A PROPOSAL OF A GENERAL MODIFIED CELLULAR AUTOMATON TO IMPLEMENT RASTER DATA ANALYSIS

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A PROPOSAL OF A GENERAL MODIFIED CELLULAR AUTOMATON TO IMPLEMENT
RASTER DATA ANALYSIS

UREÑA M.A., ARIZA F.J.

Universidad de Jaén, JAÉN, SPAIN


INTRODUCTION

In general, analysis of geographic information (GI) is a complex task which requires huge computation
efforts. Moreover, the increase of digital GI has exponentially improved the scopes of GI analysis and the

amount of data required, for example the case of generalization of maps can only be achieved by means of
this huge computation effort. Among these research projects, the Agent Project was one of the most
important and has achieved its objectives by been u
sed in map production phase. Its main idea was not to
apply a series of procedures to GI data, but to allow that each GI object can be capable of determine its
own transformation, thus converting each object into an agent object, a cellular automaton with
perception.

However being a quite interesting approach, the previous idea has not been generally extended to data
analysis procedures in Geographical Information Systems (GIS), and only we can find some studies about
map algebra using cellular automata, op
timization of production processes (not related to map production)
and the calculation of Voronoi diagrams.

In the other hand, the increase in the number of processors, even on personal computers, are a benefit not
exploited by the majority of GIS. For thi
s reason, instead of adapting classical analysis procedures to run
in multithread mode, we propose the use of cellular automata (intrinsically multiprocessing). Our proposal
is centred on raster GI and use a minimum requirements cellular automaton, a modif
ied version of the
Langton’s ant that has been demonstrated that represents a universal Turing machine. Its best
characteristics are: (i) a minimum (but customizable) set of rules used to define this class of machine, (ii)
the bidimensional behaviour and (
iii) the complexity of the final behaviour which allows developing
several analysis based on a raster world description.

METHODOLOGY

The methodology proposed in this paper is briefly defined in Figure 1 and follows the same ideas proposed
in Langton’s ant.

However, Langton’s ant is a mobile automaton (as described by Wolfram 2002) and it
has to be developed not as a unique automaton but a huge set of automata in order to obtain a complex
behaviour and not a repetitive behaviour (Wolfram 2002).


Figure 1. Methodology.

This methodology defines a cellular automaton having some differences with respect to Langton’s ant.
These differences are shown in Table 1.


Table 1. Characteristics of the proposed automaton which differences it from the Langton’s ant.

Moreover, the differences between the general cycle, of a set of cellular automata and the proposed in this
paper, is changed by preordering the set of automata using a selected characteristic in order to confer more
chances for surviving than the rest of
automata. This change in the algorithm have a deeper influence in
the methodology because the Z
2

space is not increased by a delta of all automata but for a delta of the best
automata followed by the rest (in this sense is similar to the evolution of a gen
etic algorithm but not having
a quantifier for individual characteristics).

In order to test the automaton with the previously defined characteristics, we have implemented it for
determining the axes of a street inside a raster city (medium
-
sized city, Alm
ería, Andalusia, Spain, Figure
2). The characteristics of this automaton are showed in Table 2.


Table 2. Characteristics of each cellular automaton used for determining the axes of a street.


Figure 2. Selected city for testing the algorithm (black zones represent the streets).

ANALYSIS AND RESULTS

After applying the proposed automata to the image previously indicated, we can achieve a solution similar
to a straight skeletonization (Haunert and Sester, 2008) but having the continuity capability as described
by Regnauld and Mackaness (2006) for a rive
r network (this capability is a need of the streets networks) .
A detail of this solution is shown in Figure 3.


Figure 3. Detail of extracted axes.

However, this automaton has to be improved, especially in square zones, where the distances to different
objects create a larger number of automata that can survive but do not represent the real axis (or the
desired street axis).

CONCLUSIONS AND FUTURE PLA
NS

Our results show that the defined automata can successfully determine the axis of a street (and thus the
axis of almost any closed polygon). Because the automaton is defined in an increasing way, it can be
applied (changing the parameters defined for cr
eating, living and dying) for obtaining an analysis which is
constructed increasingly based on the previous values on a limited region (e.g. determining the minimum
cost path between points, determining buffers, etc.). In future works, we will apply this k
ind of automaton
to other GI analysis like hydrological analysis, simulation and expand to regions analysis and non
-
grid or
non
-
equidistant data information.

ACKNOWLEDGMENTS

This work has been partially funded by the Ministry of Science and Technology of S
pain under Grant No.
BIA2003
-
02234 and by the Regional Ministry of Innovation, Science and Enterprise of Andalusia (Spain)
under Grant No. P08
-
TIC
-
4199.

REFERENCES

Haunert, J.H. and Sester, M. (2008). “Area collapse of road centrelines based on straight sk
eletons,
Geoinformatica”, 12(2): 169
-
191. DOI: 10.1007/s10707
-
007
-
0028
-
x.

Regnauld, N. and Mackaness, W. (2006). “Creating a hydrographic network from its cartographic
representation: a case of study using Ordnance MasterMap Data”, International Journal of

Geographical
Information Science, 20 (6): 611
-
631.

Wolfram, S. (2002). A new kind of science. Ed. Wolfram Media (Champaign, IL). 1197 pp. Accessed on
-
line: http://www.wolframscience.com/nksonline/toc.html (last access: February 7th, 2011).