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/$\sim$pajdla/cmp/phd/phd-intro/
and the literature referenced there.

1. 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.
2. The book [2] by H.B.Michaelson teaches how to write and present research material.
3. 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.
4. The basic principles for most mathematics is here [4]. 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.
5. A very good text book for matrix calculus [5] by E.Krajník. Do exercises in the book!
6. Everybody should read this excellent book [6] by P.R.Halmos. Do exercises in the book!
7. 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!
8. 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 19-th century. Old results are good results!
9. 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.
10. 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].

Bibliography

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.
Finite-Dimensional 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 82-91. 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.