Here
is a useful book (the title is correct!) that covers a wealth of processing
tools in a single volume accessible to experts and novices alike. Topics
include analytic geometry, linear algebra, least squares solutions, principal
component analysis and singular value decomposition, spectral transforms,
solution of linear systems, and graphs and images, to name a few. All topics are applicable to image processing
and most are applicable to other areas as well.
Each
chapter is stand-alone so the reader can learn the material quickly without the
need to study earlier chapters to understand later chapters. If the reader
doesn’t know what he needs, the table of contents shows the reader what’s in
each chapter and whether the material might apply to his problem.
The
text is lucid, easy to read, and follows a logical progression. Equations are
explained and the authors provide ample figures and pictures to illustrate the
concepts and discussions.
For
example, the authors discuss how to determine is two lines intersect in 3-space
with a step-by-step development of the mathematics and resulting algorithm. Next,
they show how to fit a line to data points in a least squares sense and give pictorial
examples in 2- and 3-space. The chapter on Least-Squares Solutions shows how to
fit, say a curve to data points from an edge of an image and how to weight the
data points to compensate for outliers. The chapter on spectral transforms
provides an excellent discussion on image compression techniques such as the
Discrete Cosine Transform and Laplacian smoothing.
Incidentally,
the book intuitively discusses how one can use Laplacian equations for image
reconstruction and image manipulation. There is an image, for example, where
most of the image is missing but with an image completeness algorithm based on
smoothness (that is, find the best image that is smooth relative to the known
data) one sees a fitted image quite close to the original. (Incidentally, it has
always amazed me how much information one can discard from an image and yet
still recover the original image, almost precisely.)
What
is more, the book discusses Poisson panoramic image stitching and shows a
beautiful example of city landscape before and after the processing. This tells
part of the story of current digital cameras that allow one to take multiple
pictures of a scene with each picture angularly offset from the other. The processed
image is a smooth panoramic view that would be unobtainable otherwise. The
stitching and smooth transition between images is both natural and
unnoticeable.
On
a slightly negative note, the chapter on topology is a bit weak. Of course, topology is a complicated and
involved topic and while the gist of it can be explained succinctly,
applications require more space than the authors had to produce a well-balanced
text. Still, as a reference that at least mentions this topic the authors do an
admirable job summarizing the details.
In
conclusion, this book is a good collection of algorithms and tools for computer
graphics. The topics are useful, well-presented, and collected in a single book
for easy access. If you work in this area, you’ll find this book beneficial.
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