One of my greatest hates is the edited book with chapters
from a number of different authors, some of which have
evidently been written in haste against the final deadline, and
most of which show marked divergence of content, opinion,
notation and presentation. I am very relieved to be able to
say that, though edited, this volume does not fall into
this stereotype, in spite - or perhaps partly because - of the
relatively few authors who have contributed to it. Indeed, it
falls into the category of a profound study of one major,
topical aspect of machine (or computer) vision, and provides
suitable contrasts which display the complexities of this
subject area, while at the same time bringing the reader to a
clear understanding of the problems, the principles and the
ways in which solutions can be found. With seven main
chapters (the first `chapter' is only a five-page overview of the
others, and there is no concluding chapter), it is surprising
how much is packed into the volume and how skilfully the
overlapping themes have been brought together - illustrating
in fact that these themes are core to the subject and at the
same time showing from different perspectives how they can
be handled. Perhaps most important amongst these recurring
themes are the roles of robust algorithms and robust statistics,
the problems of ambiguity and (for example) `dangerous
surfaces', the problems of focusing (which severely affects
camera calibration), the importance of nonlinear distortions
(which in high accuracy work absolutely have to be corrected
for) and, naturally, the measurement of camera parameters
(which are, as is now standard, divided into `internal' and
`external' parameters). This skilful compilation is particularly
welcome considering that in the Preface the Editor states
`This is not a textbook. Therefore, it is neither consistent in
diction nor content.'
Having succeeded on the coherence front, the book could
fall into another serious trap: it is stated to be the result of a
workshop on the same topic as the title of the book, held as
long ago as July 1992, having `for various reasons' only
reached publication in the current form almost a decade later.
In a fast moving subject such as 3D vision this could be a
serious problem, and make the volume totally irrelevant.
However, I did not find it thus. Clearly, the authors have not
been idly twiddling their thumbs all this time: they have
managed to update the chapters sufficiently to be of high
relevance to the present. All the authors are international
figures, and interestingly, the authors of the last chapter have
recently written a major textbook on the geometry of multiple
images, whose contents are well reflected in their chapter.
Of great importance to this volume is the fact that the
thinking comes from two directions, photogrammetry and
computer vision, there being four chapters on the former and
three on the latter topic. Over time, these two subjects have
become so large that it is difficult to know the whole of
either, let alone the whole of both, as they have grown up
with different motivations in different backgrounds. Yet it
has become imperative to put the two together, so as not to
have to re-invent the wheel many times in different contexts
(I hardly think the `Not Invented Here' syndrome has been
important in this respect). This volume, and no doubt the
workshop on which it was based, has managed to do this, and
has enlivened and enriched the whole area. Incidentally, I
ought to summarize the difference between the two
constituent disciplines: computer vision is aimed at studying
the real (largely 3D) world from the medium of images,
which it takes as incidental; while photogrammetry regards
the images themselves as the core representation and aims to
make this representation as accurate as possible (the aim, par
excellence, of photogrammetry is automatic production of
maps from remotely sensed images).
So far I may have given the impression that this volume is
exemplary in all aspects. However, it will be hard work for
readers who are not au fait with 3D vision. For one thing, the
mathematics of 3D vision is by no means trivial; what is
more, there are vitally important theorems stretching back
over many years (cf a key paper by H C Longuet-Higgins on
`A computer algorithm for reconstructing a scene from two
projections' Nature (1981), not to mention the still
highly relevant Kruppa relations which date from as long ago
as 1913). Then there are the pitfalls - in particular ambiguity,
which makes itself manifest in many forms - starting with the
minimum number of points required for 3D recognition and
orientation, which depends strongly on whether the
perspective is full or weak and whether the points are
coplanar or non-coplanar, and going on to more complex
`dangerous surfaces' - thereby broadening the subject from
the possible or impossible to interpret category to the stable
or unstable measurement situation, to which the solutions
offered by robust statistics are intimately linked. It goes
without saying that it is not the fault of the authors that the
subject area is complex and that the tools required to tackle it
in anger are not trivial. However, the result is that the reader
will need a basic knowledge of 3D vision before studying this
volume, and at the very least he or she should have read a
basic textbook on the subject (there are now a number of such
texts), and should, in addition, have a substantial pile of
original papers for reference. Having all this to hand, the
reader will learn a great deal from this volume: its xi + 235
pages are packed with concentrated, interesting material that
is well written and constructed, and contain vitally important
lessons for the student and the practitioner. The browser will
also be able to learn something. The sections on robust
estimation, image distortions, problems caused by focusing,
ambiguity and so forth, are didactic, and the reader will be
much aided by the valuable unifying index.
Finally, I ought to list the various chapters, so that readers
will know what they have in store for them. Without
exception, they are all worthy of serious study and none is a
`space filler':
A Gruen: `Introduction' (5 pp, no references)
B P Wrobel: `Minimum solutions for orientation' (56 pp,
121 references)
W Förstner: `Generic estimation procedures for orientation
with minimum and redundant information' (32 pp, 20 references)
C S Fraser: `Photogrammetric camera component
calibration: a review of analytical techniques' (27 pp, 24 references)
D B Gennery: `Least-squares camera calibration including
lens distortion and automatic editing of calibration points'
(14 pp, 7 references)
R G Willson and S A Shafer: `Modelling and calibration
of variable-parameter camera systems' (25 pp, 1 reference)
A Gruen and H A Beyer: `System calibration through self-calibration'
(31 pp, 13 references)
Q-T Luong and O D Faugeras: `Self-calibration of a
stereo rig from unknown camera motions and point
correspondences' (35 pp, 50 references).
Clearly, the 236 references are rather unevenly distributed
between the chapters. However, collectively they are highly
useful and a fair proportion do fall in the hidden decade
1992-2001 (I counted 62 that had been published over this
period, though only 16 from 1995-2001).
Overall, I have no hesitation in recommending this book to
those who will be working in this area. It is a highly relevant
and topical work which also contains valuable reference
material for the non-specialist: it also does an excellent job of
reuniting two subject areas that had gone their own ways over
a period of some 30 years.
E R Davies