Abstract
This paper introduces an algebraic framework for a topological analysis of time-varying 2D digital binary–valued images, each of them defined as 2D arrays of pixels. Our answer is based on an algebraic-topological coding, called AT–model, for a nD (n=2,3) digital binary-valued image I consisting simply in taking I together with an algebraic object depending on it. Considering AT–models for all the 2D digital images in a time sequence, it is possible to get an AT–model for the 3D digital image consisting in concatenating the successive 2D digital images in the sequence. If the frames are represented in a quadtree format, a similar positive result can be derived.
This work has been partially supported by the PAICYT research project FQM–296 from Junta de Andalucia.
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Gonzalez–Diaz, R., Medrano, B., Real, P., Sánchez–Peláez, J. (2005). Algebraic Topological Analysis of Time-Sequence of Digital Images. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2005. Lecture Notes in Computer Science, vol 3718. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11555964_18
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DOI: https://doi.org/10.1007/11555964_18
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