Canonical Encoding of the Combinatorial Pyramid

This paper presents a novel framework to encode a combinatorial pyramid. A combinatorial pyramid is a hierarchy of successively reduced combinatorial maps. Important properties of the combinatorial pyramids such as topology preservation, the process global and local features within the same data structure, etc. made them useful for image processing and pattern recognition tasks. Their advantages have been widely proved in the literature. Nevertheless, the main disadvantage of this approach is the high rate of memory requirement. A combinatorial map of an image maybe stored in an array of size approximately equal to four times the number of pixels of the image. Furthermore, every level of the combinatorial pyramid stores a different combinatorial map. In respond to this problem a canonical encoding of the combinatorial pyramid is provided. It consists of a single array where its elements are ordered with respect to the construction history of the pyramid. In this manner the memory consumptions are equal to the size of the initial combinatorial map and do not depend on the number of pyramid’s levels. In addition, this canonical encoding allows the whole reconstruction of the pyramid in both directions: from the base to the top level and from the top to the base level, without additional information.