Reading list for CMP students interested in geometry of Computer Vision
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
and the literature referenced there.
- A very interesting work  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  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  by F.Buekenhout.
- The basic principles for most mathematics is here . In
my opinion, this is the best book for a non-mathematician 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  by
E.Krajník. Do exercises in the book!
- Everybody should read this excellent
book  by P.R.Halmos. Do exercises in
- The text book  by R.J.Mihalek gives solid
backgrounds in projective planes and spaces in a modern way. Do
exercises in the book!
- The paper  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 19-th century. Old results
are good results!
- The book  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  by Faugeras et.
al covers basically the same area as the book  but
some mathematical tools are described better and in more detail.
Literature  provides a general background in
philosophy of science. It is easy and enjoyable reading. It as an
appetizer for more difficult readings.
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  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 , tackling the
same topic, has appeared one year later. The book 
is more practical and easily accessible to everyone who has basic
mathematical knowledge from the literature above. The
book  more elaborates on certain
mathematical tools and is better to be read after .
Thomas S. Kuhn.
The Structure of Scientific Revolutions.
The University of Chicago Press, Chicago, 1970.
Herbert B. Michaelson, editor.
How to Write and Publish Engineering Papers and Reports.
Professionals Writing Series. Isi Press, Philadelphia, USA, 2nd
Handbook of Incidence Geometry : Buildings and Foundations,
chapter An Introduction to Incidence Geometry.
Elsevier, Amsterdam, the Netherlands, 1995.
Paul R. Halmos.
Naive Set Theory.
Undergraduate Texts in Mathematics. Springer, New York, USA, 1974.
Vydavatelství CVUT, Praha, Czech Republic, 1 edition, March
P. R. Halmos.
Finite-Dimensional Vector Spaces.
Van Nostrand, Princeton, New Jersey, 1958.
R. J. Mihalek.
Projective Geometry and Algebraic Structures.
Academic Press, New York, USA, 1972.
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 82-91. SPIE, 1993.
R. Hartley and A. Zisserman.
Multiple View Geometry in Computer Vision.
Cambridge University Press, Cambridge, UK, 2000.
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.