Abstract
In this paper we develop the notion of a generalized matrix product that includes in its formulation the common matrix and vector products of linear algebra. After defining the generalized matrix product and investigating some of its properties, we provide some specific examples of its use in image processing.
Similar content being viewed by others
References
G.X. Ritter, “Recent Developments in Image Algebra”, in Advances in Electronics and Electron Physics, vol. 80, Academic Press, New York, 1991, pp. 243–308.
G.X. Ritter, “Heterogeneous Matrix Products”, Proc. Soc. Photo.-Opt. Instrum. Engg., vol. 1568, 1991, pp. 92–100.
G. Birkhoff and J. Lipson, “Heterogeneous Algebras”, J. Combin. Theory, vol. 8, 1970, pp. 115–133.
G.X. Ritter, J.N. Wilson, and J.L. Davidson, “Image Algebra: An Overview”, Comput. Vis., Graph., Image Process., vol. 49, 1990, pp. 297–331.
I. Pitas and A.N. Venetsanopoulos, “Morphological Shape Decomposition”, IEEE Trans. Patt. Anal. Mach. Intell., vol. 12, 1990, pp. 38–45.
L. Wu and Z. Xie, “Scaling Theorems for Zero-Crossings”, IEEE Trans. Patt. Anal. Mach. Intell., vol. 12, 1990, pp. 46–54.
L.M. Hhr, Parallel Computer Vision, Academic Press, Orlando, FL, 1987.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ritter, G.X., Zhu, H. The generalized matrix product and its applications. J Math Imaging Vis 1, 201–213 (1992). https://doi.org/10.1007/BF00129875
Issue Date:
DOI: https://doi.org/10.1007/BF00129875