CSc 83010

** The Geometry of Digital
Spaces**

Wednesdays 2:00 -4:00 p.m. -
3 credits - Professor
Gabor T. Herman **CODE: 37133**

Description:

There are many areas of science and engineering where multi-dimensional discrete data are collected and analyzed; e.g., neuroscience, medical imaging, industrial inspection, geoscience and fluid dynamics to name a few. In attempting to design and to prove the validity of computational procedures for the visualization and analysis of the information in such data, the need for a mathematical theory of surfaces, objects, and their boundaries in discrete spaces is essential. Such a theory - the geometry of digital spaces - is the subject matter of this course.

The course will be an introduction to this mathematical field that has been developed to provide a framework in which practical algorithms, such as those designed for the detection of three-dimensional surfaces, can be discussed. The approach of the course will be application motivated: the theoretical concepts and questions will be introduced in relation to their use in solving problems that arise in designing algorithms for multi-dimensional data processing.

**Textbook:**

Gabor T. Herman
:
Geometry of Digital Spaces
, Birkhäuser Boston, 1998

(**
see a review of this book by Azriel Rosenfeld**
).