CAP 6418 Section 4694X (Fall 1996)

Image Algebra

Instructor

Joseph N. Wilson

Course Description (http://www.cise.ufl.edu/~jnw/IA_syllabus.html)

This course focuses on the algebraic theory concerned with the transformation and analysis of images. The central theme of this course is image algebra, a comprehensive and unifying mathematical theory of image transformations, image analysis, and image understanding in the discrete as well as the continuous domain. Relationships between image algebra, linear algebra, lattice algebras, and other mathematical systems are explored. The course will provide a critical review and discussion of different mathematical models of images, algebraic image manipulation systems, and algebraic notations for specifying computer vision algorithms. A variety of image processing algorithms will be implemented using image algebra software environments. Algorithm optimization techniques employing image algebraic methods will be explored.

Prerequisite

CAP6657 (Computers and Vision) or some Image and Signal Processing course or industrial experience or consent of instructor.

This Semester's Offering

Course information will be provided via the World-Wide Web from the URL http://www.cise.ufl.edu/~jnw/IA_Course/.

Students will employ the Image Algebra C++ (iac++ ) library and the Lockheed Martin PAL SIMD parallel machine (9,216 parallel processors gathered together in a box about 1/2 cubic foot in volume) to prepare programming assignments. (No prior C++ knowledge is required if the student is willing to learn.)

Required Texts

G. Ritter and J. Wilson, Handbook of Computer Vision Algorithms in Image Algebra, CRC Press, 1996.

Selected readings from G.Ritter Image Algebra, (These will be made available from the University Copy Center.)

Credit

3 hours

Course Place and Time

TUR 2333, Tuesday periods 2 & 3, Thursday period 3.

Grading

Presentations and Projects (65%), Final Examination (35%).

Outline of Topics

• Image models
• Mathematical morphology
• Fundamental image algebra operands, value and spatial transforms, and functional composition
• Template pointwise and product operations and recursive template operations
• Applications of image algebra
• The linear algebra sub-algebra of image algebra
• Expressing linear transforms using templates and functional composition
• Template decompositions using linear algebra techniques
• Polynomial algebra, image algebra, and polynomial template decomposition
• Minimax algebra, image algebra, and minimax template decomposition
• Topics in computer implementation of image algebra

Student Presentations

Student classroom presentations will involve preparing some lecture material and presenting it to the class. Students will probably each make two 30 minute presentations during the semester (or fewer if class size is large). Topics will vary, but might include the following kinds of aspects:

• Relations of image algebra subalgebras to other mathematical structures,
• Discussion of Image processing and computer vision (IP/CV) algorithms expressed in image algebra,
• Image algebra implementation techniques

Projects

Projects will involve contributing to the body of knowledge of image algebra by

• Developing new or improved expressions of IP/CV algorithms in image algebra
• Developing computer implementions of existing image algebra algorithms with the image algebra C++ (iac++ ) library