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Image processing: the fundamentals

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Bibliographic Details
Main Authors:	Petrou, Maria 1953-2012 (Author), Petrou, Costas (Author)
Format:	Book
Language:	English
Published:	Chichester Wiley 2010
Edition:	2. ed.
Subjects:	Image processing / Digital techniques Image processing > Digital techniques Bildverarbeitung
Online Access:	Inhaltsverzeichnis
Item Description:	Includes bibliographical references and index Hier auch später erschienene, unveränderte Nachdrucke
Physical Description:	XXIII, 794 S. Ill., graph. Darst. 1 CD-ROM (12 cm)
ISBN:	9780470745861

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adam_text	Contents Preface xxiii 1 Introduction 1 Why do we process images? ............................... 1 What is an image? .................................... 1 What is a digital image? ................................. 1 What is a spectral band? ................................ 2 Why do most image processing algorithms refer to grey images, while most images we come across are colour images? ........................ 2 How is a digital image formed? ............................. 3 If a sensor corresponds to a patch in the physical world, how come we can have more than one sensor type corresponding to the same patch of the scene? ..... 3 What is the physical meaning of the brightness of an image at a pixel position? . . 3 Why are images often quoted as being 512 χ 512, 256 χ 256, 128 χ 128 etc? .... 6 How many bits do we need to store an image? ..................... 6 What determines the quality of an image? ....................... 7 What makes an image blurred? ............................. 7 What is meant by image resolution? .......................... 7 What does good contrast mean? ........................... 10 What is the purpose of image processing? ....................... 11 How do we do image processing? ............................ 11 Do we use nonlinear operators in image processing? ................. 12 What is a linear operator? ................................ 12 How are linear operators defined? ............................ 12 What is the relationship between the point spread function of an imaging device and that of a linear operator? ........................... 12 How does a linear operator transform an image? ................... 12 What is the meaning of the point spread function? .................. 13 Box 1.1. The formal definition of a point source in the continuous domain ..... 14 How can we express in practice the effect of a linear operator on an image? .... 18 Can we apply more than one linear operators to an image? ............. 22 Does the order by which we apply the linear operators make any difference to the result? ............ ............................ 22 Box 1.2. Since matrix multiplication is not commutative, how come we can change the order by which we apply shift invariant linear operators? ......... 22 Box 1.3. What is the stacking operator? ........................ 29 What is the implication of the separability assumption on the structure of matrix ΗΊ 38 How can a separable transform be written in matrix form? ............. 39 What is the meaning of the separability assumption? ................. 40 Box 1.4. The formal derivation of the separable matrix equation .......... 41 What is the take home message of this chapter? .................. 43 What is the significance of equation (1.108) in linear image processing? ...... 43 What is this book about? ................................ 44 Image Transformations 47 What is this chapter about? ............................... 47 How can we define an elementary image? ....................... 47 What is the outer product of two vectors? ....................... 47 How can we expand an image in terms of vector outer products? .......... 47 How do we choose matrices hc and hrl ......................... 49 Wbat is a unitary matrix? ................................ 50 What is the inverse of a unitary transform? ...................... 50 How can we construct a unitary matrix? ........................ 50 How should we choose matrices U and V so that g can be represented by fewer bits than ƒ?....................................... 50 What is matrix diagonalisation? ............................ 50 Can we diagonalise any matrix? ............................. 50 2.1 Singular value decomposition ......................... 51 How can we diagonalise an image? ........................... 51 Box 2.1. Can we expand in vector outer products any image? ............ 54 How can we compute matrices U, V and Λ 2 needed for image diagonalisation? . . 56 Box 2.2. What happens if the eigenvalues of matrix ggT are negative? ....... 56 What is the singular value decomposition of an image? ................ 60 Can we analyse an eigenimage into eigenimages? ................... 61 How can we approximate an image using SVD? .................... 62 Box 2.3. What is the intuitive explanation of SVD? ................. 62 What is the error of the approximation of an image by SVD? ............ 63 Howt can we minimise the error of the reconstruction? ................ 65 Are there any sets of elementary images in terms of which any image may be expanded? 72 What is a complete and orthonormal set of functions? ................ 72 Are there any complete sets of orthonormal discrete valued functions? ....... 73 2.2 Haar, Walsh and Hadamard transforms .................. 74 How are the Haar functions defined? .......................... 74 How are the Walsh functions defined? ......................... 74 Box 2.4. Definition of Walsh functions in terms of the Rademacher functions ... 74 How can we use the Haar or Walsh functions to create image bases? ........ 75 How can we create the image transformation matrices from the Haar and Walsh functions in practice? ................................ 76 What do the elementary images of the Haar transform look like? .......... 80 Can we define an orthogonal matrix with entries only +1 or -1?.......... 85 Box 2.5. Ways of ordering the Walsh functions .................... 86 What do the basis images of the Hadamard/Walsh transform look like? ...... 88 What are the advantages and disadvantages of the Walsh and the Haar transforms? 92 What is the Haar wavelet? ................................ 93 2.3 Discrete Fourier transform .......................... 94 What is the discrete version of the Fourier transform (DFT)? ............ 94 Box 2.6. What is the inverse discrete Fourier transform? ............... 95 How can we write the discrete Fourier transform in a matrix form? ......... 96 Is matrix U used for DFT unitary? ........................... 99 Which are the elementary images in terms of which DFT expands an image? . . . 101 Why is the discrete Fourier transform more commonly used than the other transforms? ..................................... 105 What does the convolution theorem state? ....................... 105 Box 2.7. If a function is the convolution of two other functions, what is the rela¬ tionship of its DFT with the DFTs of the two functions? ............ 105 How can we display the discrete Fourier transform of an image? ........... 112 What happens to the discrete Fourier transform of an image if the image is rotated? ...................................... 113 What happens to the discrete Fourier transform of an image if the image is shifted? ...................................... 114 What is the relationship between the average value of the image and its DFT? . . 118 What happens to the DFT of an image if the image is scaled? ............ 119 Box 2.8. What is the Fast Fourier Transform? ..................... 124 What are the advantages and disadvantages of DFT? ................. 126 Can we have a real valued DFT? ............................ 126 Can we have a purely imaginary DFT? ......................... 130 Can an image have a purely real or a purely imaginary valued DFT? ........ 137 2.4 The even symmetric discrete cosine transform (EDCT) ........ 138 What is the even symmetric discrete cosine transform? ................ 138 Box 2.9. Derivation of the inverse ID even discrete cosine transform ........ 143 What is the inverse 2D even cosine transform? .................... 145 What are the basis images in terms of which the even cosine transform expands an image? ........................................ 146 2.5 The odd symmetric discrete cosine transform (ODCT) ........ 149 What is the odd symmetric discrete cosine transform? ................ 149 Box 2.10. Derivation of the inverse ID odd discrete cosine transform ........ 152 What is the inverse 2D odd discrete cosine transform? ................ 154 What are the basis images in terms of wyhich the odd discrete cosine transform expands an image? ................................. 154 2.6 The even antisymmetric discrete sine transform (EDST) ....... 157 What is the even antisymmetric discrete sine transform? ............... 157 Box 2.11. Derivation of the inverse ID even discrete sine transform ......... 160 What is the inverse 2D even sine transform? ...................... 162 What are the basis images in terms of which the even sine transform expands an image? ........................................ 163 What happens if we do not remove the mean of the image before we compute its EDST? ........................................ 166 2.7 The odd antisymmetric discrete sine transform (ODST) ....... 167 What is the odd antisymmetric discrete sine transform? ............... 167 Box 2.12. Derivation of the inverse ID odd discrete sine transform ......... 171 What is the inverse 2D odd sine transform? ...................... 172 What are the basis images in terms of which the odd sine transform expands an image? ........................................ 173 What is the take home message of this chapter? .................. 176 3 Statistical Description of Images 177 What is this chapter about? ............................... 177 Why do we need the statistical description of images? ................ 177 3.1 Random fields .................................. 178 WThat is a random field? ................................. 178 What is a random variable? ............................... 178 Wrhat is a random experiment? ............................. 178 How do we perform a random experiment with computers? ............. 178 How do we describe random variables? ......................... 178 Wbat is the probability of an event? .......................... 179 What is the distribution function of a random variable? ............... 180 What is the probability of a random variable taking a specific value? ........ 181 Wbat is the probability density function of a random variable? ........... 181 How do we describe many random variables? ..................... 184 What relationships may η random variables have with each other? ......... 184 How do we define a random field? ........................... 189 How can we relate two random variables that appear in the same random field? . . 190 How can we relate two random variables that belong to two different random fields? ........................................ 193 If we have just one image from an ensemble of images, can we calculate expectation values? ........................................ 195 When is a random field homogeneous with respect to the mean? .......... 195 AVhen is a random field homogeneous with respect to the autocorrelation function? 195 How can we calculate the spatial statistics of a random field? ............ 196 How do we compute the spatial autocorrelation function of an image in practice? . 196 When is a random field ergodic with respect to the mean? .............. 197 When is a random field ergodic with respect to the autocorrelation function? . . . 197 What is the implication of ergodicity? ......................... 199 Box 3.1. Ergodicity. fuzzy logic and probability theory ................ 200 How can we construct a basis of elementary images appropriate for expressing in an optimal way a whole set of images? ........................ 200 3.2 Karhunen-Loeve transform .......................... 201 Wbat is the Karhunen-Loeve transform? ........................ 201 Why does diagonalisation of the autocovariance matrix of a set of images define a desirable basis for expressing the images in the set? ............... 201 How can we transform an image so its autocovariance matrix becomes diagonal? . 204 What is the form of the ensemble autocorrelation matrix of a set of images, if the ensemble is stationary with respect to the autocorrelation? .......... 210 How do we go from the ID autocorrelation function of the vector representation of an image to its 2D autocorrelation matrix? ................... 211 How can we transform the image so that its autocorrelation matrix is diagonal? . . 213 How do we compute the K-L transform of an image in practice? .......... 214 How do we compute the Karhunen-Loeve (K-L) transform of an ensemble of images? ....................................... 215 Is the assumption of ergodicity realistic? ........................ 215 Box 3.2. How can we calculate the spatial autocorrelation matrix of an image, when it is represented by a vector? ........................... 215 Is the mean of the transformed image expected to be really 0? ........... 220 How can we approximate an image using its K-L transform? ............. 220 What is the error with which we approximate an image when we truncate its K-L expansion? ..................................... 220 What are the basis images in terms of which the Karhunen-Loeve transform expands an image? ...................................... 221 Box 3.3. What is the error of the approximation of an image using the Karhunen- Loeve transform? .................................. 226 3.3 Independent component analysis ...................... 234 What is Independent Component Analysis (ICA)? .................. 234 What is the cocktail party problem? .......................... 234 Howr do we solve the cocktail party problem? ..................... 235 What does the central limit theorem say? ....................... 235 What do we mean by saying that the samples of Xi(t) are more Gaussianly dis¬ tributed than either S (t) or S2(t) in relation to the cocktail party problem? Are we talking about the temporal samples of Xi(t), or are we talking about all possible versions of Xi (í) at a given time? .................. 235 Howt do we measure non- Gaussiani ty? ......................... 239 How are the moments of a random variable computed? ................ 239 How is the kurtosis defined? ............................... 240 How is negentropy defined? ............................... 243 How is entropy defined? ................................. 243 Box 3.4. From all probability density functions with the same variance, the Gaussian has the maximum entropy ............................. 246 How is negentropy computed? .............................. 246 Box 3.5. Derivation of the approximation of negentropy in terms of moments . . . 252 Box 3.6. Approximating the negentropy with nonquadratic functions ........ 254 Box 3.7. Selecting the nonquadratic functions with which to approximate the ne¬ gentropy ....................................... 257 How do we apply the central limit theorem to solve the cocktail party problem? . . 264 How may ICA be used in image processing? ...................... 264 How do we search for the independent components? ................. 264 Howt can we whiten the data? .............................. 266 How can we select the independent components from whitened data? ........ 267 Box 3.8. How does the method of Lagrange multipliers work? ............ 268 Box 3.9. How can wTe choose a direction that maximises the negentropy? ...... 269 How do we perform ICA in image processing in practice? .............. 274 How do we apply ICA to signal processing? ...................... 283 What are the major characteristics of independent component analysis? ...... 289 What is the difference between ICA as applied in image and in signal processing? . 290 What is the take home message of this chapter? .................. 292 Image Enhancement 293 What is image enhancement? .............................. 293 How can we enhance an image? ............................. 293 What is linear filtering? ................................. 293 4.1 Elements of linear filter theory ........................ 294 How do we define a 2D filter? .............................. 294 How are the frequency response function and the unit sample response of the filter related? ....................................... 294 Why are we interested in the filter function in the real domain? ........... 294 Are there any conditions which h{k.l) must fulfil so that it can be used as a convo¬ lution filter? ..................................... 294 Box 4.1. What is the unit sample response of the 2D ideal low pass filter? ..... 296 What is the relationship between the ID and the 2D ideal lowpass filters? ..... 300 How can we implement in the real domain a filter that is infinite in extent? .... 301 Box 4.2. ¿-transforms .................................. 301 Can we define a filter directly in the real domain for convenience? ......... 309 Can we define a filter in the real domain, without side lobes in the frequency domain? ....................................... 309 4.2 Reducing high frequency noise ........................ 311 What are the types of noise present in an image? ................... 311 What is impulse noise? .................................. 311 What is Gaussian noise? ................................. 311 What is additive noise? ................................. 311 What is multiplicative noise? .............................. 311 What is homogeneous noise? .............................. 311 What is zero-mean noise? ................................ 312 What is biased noise? .................................. 312 What is independent noise? ............................... 312 What is uncorrelated noise? ............................... 312 What is white noise? ................................... 313 What is the relationship between zero-mean uncorrelated and white noise? .... 313 What is iid noise? .................................... 313 Is it possible to have white noise that is not iid? ................... 315 Box 4.3. The probability density function of a function of a random variable . . . 320 Why is noise usually associated with high frequencies? ................ 324 How do we deal with multiplicative noise? ....................... 325 Box 4.4. The Fourier transform of the delta function ................. 325 Box 4.5. Wiener-Khinchine theorem .......................... 325 Is the assumption of Gaussian noise in an image justified? .............. 326 How do we remove shot noise? ............................. 326 What is a rank order filter? ............................... 326 What is median filtering? ................................ 326 What is mode filtering? ................................. 328 How do we reduce Gaussian noise? ........................... 328 Can we have weighted median and mode filters like we have weighted mean filters? 333 Can we filter an image by using the linear methods we learnt in Chapter 2? .... 335 How do we deal with mixed noise in images? ..................... 337 Can we avoid blurring the image when we are smoothing it? ............. 337 What is the edge adaptive smoothing? ......................... 337 Box 4.6. Efficient computation of the local variance ................. 339 How does the mean shift algorithm work? ....................... 339 What is anisotropic diffusion? .............................. 342 Box 4.7. Scale space and the heat equation ...................... 342 Box 4.8. Gradient, Divergence and Laplacian ..................... 345 Box 4.9. Differentiation of an integral with respect to a parameter ......... 348 Box 4.10. From the heat equation to the anisotropic diffusion algorithm ...... 348 How do we perform anisotropic diffusion in practice? ................. 349 4.3 Reducing low frequency interference .................... 351 When does low frequency interference arise? ...................... 351 Can variable illumination manifest itself in high frequencies? ............ 351 In which other cases may we be interested in reducing low frequencies? ....... 351 What is the ideal high pass filter? ........................... 351 How can we enhance small image details using nonlinear filters? ........... 357 What is unsharp masking? ................................ 357 How can we apply the unsharp masking algorithm locally? .............. 357 How does the locally adaptive unsharp masking work? ................ 358 How does the retinex algorithm work? ......................... 360 Box 4.11. Which are the grey values that are stretched most by the retinex algorithm? ...................................... 360 How can we improve an image which surfers from variable illumination? ...... 364 What is homomorphic filtering? ............................. 364 What is photometric stereo? ............................... 366 What does flatfielding mean? .............................. 366 How is flatfielding performed? .............................. 366 4.4 Histogram manipulation ............................ 367 What is the histogram of an image? .......................... 367 When is it necessary to modify the histogram of an image? ............. 367 How can we modify the histogram of an image? .................... 367 What is histogram manipulation? ............................ 368 What affects the semantic information content of an image? ............. 368 How can we perform histogram manipulation and at the same time preserve the information content of the image? ......................... 368 What is histogram equalisation? ............................ 370 Why do histogram equalisation programs usually not produce images with flat his¬ tograms? ...................................... 370 How do we perform histogram equalisation in practice? ............... 370 Can we obtain an image with a perfectly flat histogram? ............... 372 What if we do not wish to have an image with a fiat histogram? .......... 373 How do we do histogram hyperbolisation in practice? ................. 373 How do we do histogram hyperbolisation with random additions? .......... 374 Why should one wish to perform something other than histogram equalisation? . . 374 What if the image has inhomogeneous contrast? ................... 375 Can we avoid damaging flat surfaces while increasing the contrast of genuine tran¬ sitions in brightness? ................................ 377 How can we enhance an image by stretching only the grey values that appear in genuine brightness transitions? .......................... 377 How do we perform pairwise image enhancement in practice? ............ 378 4.5 Generic deblurring algorithms ........................ 383 How does mode filtering help deblur an image? .................... 383 Can we use an edge adaptive window to apply the mode filter? ........... 385 How can mean shift be used as a generic deblurring algorithm? ........... 385 What is toboggan contrast enhancement? ....................... 387 How do we do toboggan contrast enhancement in practice? ............. 387 What is the take home 1 message of this chapter? .................. 393 5 Image Restoration 395 WThat is image restoration? ............................... 395 Why may an image require restoration? ........................ 395 What is image registration? ............................... 395 How is image restoration performed? .......................... 395 What is the difference between image enhancement and image restoration? .... 395 5.1 Homogeneous linear image restoration: inverse filtering ........ 396 How do we model homogeneous linear image degradation? .............. 396 How may the problem of image restoration be solved? ................ 396 How may we obtain information on the frequency response function H(u, v) of the degradation process? ................................ 396 If we know the frequency response function of the degradation process, isn t the solution to the problem of image restoration trivial? .............. 407 What happens at frequencies where the frequency response function is zero? .... 408 Will the zeros of the frequency response function and the image always coincide? ....................................... 408 How can we avoid the amplification of noise? ..................... 408 How do we apply inverse filtering in practice? ..................... 410 Can we define a filter that will automatically take into consideration the noise in the blurred image? ................................. 417 5.2 Homogeneous linear image restoration: Wiener filtering ....... 419 How can we express the problem of image restoration as a least square error esti¬ mation problem? .................................. 419 Can we find a linear least squares error solution to the problem of image restoration? ..................................... 419 What is the linear least mean square error solution of the image restoration problem? ...................................... 420 Box 5.1. The least squares error solution ........................ 420 Box 5.2. From the Fourier transform of the correlation functions of images to their spectral densities .................................. 427 Box 5.3. Derivation of the Wiener filter ........................ 428 What is the relationship between Wiener filtering and inverse filtering? ...... 430 How can we determine the spectral density of the noise field? ............ 430 How can we possibly use Wiener filtering, if we know nothing about the statistical properties of the unknown image? ........................ 430 How do we apply Wiener filtering in practice? ..................... 431 5.3 Homogeneous linear image restoration: Constrained matrix inversion 436 If the degradation process is assumed linear, why don t we solve a system of linear equations to reverse its effect instead of invoking the convolution theorem? . 436 Equation (5.146) seems pretty straightforward, why bother with any other approach? ...................................... 436 Is there any way by which matrix H can be inverted? ................ 437 When is a matrix block circulant? ........................... 437 When is a matrix circulant? ............................... 438 Why can block circulant matrices be inverted easily? ................. 438 Which are the eigenvalues and eigenvectors of a circulant matrix? .......... 438 How does the knowledge of the eigenvalues and the eigenvectors of a matrix help in inverting the matrix? ................................ 439 How do we know that matrix H that expresses the linear degradation process is block circulant? ................................... 444 How can we diagonalise a block circulant matrix? ................... 445 Box 5.4. Proof of equation (5.189)........................... 446 Box 5.5. What is the transpose of matrix H? ..................... 448 How can we overcome the extreme sensitivity of matrix inversion to noise? ..... 455 How can we incorporate the constraint in the inversion of the matrix? ....... 456 Box 5.6. Derivation of the constrained matrix inversion filter ............ 459 What is the relationship between the Wiener filter and the constrained matrix in¬ version filter? .................................... 462 How do we apply constrained matrix inversion in practice? ............. 464 5.4 Inhomogeneous linear image restoration: the whirl transform .... 468 How do we model the degradation of an image if it is linear but inhomogeneous? . 468 How may we use constrained matrix inversion when the distortion matrix is not circulant? ...................................... 477 What happens if matrix H is really very big and wTe cannot take its inverse? .... 481 Box 5.7. Jacobi s method for inverting large systems of linear equations ...... 482 Box 5.8. Gauss-Seidel method for inverting large systems of linear equations .... 485 Does matrix Я as constructed in examples 5.41. 5.43, 5.44 and 5.45 fulfil the condi¬ tions for using the Gauss-Seidel or the Jacobi method? ............. 485 What happens if matrix H does not satisfy the conditions for the Gauss-Seidel method7 ................. ...................... 486 How do wre apply the gradient descent algorithm in practice? ............ 487 What happens if we do not know matrix ΗΊ ..................... 489 5.5 Nonlinear image restoration: MAP estimation .............. 490 What does MAP estimation mean? ........................... 490 How do we formulate the problem of image restoration as a MAP estimation? . . . 490 How do we select the most probable configuration of restored pixel values, given the degradation model and the degraded image? ................... 490 Box 5.9. Probabilities: prior, a priori, posterior, a posteriori, conditional ...... 491 Is the minimum of the cost function unique? ..................... 491 How can we select then one solution from all possible solutions that minimise the cost function? .................................... 493 Can we combine the posterior and the prior probabilities for a configuration x? . . 493 Box 5.10. Parseval s theorem .............................. 496 How do we model in general the cost function we have to minimise in order to restore an image? ...................................... 499 What is the reason we use a temperature parameter when we model the joint prob¬ ability density function, since its does not change the configuration for which the probability takes its maximum? ........................ 501 How does the temperature parameter allow us to focus or defocus in the solution space? ........................................ 501 How do we model the prior probabilities of configurations? ............. 501 What happens if the image has genuine discontinuities? ............... 502 How do we minimise the cost function? ........................ 503 How do we create a possible new solution from the previous one? .......... 503 How do we know when to stop the iterations? ..................... 505 How do we reduce the temperature in simulated annealing? ............. 506 How do we perform simulated annealing with the Metropolis sampler in practice? . 506 How do we perform simulated annealing with the Gibbs sampler in practice? . . . 507 Box 5.11. How can we draw random numbers according to a given probability density function? .................................. 508 Why is simulated annealing slow? ............................ 511 How can we accelerate simulated annealing? ...................... 511 How can we coarsen the configuration space? ..................... 512 5.6 Geometric image restoration ......................... 513 How may geometric distortion arise? .......................... 513 Why do lenses cause distortions? ............................ 513 How can a geometrically distorted image be restored? ................ 513 How do we perform the spatial transformation? .................... 513 How may we model the lens distortions? ........................ 514 How can we model the inhomogeneous distortion? .................. 515 How can we specify the parameters of the spatial transformation model? ...... 516 Why is grey level interpolation needed? ........................ 516 Box 5.12. The Hough transform for line detection ................... 520 WThat is the take home message of this chapter? .................. 526 6 Image Segmentation and Edge Detection 527 What is this chapter about? ............................... 527 What exactly is the purpose of image segmentation and edge detection? ...... 527 6.1 Image segmentation ............................... 528 How can we divide an image into uniform regions? .................. 528 What do we mean by labelling an image? ...................... 528 What can we do if the valley in the histogram is not very sharply defined? ..... 528 How can we minimise the number of misclassified pixels? .............. 529 How can we choose the minimum error threshold? .................. 530 What is the minimum error threshold when object and background pixels are nor¬ mally distributed? ................................. 534 WThat is the meaning of the two solutions of the minimum error threshold equation? ...................................... 535 Ho v can we estimate the parameters of the Gaussian probability density functions that represent the object and the background? ................. 537 What are the drawbacks of the minimum error threshold method? ......... 541 Is there any method that does not depend on the availability of models for the distributions of the object and the background pixels? ............. 541 Box 6.1. Derivation of Otsu s threshold ........................ 542 Are there any drawbacks in Otsu s method? ...................... 545 How can we threshold images obtained under variable illumination? ........ 545 If we threshold the image according to the histogram of In f(x, y)i are we thresholding it according to the reflectance properties of the imaged surfaces? ....................................... 545 Box 6.2. The probability density function of the sum of two random variables . . . 546 Since straightforward thresholding methods break down under variable illumination, how can we cope with it? ...................... 548 What do we do if the histogram has only one peak? ................. 549 Are there any shortcomings of the grey value thresholding methods? ........ 550 How can we cope with images that contain regions that are not uniform but they are perceived as uniform? .............................. 551 Can we improve histogramming methods by taking into consideration the spatial proximity of pixels? ................................ 553 Are there any segmentation methods that take into consideration the spatial prox¬ imity of pixels? ................................... 553 How can one choose the seed pixels? .......................... 554 How does the split and merge method work? ..................... 554 What is morphological image reconstruction? ..................... 554 How does morphological image reconstruction allow us to identify the seeds needed for the watershed algorithm? ........................... 557 How do we compute the gradient magnitude image? ................. 557 W hat is the role of the number we subtract from ƒ to create mask g in the morpho¬ logical reconstruction of ƒ by gl ......................... 558 What is the role of the shape and size of the structuring element in the morphological reconstruction of ƒ by g? ............................. 560 How does the use of the gradient magnitude image help segment the image by the watershed algorithm? ................................ 566 Are there any drawbacks in the watershed algorithm which works with the gradient magnitude image? ................................. 568 Is it possible to segment an image by filtering? .................... 574 How can we use the mean shift algorithm to segment an image? ........... 574 What is a graph? ..................................... 576 How can we use a graph to represent an image? .................... 576 How can we use the graph representation of an image to segment it? ........ 576 What is the normalised cuts algorithm? ........................ 576 Box 6.3. The normalised cuts algorithm as an eigenvalue problem .......... 576 Box 6.4. How do we minimise the Rayleigh quotient? ................. 585 How do we apply the normalised graph cuts algorithm in practice? ......... 589 Is it possible to segment an image by considering the dissimilarities between regions, as opposed to considering the similarities between pixels? ........... 589 6.2 Edge detection .................................. 591 How do we measure the dissimilarity between neighbouring pixels? ......... 591 What is the smallest possible window we can choose? ................ 592 What happens when the image has noise? ....................... 593 Box 6.5. How can we choose the weights of a 3 x 3 mask for edge detection? .... 595 What is the best value of parameter ΚΊ ........................ 596 Box 6.6. Derivation of the Sobel filters ......................... 596 In the general case, how do we decide whether a pixel is an edge pixel or not? ... 601 How do we perform linear edge detection in practice? ................ 602 Are Sobel masks appropriate for all images? ...................... 605 How can we choose the weights of the mask if we need a larger mask owing to the presence of significant noise in the image? .................... 606 Can we use the optimal filters for edges to detect lines in an image in an optimal way? .................................... 609 What is the fundamental difference between step edges and lines? .......... 609 Box 6.7. Convolving a random noise signal with a filter ............... 615 Box 6.8. Calculation of the signal to noise ratio after convolution of a noisy edge signal with a filter ................................. 616 Box 6.9. Derivation of the good locality measure ................... 617 Box 6.10. Derivation of the count of false maxima .................. 619 Can edge detection lead to image segmentation? ................... 620 What is hysteresis edge linking? ............................. 621 Does hysteresis edge linking lead to closed edge contours? .............. 621 What is the Laplacian of Gaussian edge detection method? ............. 623 Is it possible to detect edges and lines simultaneously? ................ 623 6.3 Phase congruency and the monogenie signal ............... 625 WThat is phase congruency? ............................... 625 What is phase congruency for a ID digital signal? .................. 625 How does phase congruency allow us to detect lines and edges? ........... 626 Why does phase congruency coincide with the maximum of the local energy of the signal? ........................................ 626 How can we measure phase congruency? ........................ 627 Couldn t we measure phase congruency by simply averaging the phases of the har¬ monic components? ................................. 627 How do we measure phase congruency in practice? .................. 630 How do we measure the local energy of the signal? .................. 630 Why should we perform, convolution with the two basis signals in order to get the projection of the local signal on the basis signals? ................ 632 Box 6.11. Some properties of the continuous Fourier transform ........... 637 If all we need to compute is the local energy of the signal why don t we use Parsevaľs theorem to compute it in the real domain inside a local window? ....... 647 How do we decide which filters to use for the calculation of the local energy? . . . 648 How do we compute the local energy of a ID signal in practice? ........... 651 How can we tell whether the maximum of the local energy corresponds to a sym¬ metric or an antisymmetric feature? ....................... 652 How can we compute phase congruency and local energy in 2D? .......... 659 What is the analytic signal? ............................... 659 How can we generalise the Hubert transform to 2D? ................. 660 How do we compute the Riesz transform of an image? ................ 660 How can the monogenie signal be used? ........................ 660 How do we select the even filter we use? ........................ 661 What is the take home message of this chapter? .................. 668 Image Processing for Multispectral Images 669 What is a multispectral image? ............................. 669 What are the problems that are special to multispectral images? .......... 669 What is this chapter about? ............................... 670 7.1 Image preprocessing for multispectral images .............. 671 Why may one wish to replace the bands of a multispectral image with other bands? ........................................ 671 How do we usually construct a grey image from a multispectral image? ...... 671 How can we construct a single band from a multispectral image that contains the maximum amount of image information? ..................... 671 What is principal component analysis? ......................... 672 Box 7.1. How do we measure information? ....................... 673 How do we perform principal component analysis in practice? ............ 674 What are the advantages of using the principal components of an image, instead of the original bands? ................................. 675 What are the disadvantages of using the principal components of an image instead of the original bands? ............................... 675 Is it possible to work out only the first principal component of a multispectral image if we are not interested in the other components? ................ 682 Box 7.2. The power method for estimating the largest eigenvalue of a matrix . . . 682 What is the problem of spectral constancy? ...................... 684 What influences the spectral signature of a pixel? ................... 684 What is the reflectance function? ............................ 684 Does the imaging geometry influence the spectral signature of a pixel? ....... 684 How does the imaging geometry influence the light energy a pixel receives? .... 685 How do we model the process of image formation for Lambertian surfaces? .... 685 How can we eliminate the dependence of the spectrum of a pixel on the imaging geometry? ...................................... 686 How can we eliminate the dependence of the spectrum of a pixel on the spectrum of the illuminating source? ............................. 686 What happens if we have more than one illuminating sources? ........... 687 How can we remove the dependence of the spectral signature of a pixel on the imaging geometry and on the spectrum of the illuminant? ........... 687 What do we have to do if the imaged surface is not made up from the same material? ...................................... 688 What is the spectral unmixing problem? ........................ 688 How do we solve the linear spectral unmixing problem? ............... 689 Can we use library spectra for the pure materials? .................. 689 How do we solve the linear spectral unmixing problem when we knowT the spectra of the pure components? .............................. 690 Is it possible that the inverse of matrix Q cannot be computed? ........... 693 What happens if the library spectra have been sampled at different wavelengths from the mixed spectrum? ............................. 693 What happens if we do not know which pure substances might be present in the mixed substance? .................................. 694 How do we solve the linear spectral unmixing problem if we do not know the spectra of the pure materials? ............................... 695 7.2 The physics and psychophysics of colour vision ............. 700 What is colour? ...................................... 700 What is the interest in colour from the engineering point of view? ......... 700 What influences the colour we perceive for a dark object? .............. 700 What causes the variations of the daylight? ...................... 701 How can we model the variations of the daylight? ................... 702 Box 7.3. Standard illuminants .............................. 704 What is the observed variation in the natural materials? ............... 706 What happens to the light once it reaches the sensors? ................ 711 Is it possible for different materials to produce the same recording by a sensor? . . 713 How does the human visual system achieve colour constancy? ............ 714 WThat does the trichromatic theory of colour vision say? ............... 715 What defines a colour system? ............................. 715 How are the tristimulus values specified? ........................ 715 Can all monochromatic reference stimuli be matched by simply adjusting the inten¬ sities of the primary lights? ............................ 715 Do all people require the same intensities of the primary lights to match the same monochromatic reference stimulus? ........................ 717 Who are the people with normal colour vision? .................... 717 What are the most commonly used colour systems? .................. 717 What is the CIE RGB colour system? ......................... 717 What is the XYZ colour system? ............................ 718 How do we represent colours in 3D?.......................... 718 How do we represent colours in 2D? .......................... 718 What is the chromaticity diagram? ........................... 719 Box 7.4. Some useful theorems from 3D geometry .................. 721 What is the chromaticity diagram for the CIE RGB colour system? ........ 724 How does the human brain perceive colour brightness? ................ 725 How is the alychne defined in the CIE RGB colour system? ............ 726 How is the XYZ colour system defined? ........................ 726 What is the chromaticity diagram of the XYZ colour system? ........... 728 How is it possible to create a colour system with imaginary primaries, in practice? 729 What if we wish to model the way a particular individual sees colours? ....... 729 If different viewers require different intensities of the primary lights to see white. how do we calibrate colours between different viewers? ............. 730 How do we make use of the reference white? ...................... 730 How is the sRGB colour system defined? ....................... 732 Does a colour change if we double all its tristimulus л^а1иеѕ? ............. 733 How does the description of a colour, in terms of a colour system, relate to the way we describe colours in everyday language? .................... 733 How do we compare colours? .............................. 733 Wbat is a metric? .................................... 733 Can we use the Euclidean metric to measure the difference of two colours? ..... 734 Which are the perceptually uniform colour spaces? .................. 734 How is the Luv colour space defined? .......................... 734 How is the Lab colour space defined? .......................... 735 How do we choose values for (Xn,YniZn)7 ....................... 735 How can we compute the RGB values from the Luv values? ............. 735 How can we compute the RGB values from the Lab values? ............. 736 How do we measure perceived saturation? ....................... 737 How do we measure perceived differences in saturation? ............... 737 How do we measure perceived hue? ........................... 737 How is the perceived hue angle defined? ........................ 738 Howt do we measure perceived differences in hue? ................... 738 What affects the way we perceive colour? ....................... 740 What is meant by temporal context of colour? .................... 740 What is meant by spatial context of colour? ...................... 740 Why distance matters when we talk about spatial frequency? ............ 741 How do we explain the spatial dependence of colour perception? .......... 741 7.3 Colour image processing in practice .................... 742 How does the study of the human colour vision affect the way we do image processing? ..................................... 742 How perceptually uniform are the perceptually uniform colour spaces in practice? . 742 How should we convert the image RGB values to the Luv or the Lab colour spaces? ....................................... 742 How do we measure hue and saturation in image processing applications? ..... 747 How can we emulate the spatial dependence of colour perception in image processing? ..................................... 752 What is the relevance of the phenomenon of metamerism to image processing? . . 756 How do we cope with the problem of metamerism in an industrial inspection appli¬ cation? ........................................ 756 W7hat is a Monte-Carlo method? ............................ 757 How do we remove noise from multispectral images? ................. 759 How do we rank vectors? ................................ 760 How do we deal with mixed noise in multispectral images? .............. 760 How do we enhance a colour image? .......................... 761 How do we restore multispectral images? ........................ 767 How do we compress colour images? .......................... 767 How do we segment multispectral images? ....................... 767 How do we apply fc-means clustering in practice? ................... 767 How do we extract the edges of multispectral· images? ................ 769 What is the take home message of this chapter? .................. 770 Bibliographical notes 775 References 777 Index 781
any_adam_object	1
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spelling	Petrou, Maria 1953-2012 Verfasser (DE-588)1048298361 aut Image processing the fundamentals Maria Petrou ; Costas Petrou 2. ed. Chichester Wiley 2010 XXIII, 794 S. Ill., graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Hier auch später erschienene, unveränderte Nachdrucke Image processing / Digital techniques Image processing Digital techniques Bildverarbeitung (DE-588)4006684-8 gnd rswk-swf Bildverarbeitung (DE-588)4006684-8 s DE-604 Petrou, Costas Verfasser aut Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018985732&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Petrou, Maria 1953-2012 Petrou, Costas Image processing the fundamentals Image processing / Digital techniques Image processing Digital techniques Bildverarbeitung (DE-588)4006684-8 gnd
subject_GND	(DE-588)4006684-8
title	Image processing the fundamentals
title_auth	Image processing the fundamentals
title_exact_search	Image processing the fundamentals
title_full	Image processing the fundamentals Maria Petrou ; Costas Petrou
title_fullStr	Image processing the fundamentals Maria Petrou ; Costas Petrou
title_full_unstemmed	Image processing the fundamentals Maria Petrou ; Costas Petrou
title_short	Image processing
title_sort	image processing the fundamentals
title_sub	the fundamentals
topic	Image processing / Digital techniques Image processing Digital techniques Bildverarbeitung (DE-588)4006684-8 gnd
topic_facet	Image processing / Digital techniques Image processing Digital techniques Bildverarbeitung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018985732&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT petroumaria imageprocessingthefundamentals AT petroucostas imageprocessingthefundamentals

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