### Abstract

This chapter describes a statistical approach to classification of dynamic

texture images, called parallel evolution functions (PEFs). Traditional classification

methods predict texture class membership using comparisons with

a finite set of predefined texture classes and identify the closest class. However,

where texture images arise from a dynamic texture evolving over time,

estimation of a time state in a continuous evolutionary process is required

instead. The PEF approach does this using regression modeling techniques

to predict time state. It is a flexible approach which may be based on any

suitable image features. Many textures are well suited to a morphological

analysis and the PEF approach uses image texture features derived from a

granulometric analysis of the image.

The method is illustrated using both simulated images of Boolean processes

and real images of corrosion. The PEF approach has particular advantages

for training sets containing limited numbers of observations, which

is the case in many real world industrial inspection scenarios and for which

other methods can fail or perform badly.

[41] G.W. Horgan, Mathematical morphology for analysing soil structure from images,

European Journal of Soil Science, vol. 49, pp. 161–173, 1998.

[42] G.W. Horgan, C.A. Reid and C.A. Glasbey, Biological image processing and enhancement,

Image Processing and Analysis, A Practical Approach, R. Baldock and

J. Graham, eds., Oxford University Press, Oxford, UK, pp. 37–67, 2000.

[43] B.B. Hubbard, The World According to Wavelets: The Story of a Mathematical

Technique in the Making, A.K. Peters Ltd., Wellesley, MA, 1995.

[44] H. Iversen and T. Lonnestad. An evaluation of stochastic models for analysis and

synthesis of gray-scale texture, Pattern Recognition Letters, vol. 15, pp. 575–585,

1994.

[45] A.K. Jain and F. Farrokhnia, Unsupervised texture segmentation using Gabor filters,

Pattern Recognition, vol. 24(12), pp. 1167–1186, 1991.

[46] T. Jossang and F. Feder, The fractal characterization of rough surfaces, Physica

Scripta, vol. T44, pp. 9–14, 1992.

[47] A.K. Katsaggelos and T. Chun-Jen, Iterative image restoration, Handbook of Image

and Video Processing, A. Bovik, ed., Academic Press, London, pp. 208–209, 2000.

[48] M. K¨oppen, C.H. Nowack and G. R¨osel, Pareto-morphology for color image processing,

Proceedings of SCIA99, 11th Scandinavian Conference on Image Analysis

1, Kangerlussuaq, Greenland, pp. 195–202, 1999.

[49] S. Krishnamachari and R. Chellappa, Multiresolution Gauss-Markov random field

models for texture segmentation, IEEE Transactions on Image Processing, vol. 6(2),

pp. 251–267, 1997.

[50] T. Kurita and N. Otsu, Texture classification by higher order local autocorrelation

features, Proceedings of ACCV93, Asian Conference on Computer Vision, Osaka,

pp. 175–178, 1993.

[51] S.T. Kyvelidis, L. Lykouropoulos and N. Kouloumbi, Digital system for detecting,

classifying, and fast retrieving corrosion generated defects, Journal of Coatings

Technology, vol. 73(915), pp. 67–73, 2001.

[52] Y. Liu, T. Zhao and J. Zhang, Learning multispectral texture features for cervical

cancer detection, Proceedings of 2002 IEEE International Symposium on Biomedical

Imaging: Macro to Nano, pp. 169–172, 2002.

[53] G. McGunnigle and M.J. Chantler, Modeling deposition of surface texture, Electronics

Letters, vol. 37(12), pp. 749–750, 2001.

[54] J. McKenzie, S. Marshall, A.J. Gray and E.R. Dougherty, Morphological texture

analysis using the texture evolution function, International Journal of Pattern

Recognition and Artificial Intelligence, vol. 17(2), pp. 167–185, 2003.

[55] J. McKenzie, Classification of dynamically evolving textures using evolution functions,

Ph.D. Thesis, University of Strathclyde, UK, 2004.

[56] S.G. Mallat, Multiresolution approximations and wavelet orthonormal bases of

L2(R), Transactions of the American Mathematical Society, vol. 315, pp. 69–87,

1989.

[57] S.G. Mallat, A theory for multiresolution signal decomposition: the wavelet representation,

IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.

11, pp. 674–693, 1989.

[58] B.S. Manjunath and W.Y. Ma, Texture features for browsing and retrieval of image

data, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 18,

pp. 837–842, 1996.

[59] B.S. Manjunath, G.M. Haley and W.Y. Ma, Multiband techniques for texture classification

and segmentation, Handbook of Image and Video Processing, A. Bovik,

ed., Academic Press, London, pp. 367–381, 2000.

[60] G. Matheron, Random Sets and Integral Geometry, Wiley Series in Probability and

Mathematical Statistics, John Wiley and Sons, New York, 1975.

texture images, called parallel evolution functions (PEFs). Traditional classification

methods predict texture class membership using comparisons with

a finite set of predefined texture classes and identify the closest class. However,

where texture images arise from a dynamic texture evolving over time,

estimation of a time state in a continuous evolutionary process is required

instead. The PEF approach does this using regression modeling techniques

to predict time state. It is a flexible approach which may be based on any

suitable image features. Many textures are well suited to a morphological

analysis and the PEF approach uses image texture features derived from a

granulometric analysis of the image.

The method is illustrated using both simulated images of Boolean processes

and real images of corrosion. The PEF approach has particular advantages

for training sets containing limited numbers of observations, which

is the case in many real world industrial inspection scenarios and for which

other methods can fail or perform badly.

[41] G.W. Horgan, Mathematical morphology for analysing soil structure from images,

European Journal of Soil Science, vol. 49, pp. 161–173, 1998.

[42] G.W. Horgan, C.A. Reid and C.A. Glasbey, Biological image processing and enhancement,

Image Processing and Analysis, A Practical Approach, R. Baldock and

J. Graham, eds., Oxford University Press, Oxford, UK, pp. 37–67, 2000.

[43] B.B. Hubbard, The World According to Wavelets: The Story of a Mathematical

Technique in the Making, A.K. Peters Ltd., Wellesley, MA, 1995.

[44] H. Iversen and T. Lonnestad. An evaluation of stochastic models for analysis and

synthesis of gray-scale texture, Pattern Recognition Letters, vol. 15, pp. 575–585,

1994.

[45] A.K. Jain and F. Farrokhnia, Unsupervised texture segmentation using Gabor filters,

Pattern Recognition, vol. 24(12), pp. 1167–1186, 1991.

[46] T. Jossang and F. Feder, The fractal characterization of rough surfaces, Physica

Scripta, vol. T44, pp. 9–14, 1992.

[47] A.K. Katsaggelos and T. Chun-Jen, Iterative image restoration, Handbook of Image

and Video Processing, A. Bovik, ed., Academic Press, London, pp. 208–209, 2000.

[48] M. K¨oppen, C.H. Nowack and G. R¨osel, Pareto-morphology for color image processing,

Proceedings of SCIA99, 11th Scandinavian Conference on Image Analysis

1, Kangerlussuaq, Greenland, pp. 195–202, 1999.

[49] S. Krishnamachari and R. Chellappa, Multiresolution Gauss-Markov random field

models for texture segmentation, IEEE Transactions on Image Processing, vol. 6(2),

pp. 251–267, 1997.

[50] T. Kurita and N. Otsu, Texture classification by higher order local autocorrelation

features, Proceedings of ACCV93, Asian Conference on Computer Vision, Osaka,

pp. 175–178, 1993.

[51] S.T. Kyvelidis, L. Lykouropoulos and N. Kouloumbi, Digital system for detecting,

classifying, and fast retrieving corrosion generated defects, Journal of Coatings

Technology, vol. 73(915), pp. 67–73, 2001.

[52] Y. Liu, T. Zhao and J. Zhang, Learning multispectral texture features for cervical

cancer detection, Proceedings of 2002 IEEE International Symposium on Biomedical

Imaging: Macro to Nano, pp. 169–172, 2002.

[53] G. McGunnigle and M.J. Chantler, Modeling deposition of surface texture, Electronics

Letters, vol. 37(12), pp. 749–750, 2001.

[54] J. McKenzie, S. Marshall, A.J. Gray and E.R. Dougherty, Morphological texture

analysis using the texture evolution function, International Journal of Pattern

Recognition and Artificial Intelligence, vol. 17(2), pp. 167–185, 2003.

[55] J. McKenzie, Classification of dynamically evolving textures using evolution functions,

Ph.D. Thesis, University of Strathclyde, UK, 2004.

[56] S.G. Mallat, Multiresolution approximations and wavelet orthonormal bases of

L2(R), Transactions of the American Mathematical Society, vol. 315, pp. 69–87,

1989.

[57] S.G. Mallat, A theory for multiresolution signal decomposition: the wavelet representation,

IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.

11, pp. 674–693, 1989.

[58] B.S. Manjunath and W.Y. Ma, Texture features for browsing and retrieval of image

data, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 18,

pp. 837–842, 1996.

[59] B.S. Manjunath, G.M. Haley and W.Y. Ma, Multiband techniques for texture classification

and segmentation, Handbook of Image and Video Processing, A. Bovik,

ed., Academic Press, London, pp. 367–381, 2000.

[60] G. Matheron, Random Sets and Integral Geometry, Wiley Series in Probability and

Mathematical Statistics, John Wiley and Sons, New York, 1975.

Original language | English |
---|---|

Title of host publication | Advances in Nonlinear Signal and Image Processing |

Editors | Stephen Marshall Giovanni L. Sicuranza |

Place of Publication | Cairo, Egypt |

Pages | 239-271 |

Number of pages | 33 |

Volume | 6 |

Publication status | Published - 2006 |

### Publication series

Name | EURASIP Book Series on Signal Processing and Communications |
---|---|

Publisher | Hindawi Publishing Corporation |

Volume | 6 |

### Keywords

- parallel evolution functions

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## Cite this

Gray, A., Marshall, S., & McKenzie, J. (2006). Modeling of evolving textures using granulometries. In S. M. Giovanni L. Sicuranza (Ed.),

*Advances in Nonlinear Signal and Image Processing*(Vol. 6, pp. 239-271). (EURASIP Book Series on Signal Processing and Communications; Vol. 6)..