Geometry

Work Geometry is basic to computer vision and contains many subareas. We are well aware that this page does not yet contain references on sufficient areas.

The best single reference is a paperback by Roe. It is very clear and has the most appropriate topic coverage. The book by Jennings is attractive and provides a wider perspective on the relations to math and science. The book by Smart is also clear, more expensive, and has a slightly different range of topics, tending more towards alternative geometries.

Roe, John (1993) Elementary Geometry, Oxford University Press, Oxford, UK (ISBN: 0-19-853456-6), about $30.
Jennings, George A. (1994) Modern Geometry with Applications, Springer-Verlag, New-York (ISBN: 0-387-94222-X), about $20.
Smart, James R. (1994) Modern Geometries (4th edition), Brooks/Cole (ISBN: 0-534-21198-4) about $66.

Overview of Geometry

The classic book by Hilbert and Cohn-Vossen is still in print and very readable. Great for getting ideas, but useless for quantitative details.

Hilbert, D. and S. Cohn-Vossen (1932) Geometry and the Imagination, Chelsea Publishing Co., New York, second edition, 1990, translation by P. Nemenyi of Anschauliche Geometrie, Springer-Verlag, Berlin, 1932.

Parameterized curves and surfaces

Roe, John (1993) Elementary Geometry, Oxford University Press, Oxford, UK (ISBN: 0-19-853456-6), about $30.

Spherical Geometry

A clear presentation of basic facts from spherical geometry can be found in the book by Jennings (see above) and in McCleary's differential geometry text.

McCleary, John M. (1994) Geometry from a Differentiable Viewpoint, Cambridge University Press, Cambridge UK.

Complex Numbers and Geometry

The book by Hahn is absolutely wonderful and assumes almost no background. A useful preliminary if you are having trouble reading more advanced material using complex techniques.

Hahn, Liang-shin (1994) Complex Numbers and Geometry, Mathematical Association of America, Washington DC.

Tilings, Repeating Patterns

The standard reference for tilings and patterns in 2D is the fat volume by Grünbaum and Shephard. It has everything, in detail, with lots of pictures, and it is extremely readable. Be careful: there is also an abridged edition, which is significantly less nice.

Grünbaum, Branko and G.C. Shephard (1987) Tilings and Patterns, W.H. Freeman and Co., New York.

Symmetry

The Hargittai book is an inexpensive paperback with many wonderful photos of objects illustrating different types of symmetries. You've seen similar photos in other places, but not so many and such nice photography.

Istv'an Hargittai and Magdolna Hargittai (1994) Symmetry: a Unifying Concept, Shelter Publications, Bolinas CA.

Differential geometry

A particularly clear, readable, comprehensive, and cheap introduction to differential geometry can be found in:

McCleary, John M. (1994) Geometry from a Differentiable Viewpoint, Cambridge University Press, Cambridge UK.

Computational geometry

Computational geometry is sufficiently central to computer vision that it deserves its own page.