2021-06-182021-06-182020Molina Abril, H., Real Jurado, P. y Díaz del Río, F. (2020). Generating (co)homological information using boundary scale. Pattern Recognition Letters, 133 (May 2020), 240-246.0167-8655https://hdl.handle.net/11441/111880In this paper we develop a new computational technique called boundary scale-space theory. This tech- nique is based on the topol1 ogical paradigm consisting of representing a geometric subdivided object K using a one-parameter family of geometric objects { Ki }i ≥ 1 all of them having the same number of closed pieces than K. Each piece of Ki ( ∀i ≥ 1) presents the same interior part than the corresponding one in K, and a different boundary part depending on the scale i. Working with coefficients in a field, a scale is installed for the algebraic boundary of each piece and a new invariant for cell complex isomorphisms is given in terms of the Betti numbers of the generated boundary-scale-space cell complexes. Moreover, the so called homology boundary scale-space model of K ( hbss -model for short) is introduced here. Thismodel consists of a hierarchical graph whose nodes are the homology generators of the different bound- ary scale levels and whose edges are specified by homology generators of consecutive boundary scaleindices linked by ( hbss -transition maps) preserving homology classes. Various codes for each connectedsubgraph of an hbss -model are defined, which besides being fast and efficient similarity measures for cel- lular structures, they are as well relevant interpretive tools for the hbss -model. Finally, experimentations mainly aimed at clarifying and understanding the notion of hbss -model, as well as conjecturing about new graph isomorphism invariants (seeing graphs as a 1-dimensional cell complexes), are performed.application/pdf7engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Geometric cell complexAlgebraic-topological modelScale-space modelHomology groupsHierarchical graphinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1016/j.patrec.2020.02.028