Reusing Integer Homology Information of Binary Digital Images
نویسندگان
چکیده
In this paper, algorithms for computing integer (co)homology of a simplicial complex of any dimension are designed, extending the work done in (7; 9). For doing this, the homology of the object is encoded in an algebraic-topological format (that we call AM-model). Moreover, in the case of 3D binary digital images, having as input AM-models for the images I and J , we design fast algorithms for computing the integer homology of I ∪ J , I ∩ J and I \ J .
منابع مشابه
DISCRETE TOMOGRAPHY AND FUZZY INTEGER PROGRAMMING
We study the problem of reconstructing binary images from four projections data in a fuzzy environment. Given the uncertainly projections,w e want to find a binary image that respects as best as possible these projections. We provide an iterative algorithm based on fuzzy integer programming and linear membership functions.
متن کاملChain Homotopies for Object Topological Representations
This paper presents a set of tools to compute topological information of simplicial complexes, tools that are applicable to extract topological information from digital pictures. A simplicial complex is encoded in a (non-unique) algebraic-topological format called AM-model. An AM-model for a given object K is determined by a concrete chain homotopy and it provides, in particular, integer (co)ho...
متن کاملExtending the Notion of AT-Model for Integer Homology Computation
When the ground ring is a field, the notion of algebraic topological model (AT-model) is a useful tool for computing (co)homology, representative (co)cycles of (co)homology generators and the cup product on cohomology of nD digital images as well as for controlling topological information when the image suffers local changes [6, 7, 9]. In this paper, we formalize the notion of λ-AT-model (λ bei...
متن کاملTopological Tracking of Connected Components in Image Sequences
Persistent homology provides information about the lifetime of homology classes along a filtration of cell complexes. Persistence barcode is a graphical representation of such information. A filtration might be determined by time in a set of spatiotemporal data, but classical methods for computing persistent homology do not respect the fact that we can not move backwards in time. In this paper,...
متن کاملUsing Membrane Computing for Obtaining Homology Groups of Binary 2D Digital Images
Membrane Computing is a new paradigm inspired from cellular communication. Until now, P systems have been used in research areas like modeling chemical process, several ecosystems, etc. In this paper, we apply P systems to Computational Topology within the context of the Digital Image. We work with a variant of P systems called tissuelike P systems to calculate in a general maximally parallel m...
متن کامل