Image Processing, Analysis, and Machine Vision

ISBN 0-495-08252-X




Existing text


p. 39

256 such cubes

512 such cubes

p. 41

Sensors based on photo-emission principles explore the photoelectric effect

Sensors based on photo-emission principles exploit the photoelectric effect

p. 41

This phenomenon is explored in several technological elements

This phenomenon is exploited in several technological elements

p. 43

luminophore is exponential

luminophore is described by a power-law function

p. 44

The term “high-pass filter” when discussing losses within cables suggests that low-frequency signals will be rejected.

It might be better to describe this as an “equalization” process that accentuates higher frequency components.

Eq. 3.5



p. 53

The complex Fourier transform of a sinusoid consists of two spikes, not one as implied by the text.


p. 53

The condition that \int|f(t)|dt is finite does not require an exponential decay in f(t), and would be met by a power-law decay faster than 1/|t|


p.56, Eq. 3.23



p.56, Eq. 3.23

|F|^2 = (Re F^2) + (Im F^2)


|F|^2 = (Re F)^2 + (Im F)^2



The number of possible DCT definitions seems to be half as many as stated – excluding the odd-extensions at both ends reduces the 16 initial options down by a factor of ¼ (exluding odd-odd, odd-even, even-odd, but leaving even-even).



unitary matrix

unit matrix


It is unclear whether a Jordan canonical form can be achieved by similarity transformation of a matrix unless the given matrix is Hermitian (or symmetric).



In the singular-value decomposition of a matrix, the matrix U is generally unitary, implying both row & column orthogonality, whereas V is only column orthogonal in general.



The speed of acoustic waves is generally proportional to the square-root of the elastic modulus, whereas the text implies a direct proportionality to “the elastic properties of the




The origin of chromatic aberration is more strongly influenced by the propagation through the material of the lens, rather than through air that surrounds it or the boundary between the two.


p.93, Eq.3.90

The scalar products are lacking either “.”s or transposes, e.g. n.L or n^{T}L



It would be helpful to use the example of satellite imaging of an airport to give examples of each of the four levels of image representation.



the image size is 2^{L−1}.

the image size is 2^L.


The reduction factor, \lambda appears to be defined by only an upper bound – it is unclear

whether |Mi+1|/|Mi| is intended to be equal to \lambda or whether \lambda is some form of best-fit to this ratio.



Multispectral images are more likely to be represented as vectors of matrices (or third-rank tensors) than by “binary matrices”


p. 124, l. 5+6

Output image pixel g(i,j) … f(i,j) in the input image

Output image pixel f(i,j) … g(i,j) in the input image


The paragraph breaks around “A digital image is discrete in nature and so equations (5.32)...” seem to be in the wrong place.



The expression of the Laplacian of a Gaussian is not correctly expressed within polar coordinates.

The correct expression for the Laplacian operator in 2D polar coordinates is

\frac{1}{r} \frac{\partial}{\partial r} r \frac{\partial}{\partial r} + \frac{1}{r^2} \frac{\partial^2}{\partial\theta^2}



This implies that equation 5.52 should contain a factor of (r^2/\sigma^2-2), and not (r^2/\sigma^2-1) as stated in the text. This is perhaps more straightforwardly obtained by calculating the Laplacian in Cartesian coordinates.


p. 151

The parameter D0 as used in the Gaussian filter coincides with the dispersion sigma, not sigma^2.


p. 151

As the Butterworth filter is normally used with a (power) frequency response that involves

even powers of the frequency, it might be more usual to replace n with 2n.


p. 159

The diagonal elements of the Harris matrix (equation 5.76) should involve

\(\frac{\partial f}{\partial x}\)^2


\(\frac{\partial f}{\partial y}\)^2

rather than second derivatives, to be consistent with equation 5.75. The immediately

preceeding text should also not refer to the “second derivative”.


p. 207

The bold-face on “main idea” is somewhat peculiar.


p. 215

The discussion of the Hough transform jumps rather abruptly from identifying parametric

curves to the detection of symmetry axes. It would be worth a few comments about how

the Hough transform can be formulated to detect, e.g. a mirror symmetry.


p. 238

The definition of the matching functions should probably include a scaling parameter alpha,


C_3(u,v) &=

  \frac{1}{\displaystyle 1+\sum_{(i,j)\in V}


\big(f(i+u,j+v) - h(i,j)\big)^2}

to emphasise that the fact that the matching function is sensitive to the choice of intensity

scale in f and h, and the number of pixels used in the summation. It might also be

appropriate to renumber the definitions C_n à C_(n1) so that C_2 involves squares of the pixel-differences.



In the closing sentence before algorithm 7.2 it might be worth adding “both” before “these

pixels being represented in the joint spatial-image domain”.


p. 267

The use of bold-faces in the partial derivatives \partial \psi / \partial \mathbf{n}_R  etc implies that these derivatives

are vectors or tensors (this convention often being used as a shorthand for \nabla \psi  etc).


p. 268

The Euler-Lagrange condition in equation 7.21 is incomplete when the functional being

minimized includes second-derivatives. A more complete condition also includes term

\frac{\d^2}{\d s^2}E_{{\bf v}_s}  (see LaTeX version of errata)


p. 270

The first term in equation 7.24 should have y^2_y replaced by u^2_y. It might also be worth

expressing the first term using delta notations (see LaTeX version of errata)


p. 275

The paragraph opening “Let a curve moving in time t” might better refer to a “closed



p. 278

Equation 7.40 is missing a “.” in the dot-product between\nabla \psi and \partial X / \partial t


p. 280

Equation 7.44 implies that c is a second-rank tensor. It should probably refer to the

divergence of |r_|1r_ rather than its gradient, to be consistent with the expanded form involving _xx etc. (see LaTeX version of errata)



The earlier definition of the interior of the contour has _ < 0 rather than _ > 0. To be

consistent, all terms in equation 7.47 probably needs to change sign.


p. 282

The derivation of μr. (|r_|1r_) in equation 7.47 from “μ(Length of _)” in equation 7.46

is far from trivial, and worthy of at least a brief explanation. I suspect that this term

may actually be(see LaTeX version of errata)


p. 309

The use of bold-face x etc in the first introduction of the 3D matrix I(x, y, z) doesn”t

seem consistent with immediately following use of x as a (unit) vector.


p. 338

The definition of the continuous and discrete versions of h(_x,_y) are not consistent

if the same b(x, y) is used. It is likely that the continous version will involve the Dirac

_-function, i.e. b(x, y) being infinite rather than unity on the contour so that the integral

in equation 8.2 is non-zero.


p. 339

The superscript in equation 8.6 should probably be int (math-italic) rather than “int”.


p. 340

The coefficients a_0 and b_0 are probably not translationally or rotationally invariant, unlike

the other coefficients.


p. 340

Equation 8.14 should perhaps involve uk rather than +uk so that the mean value of

a(lk) is zero.


p. 345

In the sentence “First, they change their shape less then their control polygon”, “then”

should be “than”.


p. 357

The definition of the “scale-invariant” quantity \eta_pq in equation 8.45 seems to imply that

the scale alpha  is known a priori. Given that the quantity μpq scales as _(p+q+2) under

x, y ! _x, _y, it would seem more likely that _pq should be defined as:

_pq = μpq


i.e. using μ rather than μ0. (see LaTeX version of errata)


p. 360

In algorithm 8.6, the definition of v might be more clearly expressed as Pq Pk, rather

than using an expression suggestive of the product of two vectors.


p. 368

The regions being described in Figure 8.34 a&b are unclear. It would be helpful to shade

those regions, or describe their shapes (e.g. “between the triangular boundaries in (a)”).


p. 370

After the reference to Bookstein 1991, there is a double full-stop before the sentence

starting “If such a landmark model”.


p. 460

we seek d b

we seek \delta b

p. 462, algorithm 10.4, item 4

Ends with “and halt”


Chapter 10, Fig. 10.26, p. 491

Alg. 10.9 referenced

Alg. 10.10 shall be referenced

Chapter 10, eq. 10.28, p. 494

extra right “)”

Remove right “)”

Chapter 15, p. 724, after eq. 15.9

\sigma_x and \sigma_y are defined as variances, not standard deviations


p. 771

… this other

… this and other


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