=Paper= {{Paper |id=Vol-3269/PAPER_01 |storemode=property |title=2D Image Segmentation using Cell like Spiking Neural P System |pdfUrl=https://ceur-ws.org/Vol-3269/PAPER_01.pdf |volume=Vol-3269 |authors=Y. Preethi Ceon,Hepzibah Christinal,S. Jebasingh,D. Abraham Chandy |dblpUrl=https://dblp.org/rec/conf/wins/CeonCJC22 }} ==2D Image Segmentation using Cell like Spiking Neural P System== https://ceur-ws.org/Vol-3269/PAPER_01.pdf 
2D Image Segmentation using Cell like Spiking Neural P System
Y. Preethi Ceon a, Hepzibah Christinal a, S. Jebasingh a, D. Abraham Chandy b
a Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore, India
b Department of Electronics and Communication, Karunya Institute of Technology and Sciences, Coimbatore,

  India.



                 Abstract
                 A new type of computational model that is stimulated by functions and structure of biological
                 cells is called Membrane Computing. Spiking Neural P Systems (SN P Systems) is an
                 unconventional method of computing, where in the rewriting of multisets is implemented by
                 absorbing a multiset present in the membrane region and simultaneously producing new
                 multiset of alphabets. In the present study, edge segmentation of 2D images using Cell-like
                 Spiking Neural P System with various spikes (cSN+P systems) is considered.
                  .
                 Keywords
                 Membrane Computing, cSN+P systems, Edge Based Segmentation

1. Introduction

   The study of new computational paradigms based on natural phenomena constitutes natural
Computing. It abstracts how nature "computes," resulting in new computing models. Neural networks
[15], Genetic algorithms [9], and DNA-based molecular computing [1] are some examples of well-
established fields in Natural Computing.

    A computing model that relies on function of cells and structure to process rules and generate
string languages constitutes membrane computing. In general, A P system [16], contains of a
membrane structure with compartments in which the predetermined rules that work in non-
deterministic parallel manner and are evolved using multisets of objects.

    These models can be divided into three groups based on their construction: P systems based on
structure of cell, P systems based on tissue, and P systems based on neurons [18]. Membranes are
ordered as a tree-like structure in the cell-like P System in the first system. The vesicles that make up
acell's interior serves as inspiration for such architecture.

   Tissue P systems are computational models motivated by biological systems along with chemical
reaction in which multiple individuals live and cooperate in a specific environment where objects can
modify when shifting from one region to another. The type of distributed and parallel neural-like
computing model that is stimulated by the mode neurons transfer using spikes are the type of SN P
systems. This work focuses on the approach: cSN+P System.

   SN P system [8], in which neurons communicate with one another via identically shaped electric
impulses called spikes. Using spiking and forgetting rules, the neuron processes information in the form
of spikes. The following is how spiking rules work: The current spikes are absorbed by the neuron,
andnew ones are created. Similarly, the forgetting rule is used to eliminate the count of spikes present
in the nerve cell which is predetermined. The rules get triggered, when the regular expression is

WINS-2022: Workshop on Intelligent Systems, April 22 – 24, 2022, Chennai, India.
EMAIL: hepzia@yahoo.com (Hepzibah Christinal)
ORCID: 0000-0003-3965-3183 (Hepzibah Christinal)
            Β© 2022 Copyright for this paper by its authors.
            Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
            CEUR Workshop Proceedings (CEUR-WS.org)



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matched with the count of spikes present in a neuron. As the result, the system halts which is the
computation in SN P system and the various types of spikes are transmitted to the environment.

   In computer vision, partitioning a digital image into multiple segments is a process. known as
segmentation. By shortening and/or changing an image's representation, segmentation makes the
image simpler to analyse. Substances and borders in images are typically located using image
segmentation. In more technical terms, the process of assigning a label to each which have similar visual
characteristics and same label is known as image segmentation. Few techniques that are available to
segment the image are neural network methods, watershed transformation methods, edge-based
method, region-based method and graph partitioning methods.

   Medical imaging, Traffic control system, Finger print recognition and Object detection are thefew
of the real-world applications of image segmentation. Hepzibah et al., [4,5] used for the first time, P
systems based on tissue for segmenting the 2D images which is a variant of P systems.

   The work on paper is prepared as follows: We discuss the preliminaries of cell-like spiking neural
p system with several types of spikes in section 2. We define a cSN+P systems for segmentationin 2D
image based on edge in section 3.

2. Preliminaries

2.1. Cell-Like SN+P System

   A cSN+P system [14] of the power π‘š β‰₯ 1, is of the form

                                H = (X, Q1, Q2 … , Qπ‘š, 𝑅1, … , π‘…π‘š, k0),
Where
  1.The group of alphabets is denoted by X and its is finite
  2.Q1, Q2 …, Qm are the neurons of the form

                                       Qi = (Wi, 𝑅i), 1 ≀ i ≀ π‘š,
Where
     (i) Wiє𝑂 βˆ— denotes prime multiset of spikes confined in Qi;
     (ii) 𝑅i has two rules of the succeeding form:
                                          𝐸
     (π‘Ž) The spiking rule Here V is an β†’ 𝑣, here V is an arrangement of pairs of the form (𝑉i,
                                           𝑒
      π‘‘π‘Žπ‘Ÿ) and π‘‘π‘Žπ‘Ÿ {β„Žeπ‘Ÿe, π‘œπ‘’π‘‘, i𝑛j} and E represents regular language over O.
      (𝑏) The forgetting rule 𝑉 β†’ *, with 𝑉 є𝑂 βˆ— and 𝑉є𝐸

   3.The output region of H is indicated by k0 ∈ {0, 1, …, π‘š}
                                 𝐸
    The spiking rule of the form 𝑒 β†’ 𝑣 works in the following way: The computation begins from the
neuron Qi which has maximum number of spikes and multiset w such that w Ρ” 𝐿(𝐸) and 𝑒 Ρ”
𝑠𝑒𝑏(𝐸). When the rule starts to fire, the production of multiset of spikes v Ρ” 𝐸 are consumed bythe
spikes u and are transmitted to the target indicated. If each of the neuron holds accurately the spikes v,
then the firing rule V β†’ Ξ» starts to work. Because the global clock is assumed, the system's operation
is synchronized. If n number of rules are present in the neuron at the similar time, any one of rule is
used is chosen non-deterministically. The transition of system is formed by application of firing or
forgetting rules in a neuron. Any transition sequence begins with the initial configurations. When rule
is not applicable, the computation ends and reaches its configuration.



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   The different types of spikes released from the output neuron in a tentative configuration whichis
the output of the cSN+P system. The series of spikes produced from the output neuron forms the edge
pixel generated by the cSN+P system.


3. Segmentation of 2D Images using cSN+P System

   The two -dimensional digital image 3 with size 𝑛 π‘₯ π‘š (𝑛. π‘š Ρ” Ν) is a object in four-sided net(i, j)
called pixels with 1 ≀ i ≀ 𝑛 and 1 ≀ j ≀ π‘š [3]. The ordered set of all colours in 3 be the alphabet of
colors of 3 (𝑐 βŠ† 𝑁) [4]. The number of colour of this alphabet is denoted by the size of 𝑐 βˆ’ |𝐢|. Let us
consider that for every pixel of 3 is correlated to a colour of 𝑐. The pixel (i, j) is encoded with
connected color π‘Ž Ρ” C as the object π‘Žij. The image is coded as the set {π‘Žij: π‘Ž ∈ 𝐢 𝖠 1 ≀ i ≀ 𝑛 𝖠 1
≀ j ≀ π‘š}. Pixels π‘ž1 = (𝑐, 𝑑) and π‘ž2 = (e, Ζ’) are given and they are said to be adjacent (π‘ž1. π‘ž2) = √(𝑐
– e)2 + (𝑑 βˆ’ Ζ’)2 is 1. The 4-adjacency neighborhood concept is used to study the relation between
pixels to segment the images.

    We can partition an image into regions in this manner, with each area consisting of two-by-two
nearby pixels with the same associated colour. The region's boundary is defined as the group of pixels
in particular region that have the characteristic of being next to other pixels with a variety of color
associated colour. In this section, the edge-segmentation algorithm is used to segment the images. The
labels of the pixels in the 2D images are given as input to the system. The successive application of
firing rules to the input 2D image identifies the boundary pixels and sends them to the environment.
The system applies the rules using 4 adjacency and 2 adjacency neighbourhood on the pixels of the
input image. The resultant segmented 2D image is observed in the output neuron of the system.

3.1 Image Segmentation using Cell-like Spiking Neural P System with various
     types of spikes

Theorem 3.1
    The m x n 2D image can be segmented by a Cell -like Spiking Neural P System with various types
of spikes having 1 neuron.

Proof:
   We define a family of cSN+P System for edge segmentation of 2-D images. For each 𝑛, π‘š ∈ 𝑀,
the system is defined as follows:
                                           πœ‹ = (, πœ‡, 𝜎0, 𝑅0, 𝜎0)
Where,
      β€’ O = {π‘Žij, π‘π‘˜π‘™} where π‘Žij, π‘π‘˜π‘™ are the labels of the input image
      β€’ πœ‡ = []1
      β€’ 𝜎0 = {π‘Žij, π‘π‘˜π‘™}




                                                   3
                                         π‘Žπ‘–π‘— π‘π‘˜π‘™
                                               ⁄
                                                    π‘π‘˜π‘™ β†’ ( π‘π‘˜π‘™ , π‘œπ‘’π‘‘),
                                        π‘π‘šπ‘› π‘Žπ‘₯𝑦
                                               ⁄
                                                π‘π‘šπ‘› β†’ (π‘π‘šπ‘› , π‘œπ‘’π‘‘)
                                 π‘Žπ‘–π‘— π‘Žπ‘–π‘—+1 𝑏𝑖+1𝑗 π‘Žπ‘–+1𝑗+1
                                           𝑏𝑖+1
                                                           β†’ (𝑏𝑖+1𝑗 , π‘œπ‘’π‘‘)
                                 π‘Žπ‘–π‘— 𝑏𝑖𝑗+1 π‘Žπ‘–+1𝑗 π‘Žπ‘–+1𝑗+1
                                           𝑏𝑖𝑗+1
                                                           β†’ (𝑏𝑖𝑗+1 , π‘œπ‘’π‘‘)
               𝑏𝑖𝑗 π‘Žπ‘–π‘—+1 𝑏𝑖+1𝑗 𝑏𝑖+1𝑗+1
                   𝑏𝑖𝑗 𝑏𝑖+1𝑗 𝑏𝑖+1𝑗+1
                                           β†’ (𝑏 , π‘œπ‘’π‘‘)(𝑏𝑖+1𝑗 , π‘œπ‘’π‘‘)(𝑏𝑖+1𝑗+1 , π‘œπ‘’π‘‘)
                                               𝑖𝑗
  β€’   𝑅0 =             π‘Žπ‘–π‘— π‘Žπ‘–π‘—+1 𝑏𝑖+1𝑗 𝑏𝑖+1𝑗+1
                            𝑏𝑖+1𝑗 𝑏𝑖+1𝑗+1
                                                   β†’ (𝑏𝑖+1𝑗 , π‘œπ‘’π‘‘)(𝑏𝑖+1𝑗+1 , π‘œπ‘’π‘‘)
                                 π‘Žπ‘–π‘— π‘Žπ‘–π‘—+1 𝑏𝑖+1𝑗 π‘Žπ‘–+1𝑗+1
                                           𝑏𝑖+1𝑗
                                                           β†’ (𝑏𝑖+1𝑗 , π‘œπ‘’π‘‘)
                          𝑏𝑖𝑗 𝑏𝑖𝑗+1 π‘Žπ‘–+1𝑗 π‘Žπ‘–+1𝑗+1
                                 𝑏𝑖𝑗 𝑏𝑖𝑗+1
                                                     β†’ (𝑏𝑖𝑗 , π‘œπ‘’π‘‘)(𝑏𝑖𝑗+1 , π‘œπ‘’π‘‘)
                 𝑏𝑖𝑗 𝑏𝑖𝑗+1 π‘Žπ‘–+1𝑗 𝑏𝑖+1𝑗+1
                    𝑏𝑖𝑗 𝑏𝑖𝑗+1 𝑏𝑖+1𝑗+1
                                           β†’ (𝑏𝑖𝑗 , π‘œπ‘’π‘‘)(𝑏𝑖𝑗+1 π‘œπ‘’π‘‘)(𝑏𝑖+1𝑗+1 , π‘œπ‘’π‘‘)
                         𝑏𝑖𝑗 π‘Žπ‘–π‘—+1 𝑏𝑖+1𝑗+1 π‘Žπ‘–+1𝑗+1
                                                      β†’ (𝑏𝑖𝑗 , π‘œπ‘’π‘‘)(𝑏𝑖+1𝑗 , π‘œπ‘’π‘‘)
             {                   𝑏𝑖𝑗 𝑏𝑖+1𝑗


  β€’   𝑖0 = []0




Figure 1: An example of 3x3 Image as input image

4. Overview of the computation

    The system has one membrane 𝜎0 having firing rules defined in the set 𝑅0. The multiset π‘Žij,
π‘π‘˜π‘™ spikes is present in the membrane 𝜎0. The rules in 𝑅0 are applied to the initial set of spikes where
the region 𝜎0 gets activated.

   The rule 𝑅0 is applied, when an image has different associated colours with two adjacent pixels, the
pixel with the less associated colour will remain in the same neuron and other pixels are sent out using
spiking rules.


   Similarly, the rule 𝑅0 is applied, when an image has four adjacent pixels with different associated
colours, the pixel with the less associated colour will remain in the same neuron and other pixels are
sent out using spiking rules.

                                                           π‘Žij 𝑏k𝑙
   Suppose that the system chooses firing rule                       /
                                                                         𝑏k𝑙 β†’ (𝑏k𝑙, o𝑒𝑑) non-deterministically. This rule
consumes a spike π‘Žij and sends π‘Žij spike to the environment. The edge cells are sent out using the



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                                                                                     π‘π‘šπ‘› π‘Žπ‘₯𝑦
spiking rule and other pixels will remain in the neuron 𝜎0. The firing rule                 /
                                                                                                π‘π‘šπ‘› β†’ (π‘π‘šπ‘›, o𝑒𝑑).
This rule consumes a spike π‘Žπ‘₯𝑦 and sends π‘Žπ‘₯𝑦 spike to the environment. The edge cells are sent out
using the spiking rule and other pixels will remain in the neuron 𝜎0.
                        π‘Žijπ‘Žij+1 𝑏i+1jπ‘Ži+1j+1
   If the firing rule                           β†’ (𝑏      , o𝑒𝑑) is selected by the system non-deterministically
                               𝑏i+1                    i+1j
then the system will send the spikes 𝑏i+1j out, which is four adjacency in image. Similarly, all other
rules are applied and the edge cells are sent out using the spiking rule and other pixels will remain in
the neuron 𝜎0. At last, the second set of rules are pertained and send pixels at edge to the output cell.




Figure 2: Edge-Segmented 3 x 3 image




Figure 3: An example of 4x4 Image as input image




Figure 4: After Edge-Segmentation, The 4x4 Image

5. Conclusion

   At present, we studied edge segmentation of the m x n 2D images with the aid of cSN +P systems.
Further, need to study segmentation of 3D images. Furthermore, application of the system in medical
image processing will be our future work.

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