership Function Examples
Gaussian
x c
2 Sigmoid
2
2
f gmf x; , c e 1
f smf x, a , c a x c
1 e
Triangular Trapezoidal
x a c x x a d x
f x; a, b, c max min , ,0 f x; a, b, c, d max min ,1, ,0
b a c b b a d c

48. Example: Finding an Image
Threshold
Membership Value
1
f smf x, a, c a x c
1 e
Gray Level

49. Crisp Vs. Fuzzy
 Fuzzy Sets  Crisp Sets
• Membership values on [0,1] • True/False {0,1}
• Law of Excluded Middle and Non- • Law of Excluded Middle and Non-
Contradiction do not necessarily Contradiction hold:
hold:
A A A A
A A A A
• Fuzzy Membership Function • Crisp Membership Function
• Flexibility in choosing the • Intersection (AND) , Union (OR),
Intersection (T-Norm), Union (S- and Negation (NOT) are fixed
Norm) and Negation operations

50. Image Processing
Binary
Gray Level
Color (RGB,HSV etc.)
Can we give a crisp definition to light
blue?

51. Feature Vector
• Feature
• Feature is any distinctive aspect, quality or characteristic
 Features may be symbolic (i.e., color) or numeric (i.e., height)
• The combination of d features is represented as a d-dimensional
column vector called a feature vector
 The d-dimensional space defined by the feature vector is called
feature space
 Objects are represented as points in feature space. This
representation is called a scatter plot

52. Fuzzy C-means Clustering
In fuzzy clustering, each point has a degree of belonging to clusters, as in fuzzy
logic, rather than belonging completely to just one cluster. Thus, points on the
edge of a cluster, may be in the cluster to a lesser degree than points in the center
of cluster.
Any point x has a set of coefficients giving the degree of being in the kth cluster
wk(x). With fuzzy c-means, the centroid of a cluster is the mean of all
points, weighted by their degree of belonging to the cluster:

53. Example: Finding Edges
2 1  ij
ˆ mn min 1 , min  ij ,
W i j 1  ij
g ij max gij min gij min ij
spatial spatial spatial
 ij ij 1
max gij max gij max ij
spatial global spatial

54. Summary
• Fuzzy Logic can be useful in solving Human related tasks
• Evidence Theory gives tools to handle knowledge
• Membership functions and Aggregation methods can be
selected according to the problem at hand
• Fuzzy logic can model nonlinear functions of arbitrary
complexity.
• Fuzzy logic is tolerant of imprecise data.

55. MODULE
5

56. Acknowledgement
•We are thankful to our mentor Mr. Soumyadip Dhar for guiding
us through our project .

59. The presentation was
brought to you by
• Jishnu Mukherjee
• Lahaul Seth
• Rahul Kar