## 87 Kmeans Clustering Algorithm

In A-means clustering approach, we partition the set of input patterns S into a set of K partitions, where K is known in advance. The method is based on the identification of the centroids of each of the K clusters. Thus, instead of computing the pairwise interpattern distances between all the patterns in all the clusters, here the distances may be computed only from the centroids. The method thus essentially boils down to searching for a best set of K centroids of the clusters as follows Step...

## 11 Fundamentals Of Image Processing

We are in the midst of a visually enchanting world, which manifests itself with a variety of forms and shapes, colors and textures, motion and tranquility. The human perception has the capability to acquire, integrate, and interpret all this abundant visual information around us. It is challenging to impart such capabilities to a machine in order to interpret the visual information embedded in still images, graphics, and video or moving images in our sensory world. It is thus important to...

## 45 Karhaunenloeve Transform Or Principal Component Analysis

Karhaunen-Loeve Transform or Principal Component Analysis (PCA) has been a popular technique for many image processing and pattern recognition applications. This transform which is also known as Hotelling Transform is based on the concepts of statistical properties of image pixels or pattern features 1, 2 . Principal component analysis (PCA) forms the basis of the Karhunen-Loeve (KL) transform for compact representation of data 1 . The KL transform and the theory behind the principal component...

## 171 Introduction

JPEG2000 is the new international standard for image compression 1 developed jointly by the International Organization for Standardization (ISO), and the International Electrotechnical Commission (IEC) and also recommended by International Telecommunications Union (ITU). Although JPEG (actually baseline JPEG) has been very successful in the marketplace for more than a decade, it lacks many features desired by interactive multimedia applications, its usage in current communications (wired or...

## Afcz az

Ak+i bk z)-, bk+1 ak(z) bk(z) qk+1 ak(z) bk z) k k + 1 From the above algorithm, it is clear that the greatest common divisor (gcd) of a(z) and b(z) is an, where n is the smallest integer for which bn(z) 0. The number of iterations by the while loop in the above algorithms is bounded by n < n(z) + 1. From the above algorithm, we can establish that

## B

F g-. 7.i6 Comparison of thresholding techniques (a) original image, (b) Otsu, (c) Kapoor, and (d) Renyi's Entropy. Figure 7.16 shows the thresholded images by using Otsu, Kapoor, and Renyi's entropy based thresholding algorithms, as an example. 7.4.4 Problems Encountered and Possible Solutions Quite often we encounter situations where two local maxima belong to the same global maximum in an image. Several techniques may be employed to avoid detection of such local maxima A minimum distance of...

## 54 Lifting Implementation Of The

The DWT implementation is basically frame-based as opposed to the DCT-type block-based implementation. Such an implementation requires both a large number of arithmetic computations and a large memory. Recently, a new mathematical formulation for wavelet transformation has been proposed by Swelden 11 based on spatial construction of the wavelets and a very versatile scheme for its factorization has been suggested in 12 . This new approach is called the lifting-based wavelet transform, or simply...

## 391 391

18.2 Partitioning Data for Coding 391 18.3 Tier-1 Coding in JPEG2000 392 18.3.1 Fractional Bit-Plane Coding 392 18.3.2 Examples of BPC Encoder 405 18.3.3 Binary Arithmetic Coding MQ-Coder 413 18.4 Tier-2 Coding in JPEG2000 413 18.4.1 Bitstream Formation 415 18.4.2 Packet Header Information Coding 418 18.5 Summary 419 References 420

## Xk fxkiuk0 Pk AkPkiAl WkQkiWf

Kk PkHl(HkPkHl + VkRkV )-1 xk x'k + Kk zk - h x, 0) Pk (I - KkHk)Pk An important feature of Extended Kalman filter is that the Jacobian Hk in the equation for Kalman gain Kk serves to correctly propagate only the relevant component of measurement information. For a particular problem, if the assumptions of the Kalman filter hold, then no other algorithm can out perform it. However, for a variety of real world computer vision applications, these assumptions are often unrealistic. So alternate...

## 88 Syntactic Pattern Classification

It may be noted that there exists an inherent structure inside a pattern and there is a positive interrelationship among the primitive elements which form a pattern 2, 3, 5, 8, 9 . The limitations of decision theoretic pattern classification techniques lie in their incapability to articulate this interrelationship of the pattern substructures. This has led to a new era of structural or syntactic pattern recognition. The interrelationship between pattern elements called primitives and the...

## 115 Video Mining

Currently text-based search engines are commercially available, and they are predominant in the World Wide Web for search and retrieval of information. However, demand for search and mining multimedia data based on its content description is growing. Search and retrieval of contents is no longer restricted to traditional database retrieval applications. As an example, it is often required to find a video clip of a certain event in a television studio. In the future the content customers will...

## Threelevel Signal Decomposition Threelevel Signal Reconstruction

Fig. 5.3 Three-level multiresolution wavelet decomposition and reconstruction of signals using pyramidal filter structure. Let's summarize the DWT computation here in terms of simple digital FIR filtering. Given the input discrete signal x(n) (shown as a(0, n) in Figure 5.3), it is filtered parallelly by a low-pass filter (h) and a high-pass filter (< ) at each transform level. The two output streams are then subsampled by simply dropping the alternate output samples in each stream to produce...

## 1 2 3 4 5

Fig. 11.2 Partitioning the color histogram with coherence and noncoherence pixel counts. generated from the color histograms of two images, where h and h are the count of pixels in the jth bin of the two histograms respectively, and K is the number of bins in each histogram. We can define a simple distance between two histograms as There is another distance measure between two histograms, popularly known as histogram intersection. The histogram intersection is the total number of pixels common...

## 163 Baseline Jpeg Compression

The baseline JPEG compression algorithm is widely used among the four modes in JPEG family. This is defined for compression of continuous-tone images with 1 to 4 components. Number of components for grayscale images is 1, whereas a color image can have up to four color components. The baseline JPEG allows only 8-bit samples within each component of the source image. An example of a four-component color image is a CMYK (Cyan, Magenta, Yellow, and Black) image, which is used in many applications...

## 125 Preprocessing Of Signature Patterns

The binarized signature image, as in Figure 12.3(a), is thinned using any standard thinning algorithm. The objective is to obtain a trajectory of the pen-tip. It may be observed from Figure 12.3(b) that the thinned image does not accurately capture the pen-tip trajectory, while it adequately preserves the structural information necessary for recognition. Some artifacts introduced by thinning are loops and holes in the binary image are reduced to single segments. strokes intersect on a sequence...

## 73 Edge Detector

A number of edge detectors based on a single derivative have been developed by various researchers. Amongst them most important operators are the Robert operator, Sobel operator, Prewitt operator, Canny operator, Krisch operator l - 5 , etc. In each of these operator-based edge detection strategies, we compute the gradient magnitude in accordance with the formula given below. If the magnitude of the gradient is higher than a threshold, then we detect the presence of an edge. Below we discuss...

## 83 Bayesian Decision Theory

Bayesian decision theory is a very good tool for pattern classification. Assume that there are N classes of patterns C , C2, , Cjv, and an unknown pattern x in a d-dimensional feature space x x , x2, x , , x . Hence the pattern is characterized by d number of features. The problem of pattern classification is to compute the probability of belongingness of the pattern x to each class Ci, i 1,2, ,N. The pattern is classified to the class Cfc if probability of its belongingness to Cfc is maximum....

## 1

Where d(pi,qi) yields a matching measure between the ith particle and the actual blob in the image frame. Normalize the weights if necessary and rank the particles according to the weights. Go to step 1 (i.e., resampling phase). Figure 14.2 shows a sequence of video frames, where there is a moving human figure in a static background. The color version of the figure is provided in the color page section. The tracked human figure in each color frame is shown in a blob, enclosed in a red...

## 01101100001 10011010001011011101100011110100111000 001 1010

Where the first five bits, 01101, represent the DC coefficient and the other 47 bits represent the AC coefficients. Hence, we achieved approximately 10 1 compression using baseline JPEG to compress the block as shown above. Decompression is the inverse process to decode the compressed bitstream in order to properly reconstruct the image. The inverse functions in the decompression process are obvious and the corresponding block diagram of the baseline decompression algorithm is shown in Figure...

## V

If 5 0 if V r if V g if V b, The results obtained by using either of the above transformations yield reasonably good results. Fig. 3.2 Perceptual representation of HSV color space. Fig. 3.2 Perceptual representation of HSV color space. The perceptual representation of the HSV color space has a conical shape, as shown in Figure 3.2. The Value (V) varies along the vertical axis of the cone, the Hue (H) varies along the periphery of the circle of the cone and is represented as an angle about the...

## 88787888188818818181818181818881188181818177

1717777777777676667667777 Figure 2.11(c) shows the dominant vertices along the head-and-shoulder contour of the binary image. Fig. 2.11 (a) chain code, (b) binary image, (c) dominant vertices along the contour. Fig. 2.11 (a) chain code, (b) binary image, (c) dominant vertices along the contour.

## 2

Fig. 5.2 2D Gabor filter (a) Real component, (b) Imaginary component. Fig. 5.2 2D Gabor filter (a) Real component, (b) Imaginary component. Each of the complex Gabor filters has the real (even) and imaginary (odd) parts that are conveniently implemented as the spatial mask of M x M sizes. For a symmetric region of support, M is preferred to be an odd number. A class of self-similar functions, referred to as Gabor wavelets, can be obtained by appropriate dilation and rotation of the mother Gabor...

## 106 Fuzzy Methods Of Contrast Enhancement

The human eye does not respond to subtle differences in illumination. The purpose of contrast enhancement is to improve the overall visibility of the image gray levels. This may be achieved by transforming the image gray levels in such a way that the dark pixels appear darker and light pixels appear lighter. Such a transform increases the differences in gray level intensity and thus enables our vision system to discern these differences. The contrast stretching algorithms may employ...

## A joy K

Copyright 2005 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the...

## H ft

Fig. 12.4 Chest Image (a) Original, enhanced by (b) histogram equalization, (c) local area histogram equalization, (d) another input original image, (e) enhanced by contrast limited adaptive histogram equalization. Figure 12.4(a) is the original chest x-ray image. In Figure 12.4(b) and (c), the lung boundaries and edges of the bones are enhanced using histogram equalization and local area histogram equalization respectively. Figure 12.4(d) is another original chest x-ray image and the enhanced...

## 344 Perceptually Uniform Color Space

Although both RGB and CMYK color models are extremely useful for color representation, color processing, and also for development of hardware, these models are in no way similar to the human vision model. One of the major limitations of the RGB color space is that it is a nonuniform one. Uniform color space is one in which the Euclidean color distance between two color points at any part of the color space corresponds to the perceptual difference between the two colors by the human vision...

## 59

4.2.1 One-Dimensional Fourier Transform 62 4.2.2 Two-Dimensional Fourier Transform 63 4.2.3 Discrete Fourier Transform (DFT) 64 4.2.4 Transformation Kernels 64 4.2.5 Matrix Form Representation 65 4.2.7 Fast Fourier Transform 68 4.3 Discrete Cosine Transform 70 4.4 Walsh-Hadamard Transform (WHT) 72 4.5 Karhaunen-Loeve Transform or Principal Component Analysis 73 4.5.1 Covariance Matrix 75 4.5.2 Eigenvectors and Eigenvalues 75 4.5.3 Principal Component Analysis 76 4.5.4 Singular Value...

## 128 Xray Imaging

X-ray images on photographic films are the oldest and most frequently used form of medical imaging. X-ray imaging is the fastest and easiest way for a physician to view and assess broken bones, a cracked skull or in back bone. X-ray is useful in detecting more adverse forms of cancer in bones. Diagnostic X-ray images can be created by passing small highly controlled amounts of radiation through the body, capturing the resulting shadows and reflections on a photographic plate. The X - ray images...

## Gxy X Hklfx kV l rixy

Here w represents the convolution window. A simple 3x3 blurring functions may look like this There are conventional methods like inverse filtering, Wiener filtering, Kalman filtering, Algebraic approach, etc., to restore the original object. In all these cases we assume that the blurring function H is known. If H is known, then obviously we can get back or restore the original image f x,y , simply by convolving the degraded image with the inverse of the blurring function. To remove the noise,...

## 124 Defense surveillance

Application of image processing techniques in defense surveillance is an important area of study. There is a continuous need for monitoring the land and oceans using aerial surveillance techniques. Suppose we are interested in locating the types and formation of Naval vessels in an aerial image of ocean surface. The primary task here is to segment different objects in the water body part of the image. After extracting the segments, the parameters like area, location, perimeter, compactness,...

## Preface

There is a growing demand of image processing in diverse application areas, such as multimedia computing, secured image data communication, biomedical imaging, biometrics, remote sensing, texture understanding, pattern recognition, content-based image retrieval, compression, and so on. As a result, it has become extremely important to provide a fresh look at the contents of an introductory book on image processing. We attempted to introduce some of these recent developments, while retaining the...