Reading list for CMP students interested in geometry of Computer Vision
Tomáš Pajdla
pajdla@cmp.felk.cvut.cz
The reading list suggests the literature that helps us to do good and
interesting research. The reading covers relevant philosophy of
science, mathematics, and computer vision. I recommend to read the
literature in the displayed order. I assume that the students have
read the material
http://cmp.felk.cvut.cz/pajdla/cmp/phd/phdintro/
and the literature referenced there.
 A very interesting work [1] by T.S.Kuhn
suggests how science develops and why it may be difficult to
understand other scientists. It represents the main stream in
contemporary philosophy of science.
 The book [2] by H.B.Michaelson teaches how to
write and present research material.
 An interesting definition of geometry and its role in
mathematics, as well as the definition of mathematics itself, can be
found in this concise and remarkably clear
chapter [3] by F.Buekenhout.
 The basic principles for most mathematics is here [4]. In
my opinion, this is the best book for a nonmathematician to acquire
solid understanding of the concepts such as set, mapping,
function, relations, order, and mathematical induction. It is
absolutely necessary to read first fifteen chapters of this short
but brilliant textbook.
 A very good text book for matrix calculus [5] by
E.Krajník. Do exercises in the book!
 Everybody should read this excellent
book [6] by P.R.Halmos. Do exercises in
the book!
 The text book [7] by R.J.Mihalek gives solid
backgrounds in projective planes and spaces in a modern way. Do
exercises in the book!
 The paper [8] by T.Buchanan shows that much of
the theory used in recent computer vision research was known to
German mathematicians at the end of the 19th century. Old results
are good results!
 The book [9] by R.Hartley and A.Zisserman
represents the state of the art in the geometry of computer vision.
It contains a good review of literature. You have to read the
mathematical books above to really understand it.
 The book [10] by Faugeras et.
al covers basically the same area as the book [9] but
some mathematical tools are described better and in more detail.
Literature [1] provides a general background in
philosophy of science. It is easy and enjoyable reading. It as an
appetizer for more difficult readings.
Literature [3,4,5,6,7]
provides mathematical backgrounds. This literature must be
studied. All students, even those who know the subject from previous
studies, should go through the exercises.
The book [9] is a recent monograph related to
geometrical problems in computer vision. It has to be read and
understood by those who want to make a contribution in this field.
Another monograph [10], tackling the
same topic, has appeared one year later. The book [9]
is more practical and easily accessible to everyone who has basic
mathematical knowledge from the literature above. The
book [10] more elaborates on certain
mathematical tools and is better to be read after [9].
 1

Thomas S. Kuhn.
The Structure of Scientific Revolutions.
The University of Chicago Press, Chicago, 1970.
 2

Herbert B. Michaelson, editor.
How to Write and Publish Engineering Papers and Reports.
Professionals Writing Series. Isi Press, Philadelphia, USA, 2nd
edition, 1986.
CMP.book.YC31.
 3

E. Buekenhout.
Handbook of Incidence Geometry : Buildings and Foundations,
chapter An Introduction to Incidence Geometry.
Elsevier, Amsterdam, the Netherlands, 1995.
CMP.book.A222.
 4

Paul R. Halmos.
Naive Set Theory.
Undergraduate Texts in Mathematics. Springer, New York, USA, 1974.
CMP.book.A237.
 5

Eduard Krajník.
Maticový pocet.
Vydavatelství CVUT, Praha, Czech Republic, 1 edition, March
2000.
CMP.book.A193.
 6

P. R. Halmos.
FiniteDimensional Vector Spaces.
Van Nostrand, Princeton, New Jersey, 1958.
CMP.book.A229.
 7

R. J. Mihalek.
Projective Geometry and Algebraic Structures.
Academic Press, New York, USA, 1972.
CMP.book.AC59.
 8

T. Buchanan.
Photogrammetry and projective geometry  an historical survey.
In A.D. Barret and D.M.Jr Keown, editors, Integrating
Photogrammetric Techniques with Scene Analysis and Machine Vision., volume
1944, pages 8291. SPIE, 1993.
 9

R. Hartley and A. Zisserman.
Multiple View Geometry in Computer Vision.
Cambridge University Press, Cambridge, UK, 2000.
CMP.book.B207.
 10

Olivier Faugeras, Quang Tuan Luong, and Théo Papadopoulo.
The Geometry of Multiple Images : The Laws That Govern the
Formation of Multiple Images of a Scene and Some of Their Applications.
MIT Press, Cambridge, Massachusetts, 2001.
CMP.book.B227.
Tomas Pajdla
20030210