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Image algebra is a rigorous, concise notation that unifies linear and nonlinear mathematics in the image domain.
Image algebra was developed under DARPA and US Air Force sponsorship at University of Florida for over 15 years
beginning in 1984. Image algebra has been implemented in a variety of programming languages designed specifically to
support the development of image processing and computer vision algorithms and software. The University of Florida has
been associated with development of the languages FORTRAN, Ada, Lisp, and C++. The latter implementation involved
a class library, iac++, that supported image algebra programming in C++.
Since image processing and computer vision are generally performed with operands that are array-based, the
Matlab™ programming language is ideal for implementing the common subset of image algebra. Objects include sets
and set operations, images and operations on images, as well as templates and image-template convolution operations.
This implementation, called Image Algebra Matlab (IAM), has been found to be useful for research in data, image, and
video compression, as described herein. Due to the widespread acceptance of the Matlab programming language in the
computing community, IAM offers exciting possibilities for supporting a large group of users. The control over an
object's computational resources provided to the algorithm designer by Matlab means that IAM programs can employ
versatile representations for the operands and operations of the algebra, which are supported by the underlying libraries
written in Matlab. In a previous publication, we showed how the functionality of IAC++ could be carried forth into a
Matlab implementation, and provided practical details of a prototype implementation called IAM Version 1.
In this paper, we further elaborate the purpose and structure of image algebra, then present a maturing
implementation of Image Algebra Matlab called IAM Version 2.3, which extends the previous implementation of IAM to
include polymorphic operations over different point sets, as well as recursive convolution operations and functional
composition. We also show how image algebra and IAM can be employed in image processing and compression
research, as well as algorithm development and analysis.
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