Abstract: Over the past 30 years,
geostatistics has proved its superiority as a method for estimating
reserves in most types of mines (precious metals, iron ore, base
metals, etc.). Its application to the petroleum industry is more
recent, but it has nevertheless demonstrated its usefulness,
particularly for contour mapping and for modelling and simulating the
internal heterogeneity of reservoirs. Its use has been extended to
other fields such as (in a non-extensive list), environmental science,
hydrogeology, pollution control, agriculture and even fisheries,
wherever the time component as well as the spatial variability is
important. The basic tool, and probably one of the most used in
geostatistics, the variogram, is used to quantify spatial correlations
between observations. In fact, this method has become one of the most
important - although not necessary - in any natural resource modelling
and planning study. For instance, once a mathematical function (or
functions) has been fitted to the experimental variogram, this model
can be used to estimate values at unsampled points, by a estimation
procedure called kriging (Krige, Matheron, 1970’s), which has been
found to be an exact interpolator. The most old and common method for
variogram fitting, is “by eye”, where an operator interacts visually
finding the bests parameters (number of structures, ranges, angles of
anisotropy, etc) for the best model fitting. In the present work,
however, automatic modelling of variograms is required because is
needed the estimation of variogram parameters of an high number of
digital images. Indeed we are looking to avoid subjective
interpretation of the data by the user. In order to overcome this
problem, a Genetic Algorithm was, for the first time, fully
implemented, and a novel bio-inpired strategy used in recent works -
entitled Neoteny - was used for better convergence. Results on several
test variogram models (and on their parameters), point to errors less
than 1%.
Keywords: Geostatistics, Variogram
Fitting, Image Analysis, Nonlinear Minimization, Genetic Algorithms,
Artificial Neoteny, Evolutionary Computation
Related
Works:
55. Vitorino Ramos, Pedro
Pina, Exploiting and Evolving Rn
Mathematical Morphology
Feature
Spaces, in Ronse Ch., Najman L., Decencière E. (Eds.), Mathematical Morphology: 40
Years On, pp. 465-474, Springer,
Dordrecht,
The Netherlands, 2005.
31. Vitorino Ramos,
Fernando Muge, Map Segmentation by Colour Cube
Genetic K-Mean
Clustering, Proc. of ECDL´2000 - 4th European
Conference on Research and Advanced
Technology for Digital Libraries, J. Borbinha and
T. Baker (Eds.), ISBN 3-540-41023-6, Lecture Notes in Computer Science,
Vol. 1923, pp. 319-323, Springer-Verlag
-Heidelberg, Lisbon, Portugal,
18-20 Sep. 2000.
51. Vitorino Ramos, Ajith
Abraham, Evolving a Stigmergic Self-Organized
Data-Mining, in ISDA-04,
4th Int. Conf. on Intelligent Systems, Design and Applications,
Budapest, Hungary, ISBN 963-7154-30-2, pp. 725-730, August 26-28, 2004.
53. Vitorino Ramos,
Jonathan Campbell, John Slater, John Gillespie, Ivan F. Bendezu and
Fionn Murtagh, Swarming around Shellfish Larvae
Images, in WCLC-05, 2nd
World
Congress on Lateral Computing, Bangalore,
India, 16-18 Dec., 2005.
70. Ramos, V., Fernandes, C.,
Rosa, A.C., Abraham, A., Computational Chemotaxis
in Ants and Bacteria
over Dynamic
Environments, submitted to CEC´07 -
Congress on Evolutionary
Computation, IEEE Press,
Singapore, 25-28 Sep. 2007.
69. Fernandes, C.,
Rosa, A.C., Ramos V., Binary Ant Algorithm,
to appear in GECCO´07 - Genetic and Evolutionary
Computation Conference, ACM
Press, London, UK, 7-11 July, 2007.
62. Abraham, Ajith;
Grosan, Crina; Ramos, Vitorino (Eds.), Swarm Intelligence in Data
Mining, Studies in Computational Intelligence (series), Vol. 34, Springer-Verlag, ISBN:
3-540-34955-3, 267 p., Hardcover, 2006.
39. Vitorino Ramos,
Fernando Muge, Pedro Pina, Self-Organized Data
and Image Retrieval as a
Consequence of Inter-Dynamic Synergistic Relationships in Artificial
Ant Colonies, in Javier Ruiz-del-Solar, Ajith Abraham and Mario
Köppen (Eds.), Frontiers in Artificial Intelligence and
Applications, Soft Computing Systems
- Design, Management and
Applications, 2nd Int. Conf. on Hybrid Intelligent
Systems, IOS
Press, Vol. 87, ISBN 1 5860 32976, pp. 500-509, Santiago, Chile,
Dec.
2002.
35. Vitorino Ramos, The
Biological Concept of Neoteny in Evolutionary Colour Image Segmentation
- Simple Experiments in Simple Non-Memetic Genetic Algorithms, in Applications of Evolutionary
Computation, (Eds.), EvoIASP´01 -
3rd European Workshop on Evolutionary Computation in Image Analysis and
Signal Processing [helded by EuroGP´01 - European Conference on
Genetic Programming], Lake Como, Milan, Italy, Lecture Notes in
Computer Science, Vol. 2037, pp. 364-378, Springer-Verlag,
Berlin-Heidelberg, April 18-20, 2001.
37. Vitorino Ramos, On
the Implicit and on the Artificial - Morphogenesis and Emergent
Aesthetics in Autonomous Collective Systems, in ARCHITOPIA Book, Art,
Architecture and Science, INSTITUT D'ART CONTEMPORAIN, J.L.
Maubant et
al. (Eds.), pp. 25-57, Chapter 2, ISBN 2905985631 - EAN 9782905985637,
France, Feb. 2002.