MOLINA ABRIL , Helena

Computing and representing topological information form an important part in many applications such as image representation and compression, classification, pattern recognition, geometric modelling, etc. The homology of digital objects is an algebraic notion that provides a concise description of their topology in terms of connected components,...

Given a 3D binary voxel-based digital object V, an algorithm for computing homological information for V via a polyhedral cell complex is designed. By homological information we understand not only Betti numbers, representative cycles of homology classes and homological classification of cycles but also the computation of homology numbers...

In [4], given a binary 26-adjacency voxel-based digital volume V, the homological information (that related to n-dimensional holes: connected components, "tunnels" and cavities) is extracted from a linear map (called homology gradient vector field) acting on a polyhedral cell complex P(V) homologically equivalent to V. We develop here an...

High resolution image data require a huge amount of computational resources. Image pyramids have shown high performance and flexibility to reduce the amount of data while preserving the most relevant pieces of information, and still allowing fast access to those data that have been considered less important before. They are able to preserve an...

One of the main problems of the existing methods for the segmentation of cerebral vasculature is the appearance in the segmentation result of wrong topological artefacts such as the kissing vessels. In this paper, a new approach for the detection and correction of such errors is presented. The proposed technique combines robust...

We present here a topo–geometrical description of a subdivided nD object called homological spanning forest representation. This representation is a convenient tool in order to completely control not only geometrical, but also advanced topological information of a given object. By codifying the underlying algebraic topological machinery in...

We introduce here a new F2 homology computation algorithm based on a generalization of the spanning tree technique on a finite 3-dimensional cell complex K embedded in ℝ3. We demonstrate that the complexity of this algorithm is linear in the number of cells. In fact, this process computes an algebraic map φ over K, called homology gradient...

A 2D topology-based digital image processing framework is presented here. This framework consists of the computation of a flexible geometric graph-based structure, starting from a raster representation of a digital image I. This structure is called Homological Spanning Forest (HSF for short), and it is built on a cell complex associated to I....

Morse theory is a fundamental tool for analyzing the geometry and topology of smooth manifolds. This tool was translated by Forman to discrete structures such as cell complexes, by using discrete Morse functions or equivalently gradient vector fields. Once a discrete gradient vector field has been defined on a finite cell complex, information...

Once a discrete Morse function has been defined on a finite cell complex, information about its homology can be deduced from its critical elements. The main objective of this paper is to define optimal discrete gradient vector fields on general finite cell complexes, where optimality entails having the least number of critical elements. Our...

This paper introduces a new method to rep- resent the surface of objects using two dimensional com- binatorial maps. The classical de nition of two dimen- sional combinatorial maps is extended here by adding a \back face" that corresponds to the non{visible part of the object. As a rst step, every object in the scene is extracted in one image...

Triangle three-dimensional meshes have been widely used to represent 3D objects in several applications. These meshes are usually surfaces that require a huge amount of resources when they are stored, processed or transmitted. Therefore, many algorithms proposing an efficient compression of these meshes have been developed since the early...

Homological characteristics of digital objects can be obtained in a straightforward manner computing an algebraic map φ over a finite cell complex K (with coefficients in the finite field F2={0,1}) which represents the digital object [9]. Computable homological information includes the Euler characteristic, homology generators and...

In this paper, we present a direct computational application of Homological Perturbation Theory (HPT, for short) to computer imagery. More precisely, the formulas of the A ∞–coalgebra maps Δ 2 and Δ 3 using the notion of AT-model of a digital image, and the HPT technique are implemented. The method has been tested on some specific examples,...

The paper analyzes the connectivity information (more precisely, numbers of tunnels and their homological (co)cycle classification) of fractal polyhedra. Homology chain contractions and its combinatorial counterparts, called homological spanning forest (HSF), are presented here as an useful topological tool, which codifies such information and...

Connected component labeling (CCL) of binary images is one of the fundamental operations in real time applications. The adjacency tree (AdjT) of the connected components offers a region-based representation where each node represents a region which is surrounded by another region of the opposite color. In this paper, a fully parallel algorithm...

In 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 (...

Several features of image segmentation make it suitable for bio–inspired techniques. It can be parallelized, locally solved and the input data can be easily encoded using representations inspired by nature. In this paper, we present a new hardware system that follows the Membrane Computing approach, and performs edge–based segmentation, noise...

Segmentation in computer vision refers to the process of partitioning a digital image into multiple segments (sets of pixels). It has several features which make it suitable for techniques inspired by nature. It can be parallelized, locally solved and the input data can be easily encoded by bio-inspired representations. In this paper, we...

In this paper we present a new software tool for dealing with the problem of segmentation in Digital Imagery. The implementation is inspired in the design of a tissue-like P system which solves the problem in constant time due the intrinsic parallelism of Membrane Computing devices.

In this paper we design a new family of relations between (co)homology classes, working with coefficients in a field and starting from an AT-model (Algebraic Topological Model) AT(C) of a finite cell complex C These relations are induced by elementary relations of type "to be in the (co)boundary of" between cells. This high-order...

Taking advantage of the topological and isotopic properties of binary digital images, we present here anew algorithm for connected component labeling (CLL). A local-to-global treatment of the topologicalinformation within the image, allows us to develop an inherent parallel approach. The time complexityorder for an image of m ×n pixels, under...

This paper analyses the topological information of a digital object O under a combined combinatorial-algebraic point of view. Working with a topology-preserving cellularization K(O) of the object, algebraic and combinatorial tools are jointly used. The combinatorial entities used here are vector fields, V-paths and directed graphs. In the...

A novel, flexible (non-unique) and topologically consistent representation called CRIT (Contour-Region incidence Tree) for a color 2D digital image I is defined here. The CRIT is a tree containing all the inter and intra connectivity information of the constant-color regions. Considering I as an abstract cell complex (ACC), its topological...