Uptu Eec-068 Puta

7/28/2019 Uptu Eec-068 Puta

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SULUTION OF IMAGE PROCESSING (EEC-068)Dr. Bhupal Singh, Professor EN Department

1) a

Solution:The perceived intensity or brightness of the stripes of constant intensities,

is different that then their actual ones around the boundary. These

seemingly scalloped bands are called Mach bandsafter Ernst Mach whofirst described the phenomenon in 1865.

Luminance is a photometric measure of the luminous intensity per unit area of light

traveling in a given direction. It describes the amount of light that passes through or is

emitted from a particular area, and falls within a given solid angle.

Brightness is an attribute of visual perception in which a source appears to be radiating or

reflecting light.

Contrast is the difference in luminance and/or colour that makes an object (or its

representation in an image or display) distinguishable. In visual perception of the real world,

contrast is determined by the difference in the colour and brightness of the object and other

objects within the same field of view.

The number of pixel per frame =Channel capacity/Frame rate =8/30 MP

1(a) Solution


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In signal processing, the Nyquist rate, named after Harry Nyquist, is two times the

bandwidth of a band limited signal. The sampling frequency is called fold over frequency.

Aliasing is appearing of frequency above Nyquist rate as low frequency signal. In the case of

frequency is defined as periodicity of intensity pattern along x-axis and y-axis.

Thus the sampling results in scaling magnitude of analog spectrum by factor 1/T and infinite

many replicas of the spectrum displaced from each other by integer multiples of T . The

faith full recovery of the original signal from the sampled signal one is possible if the

spectrum of the sampled signal does not overlap that amount to say that mmT > that

is mT > 2 . Where m maximum frequency content of the signal. In order to recover

original signal from the sampled DAC is out need to be passed through a low pass filter offollowing characteristics.


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2(a) For an image f(m,n) of the size NxM The DFT is defined as follows

lm

M

N

n

M

m

km

N WWnmflkF

= =

=1

0

1_

0

],[],[ where, MN WandW are Nth and Mth root of unity.

The DFT follows following Properties

1. Linearity

2. Periodicity

3. Parsevals. Theorem

4. Shifting

5. Circular Convolution

2(b) Solution

DCT stands for Discrete Cosine Transform and for image f(m,n) of size MxN it is defined as

follows

],[)2

)12(cos()

2

)12(cos()()(

22],[

1

0

1_

0

2/12/1

nmfM

nk

N

mknn

NMlkF

N

n

M

m

DCT

++

=

= =

Where

==

otherwisefor

102/1)(

The DCT satisfies following properties

1. Linearity


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2. Periodicity

3. Energy Compactation

2 Solution

Given image

=

1212

1231

2112

1211

),( nmf

Hadamard trandform is recursively, defined as follows:

Where

In present case we requires second order Hadamard transform matrix

=

11111111

1111

1111

2

12H

Therefore the HT of the image is given as

==

1111

1111

1111

1111

2

1

1212

1231

2112

1211

1111

1111

1111

1111

2

1),(),( 22

THnmfHvuF

=0242

4202

6020

20224

4

1

),( vuF

3(a) Solution

Spatial domain g(x, y) = h(x, y) f(x, y) + (x, y)

Frequency domain

G(u, v) = H(u, v) F(u, v) + N(u, v)


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H(u, v): Degradation function

(x, y): Additive noise term

The objective is to find an estimate (f(x, y)) of the original image f(x, y). The more we know

about H and , the closer the estimate will be to f(x, y).

The degradation is mainly distortion due image sensor or acquisitionprocess or noise addition in the process.

WIENER FILTER:

For Wiener Filter:


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3(b) Solution:

Given

=

0012

2223

3332

2333

),( nmf

The no of symbols are 4 that is (0, 1, 2, 3)

The frequency table of the symbols is given as

Symbol ( ix ) 0 1 2 3

Frequency( if ) 2 1 6 7

=4

/)( iii ffxp1/8 1/16 3/8 7/16

Sort the symbols descending order of frequency

Then pick the two least frequent symbols assign 3 bit code 111 and 110 connect and addnext lowest assign 11 the 10 to new entry finally connect forth symbol assign 1 to the parent

and 0 to the new entrant, this process continues till probability sums out to be 1. In case

following is the result.

Symbol 3=0 (bit)

Symbol 2=10 (bits)

Symbol 1=110 (bits)

Symbol 0=111 (bits)

3 Solution

Shannon denoted the entropyHof a discrete variablesXwith possible values {x1, .,xn} andprobability mass functionp(X) as,

For maximum entropy iallforxp

XH

i

0)(

)(=

Or iallforxp ie 0)(log1 =

That iallforexp i =)( This shows that the probability of the symbols should be same.

4(a) Solution


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In computer vision, Segmentation is the process of partitioning a digital image into multiple

segments (sets ofpixels, also known as superpixels). The goal of segmentation is to simplify

and/or change the representation of an image into something that is more meaningful and

easier to analyze. Image segmentation is typically used to locate objects and boundaries

(lines, curves, etc.) in images. More precisely, image segmentation is the process of assigning

a label to every pixel in an image such that pixels with the same label share certain visual

characteristics

Thresholding

The simplest method of image segmentation is called the thresholding method. This method

is based on a clip-level (or a threshold value) to turn a gray-scale image into a binary

image.The key of this method is to select the threshold value (or values when multiple-levels

are selected). Several popular methods are used in industry including the maximum entropy

method, Otsu's method (maximum variance), and et al. k-means clustering can also be used.

Clustering methods

The K-means algorithm is an iterative technique that is used to partition an image into K

clusters. The basic algorithm is:

-PickKcluster centers, eitherrandomly or based on some heuristic

-Assign each pixel in the image to the cluster that minimizes the distance between thepixel and the cluster center

-Re-compute the cluster centers by averaging all of the pixels in the cluster

-Repeat steps 2 and 3 until convergence is attained (e.g. no pixels change

clusters)

4(b) Solution

Image segmentation is a fundamental process in many image, video, and computer vision

applications. It is often used to partition an image into sep-aerate regions, which ideally

correspond to different real-world objects. It is a critical step towards con-tent analysis and

image understanding. Many segmentation methods have been developed, but there is still no

satisfactory performance measure, which makes it hard to compare different segmentation

methods, or even different parameterizations of a single method. However, the ability to

compare two segmentations (generally obtained via two different methods/parameterizations)
http://en.wikipedia.org/wiki/Computer_visionhttp://en.wikipedia.org/wiki/Digital_imagehttp://en.wikipedia.org/wiki/Image_segmenthttp://en.wikipedia.org/wiki/Set_(mathematics)http://en.wikipedia.org/wiki/Pixelhttp://en.wikipedia.org/wiki/Thresholding_(image_processing)http://en.wikipedia.org/wiki/Otsu's_methodhttp://en.wikipedia.org/wiki/K-meanshttp://en.wikipedia.org/wiki/K-means_algorithmhttp://en.wikipedia.org/wiki/Iterativehttp://en.wikipedia.org/wiki/Iterativehttp://en.wikipedia.org/wiki/Cluster_analysishttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Randomhttp://en.wikipedia.org/wiki/Heuristichttp://en.wikipedia.org/wiki/Distancehttp://en.wikipedia.org/wiki/Computer_visionhttp://en.wikipedia.org/wiki/Digital_imagehttp://en.wikipedia.org/wiki/Image_segmenthttp://en.wikipedia.org/wiki/Set_(mathematics)http://en.wikipedia.org/wiki/Pixelhttp://en.wikipedia.org/wiki/Thresholding_(image_processing)http://en.wikipedia.org/wiki/Otsu's_methodhttp://en.wikipedia.org/wiki/K-meanshttp://en.wikipedia.org/wiki/K-means_algorithmhttp://en.wikipedia.org/wiki/Iterativehttp://en.wikipedia.org/wiki/Cluster_analysishttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Randomhttp://en.wikipedia.org/wiki/Heuristichttp://en.wikipedia.org/wiki/Distance


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in an application-independent way is important: (1) to autonomously select among two

possible segmentations within a segmentation algorithm or a broader application; (2) to place

a new or existing segmentation algorithm on a solid experimental and scientific ground; and

(3) to monitor segmentation results B on the fly, so that segmentation performance can be

guaranteed and consistency can be maintained. Many image segmentation methods have

been proposed over the last several decades. As new segmentation methods have been

proposed, a variety of evaluation methods have been used to compare 1 new segmentation

methods to prior methods. These methods are fundamentally very different, and can be

partitioned based on five distinct methodologies, Supervised Methods Unsupervised Methods

Supervised evaluation methods, also known as relative evaluation methods or empirical

discrepancy methods, evaluate segmentation algorithms by comparing the resulting

segmented image against a manually-segmented reference image, which is often referred to

as a gold standard or ground-truth. The degree of similarity between the human and machine

segmented images determines the quality of the segmented image. One potential benefit of

supervised methods over unsupervised methods (discussed below) is that the direct

comparison between a segmented image and a reference image is believed to provide a finer

resolution of evaluation, and as such, discrepancy methods are commonly used for objective

evaluation. However, manually generating a reference image is a difficult, subjective, and

time-consuming task . Besides, for most images, especially natural images, we usually cannot

guarantee that one manually-generated segmentation image is better than another. In this

sense, comparisons based on such reference images are somewhat subjective. In the

supervised method the feature of the image are obtained and in future he new image are

looked for same feature based on the similarity with data base. Whereas supervised methods

evaluate segmented images the objects are classified. ages against a reference image,

unsupervised evaluation methods, also known as stand-alone evaluation methods or

empirical goodness methods do not require a reference image, but instead evaluate a

segmented image based on how well it matches a broad set of characteristics of segmented

images as desired by humans. Unsupervised evaluation is quantitative and objective. It has

distinct advantages, perhaps the most critical of which is that it requires no reference image.

A manually-created reference image is intrinsically subjective and creating such a reference

image is tedious and time-consuming, and for many applications, it is hard or maybe even


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impossible. The ability to work without reference images allows unsupervised evaluation to

operate over a wide range of conditions (or systems) and with many different types of

images. This property also makes unsupervised evaluation uniquely suitable for automatic

control of online segmentation in real-time systems, where a wide variety of images, whose

contents are not known beforehand, need to be processed.

4 The Gaussian filter for 2D is given as

y

y

x

x

yx

xxyxh

2

)(

2

)(exp(

2

1],[

22

= )

There fore the filtered image is the convolution of the filter with image f(x,y) hence

)(])[),((],[),(),((1

0

1

0

1

0

1

0

myhnxhmnfnymxhmnfyxgM

m

N

n

M

m

N

n

==

=

=

=

=

However Laplacian

2

2

2

2

),(),(y

f

x

fyxfyxg

+

==

Clearly its not separable with respect differentiation x and y.

5(a) Solution

In mathematics, a moment is, loosely speaking, a quantitative measure of the shape of a set

of points. The "second moment", for example, is widely used and measures the "width" (in a

particular sense) of a set of points in one dimension or in higher dimensions measures the

shape of a cloud of points as it could be fit by an ellipsoid

Thus in image processing moment of image is computed to characterize the object shape.

The (n,m)th order moment of the image f(x,y) is defined as follows

),(),(, = yxfyxyx nmnn

We recognize translation, rotation, scaling, affine, projective, and elastic geometric

invariants. Ratiometric invariants exist with respect to linear contrast stretching, Non-linear

intensity transforms, and to convolution.

5(b) Solution

Cameras, on the other hand, are much smaller and simple to handle, and are becoming

ubiquitous in the current computer environment. The goal of this project is to develop a


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signature verification technique suitable for signatures captured by our camera-based

acquisition system. Handwriting recognition is still an open problem, even though it has

been extensively studied for many years. Signature verification is a reduced problem that still

poses a real challenge for researchers. The literature on signature verification is quite

extensive and shows two main areas of research, off-line and on-line systems. Off-line

systems deal with a static image of the signature, i.e. the result of the action of signing while

on-line systems work on the dynamic process of generating the signature, i.e. the action of

signing itself. The system proposed in this paper falls within the category of on-line systems

since the visual tracker of handwriting captures the timing information in the generation of

the signature.

DESCRIPTION OF THE SYSTEM

The camera-based acquisition system uses computer vision techniques and estimation theory

to track the position of the pen tip in the image plane. The verification algorithm compares

the 2D shape of the signatures using a translation-invariant metric.

BLOCK DIAGRAM


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5 Solution

Automated fingerprint identification is the process of automatically matching one or many

unknown fingerprints against a database of known and unknown prints. Automated

fingerprint identification systems are primarily used by law enforcement agencies for

criminal identification initiatives, the most important of which include identifying a person

suspected of committing a crimeor linking a suspect to other unsolved crimes. Automated

fingerprint verification is a closely related technique used in applications such as

attendance and access control systems. The finger prints are identified certain features such

as the valley and ridges, the delta loop and whorl. The image first proposed and converted

into binary image. Then these features re looked properly and data base is generated. In

future same features of the finger print are obtained and compared with data base.
http://en.wikipedia.org/wiki/Fingerprinthttp://en.wikipedia.org/wiki/Databasehttp://en.wikipedia.org/wiki/Crimehttp://en.wikipedia.org/wiki/Crimehttp://en.wikipedia.org/wiki/Fingerprinthttp://en.wikipedia.org/wiki/Databasehttp://en.wikipedia.org/wiki/Crime

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Uptu Eec-068 Puta