Obtaining Homology Groups in Binary 2D Images Using P Systems

Membrane Computing is a new paradigms inspired from cellular communication. We use in this paper the computational devices called P systems to calculate in a general maximally parallel manner the homology groups of binary 2D images. So, the computational time to calculate this homology information only depends on the thickness of them.Junta de Andalucía FQM-296Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía P08-TIC-04200Ministerio de Educación y Ciencia MTM2006-03722Junta de Andalucía PO6-TIC-0226

Solving the 3-COL Problem by Using Tissue P Systems without Environment and Proteins on Cells

The 3-COL problem consists on deciding if the regions of a map can be coloured with only three colors bearing in mind that two adjacent regions must be coloured with di erent colors. It is a NP problem and it has been previously used in complexity studies in membrane computing to check the ability of a model for solving problems of such complexity class. Recently, tissue P systems with proteins on cells have been presented and its ability to solve NP-problems has been proved, but it remained as an open question to know if such model was still able to solve such problems if the environment was removed. In this paper we provide an a rmative answer to this question by showing a uniform family of tissue P systems without environment and with proteins on cells which solves the 3-COL problem in linear time

Region-based segmentation of 2D and 3D images with tissue-like P systems

Membrane Computing is a biologically inspired computational model. Its devices are called P systems and they perform computations by applying a finite set of rules in a synchronous, maximally parallel way. In this paper, we develop a variant of P-system, called tissue-like P system in order to design in this computational setting, a region-based segmentation algorithm of 2D pixel-based and 3D voxel-based digital images. Concretely, we use 4-adjacency neighborhood relation between pixels in 2D and 6-adjacency neighborhood relation between voxel in 3D for segmenting digital images in a constant number of steps. Finally, specific software is used to check the validity of these systems with some simple examples

P systems and computational algebraic topology

Membrane Computing is a paradigm inspired from biological cellular communication. Membrane computing devices are called P systems. In this paper we calculate some algebraic-topological information of 2D and 3D images in a general and parallel manner using P systems. First, we present a new way to obtain the homology groups of 2D digital images in time logarithmic with respect to the input data involving an improvement with respect to the algorithms development by S. Peltier et al. Second, we obtain an edge-segmentation of 2D and 3D digital images in constant time with respect to the input data

Searching Partially Bounded Regions with P Systems

The problem of automatically marking the interior and exterior regions of a simple curve in a digital image becomes a hard task due to the noise and the intrinsic difficulties of the media where the image is taken. In this paper, we propose a definition of the interior of a partially bounded region and present a bio-inspired algorithm for finding it in the framework of Membrane Computing.Ministerio de Economía y Competitividad TIN2012-3743

Solving the Bin-Packing Problem by Means of Tissue P System with 2-Division

The ability of tissue P systems with 2-division for solving NP problems in polynomial time is well-known and many solutions can be found in the literature to several of such problems. Nonetheless, there are very few papers devoted to the Bin-packing problem. The reason may be the difficulties for dealing with different number of bins, capacity and number of objects by using exclusively division rules that produce two offsprings in each application. In this paper we present the design of a family of tissue P systems with 2 division which solves the Bin-packing problem in polynomial time by combining design techniques which can be useful for further research

Smoothing Problem in 2D Images with Tissue-like P Systems and Parallel Implementation

Smoothing is often used in Digital Imagery to reduce noise within an image. In this paper we present a Membrane Computing algorithm for smoothing 2D images in the framework of tissue-like P systems. The algorithm has been implemented by using a novel device architecture called CUDATM, (Compute Unified Device Architecture). We present some examples, compare the obtained time and present some research lines for the future.Ministerio de Ciencia e Innovación TIN2008-04487-EMinisterio de Ciencia e Innovación TIN-2009-13192Junta de Andalucía P08-TIC-04200Junta de Andalucía PO6-TIC-02268Ministerio de Educación y Ciencia MTM2009-1271

Using membrane computing for effective homology

Effective Homology is an algebraic-topological method based on the computational concept of chain homotopy equivalence on a cell complex. Using this algebraic data structure, Effective Homology gives answers to some important computability problems in Algebraic Topology. In a discrete context, Effective Homology can be seen as a combinatorial layer given by a forest graph structure spanning every cell of the complex. In this paper, by taking as input a pixel-based 2D binary object, we present a logarithmic-time uniform solution for describing a chain homotopy operator ϕ for its adjacency graph. This solution is based on Membrane Computing techniques applied to the spanning forest problem and it can be easily extended to higher dimensions

Thresholding 2D Images with Cell-like P Systems

Thresholding is the process of splitting a digital image into sets of pixels in order to make it easier to analyze. Pixels are ordered according to a scale of one of their features as brightness or color and the ¯nal image is obtained by comparing the measure of the feature with some thresholds. In this paper we present a family of cell-like P systems which solve the thresholding problem in linear time on the number of pixels.Ministerio de Ciencia e Innovación TIN2008-04487-EMinisterio de Ciencia e Innovación TIN2009–13192Junta de Andalucía P08–TIC-0420

Array Tissue-like P Systems

Array grammars have been studied in the framework of Membrane Comput- ing by using rewriting rules from transition P systems. In this paper we present a new approach to dealing with array grammars by using tissue-like P systems and present an application to the segmentation of images in two dimensional computer graphics.Ministerio de Ciencia e Innovación TIN2008-04487-EMinisterio de Ciencia e Innovación TIN-2009-13192Junta de Andalucía P08-TIC-0420