Modeling of evolving textures using granulometries

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

Flat zones filtering, connected operators, and filters by reconstruction

This correspondence deals with the notion of connected operators. Starting from the definition for operator acting on sets, it is shown how to extend it to operators acting on function. Typically, a connected operator acting on a function is a transformation that enlarges the partition of the space created by the flat zones of the functions. It is shown that from any connected operator acting on sets, one can construct a connected operator for functions (however, it is not the unique way of generating connected operators for functions). Moreover, the concept of pyramid is introduced in a formal way. It is shown that, if a pyramid is based on connected operators, the flat zones of the functions increase with the level of the pyramid. In other words, the flat zones are nested. Filters by reconstruction are defined and their main properties are presented. Finally, some examples of application of connected operators and use of flat zones are described.Peer ReviewedPostprint (published version

Multiresolution signal decomposition schemes

[PNA-R9810] Interest in multiresolution techniques for signal processing and analysis is increasing steadily. An important instance of such a technique is the so-called pyramid decomposition scheme. This report proposes a general axiomatic pyramid decomposition scheme for signal analysis and synthesis. This scheme comprises the following ingredients: (i) the pyramid consists of a (finite or infinite) number of levels such that the information content decreases towards higher levels; (ii) each step towards a higher level is constituted by an (information-reducing) analysis operator, whereas each step towards a lower level is modeled by an (information-preserving) synthesis operator. One basic assumption is necessary: synthesis followed by analysis yields the identity operator, meaning that no information is lost by these two consecutive steps. In this report, several examples are described of linear as well as nonlinear (e.g., morphological) pyramid decomposition schemes. Some of these examples are known from the literature (Laplacian pyramid, morphological granulometries, skeleton decomposition) and some of them are new (morphological Haar pyramid, median pyramid). Furthermore, the report makes a distinction between single-scale and multiscale decomposition schemes (i.e. without or with sample reduction).#[PNA-R9905] In its original form, the wavelet transform is a linear tool. However, it has been increasingly recognized that nonlinear extensions are possible. A major impulse to the development of nonlinea

Fusion of MultiSpectral and Panchromatic Images Based on Morphological Operators

International audienceNonlinear decomposition schemes constitute an alternative to classical approaches for facing the problem of data fusion. In this paper we discuss the application of this methodology to a popular remote sensing application called pansharpening, which consists in the fusion of a low resolution multispectral image and a high resolution panchromatic image. We design a complete pansharpening scheme based on the use of morphological half gradients operators and demonstrate the suitability of this algorithm through the comparison with state of the art approaches. Four datasets acquired by the Pleiades, Worldview-2, Ikonos and Geoeye-1 satellites are employed for the performance assessment, testifying the effectiveness of the proposed approach in producing top-class images with a setting independent of the specific sensor

Generalized connected operators

This paper deals with the notion of connected operators These operators are becoming popular in image processing because they have the fundamental property of simplifying the signal while preserving the contour information In a rst step we recall the basic notions involved in binary and gray level connected operators. Then we show how one can extend and generalize these operators We focus on two important issues the connectivity and the simplication criterion We will show in particular how to create connectivities that are either more or less strict than the usual ones and how to build new criteriaPeer ReviewedPostprint (published version

The Multigrid Image Transform

A second order partial differential operator is applied to an image function. To this end we consider both the Laplacian and a more general elliptic operator. By using a multigrid operator known from the so-called approximation property, we derive a multiresolution decomposition of the image without blurring of edges at coarser levels. We investigate both a linear and a nonlinear variant and compare to some established methods

Automatic Archeological Feature Extraction from Satellite VHR Images

Abstract Archaeological applications need a methodological approach on a variable scale able to satisfy the intra-site (excavation) and the inter-site (survey, environmental research). The increased availability of high resolution and micro-scale data has substantially favoured archaeological applications and the consequent use of GIS platforms for reconstruction of archaeological landscapes based on remotely sensed data. Feature extraction of multispectral remotely sensing image is an important task before any further processing. High resolution remote sensing data, especially panchromatic, is an important input for the analysis of various types of image characteristics; it plays an important role in the visual systems for recognition and interpretation of given data. The methods proposed rely on an object-oriented approach based on a theory for the analysis of spatial structures called mathematical morphology. The term ‘‘morphology’’ stems from the fact that it aims at analysing object shapes and forms. It is mathematical in the sense that the analysis is based on the set theory, integral geometry, and lattice algebra. Mathematical morphology has proven to be a powerful image analysis technique; two-dimensional grey tone images are seen as three-dimensional sets by associating each image pixel with an elevation proportional to its intensity level. An object of known shape and size, called the structuring element, is then used to investigate the morphology of the input set. This is achieved by positioning the origin of the structuring element to every possible position of the space and testing, for each position, whether the structuring element either is included or has a nonempty intersection with the studied set. The shape and size of the structuring element must be selected according to the morphology of the searched image structures. Other two feature extraction techniques were used, eCognition and ENVI module SW, in order to compare the results. These techniques were applied to different archaeological sites in Turkmenistan (Nisa) and in Iraq (Babylon); a further change detection analysis was applied to the Babylon site using two HR images as a pre–post second gulf war. We had different results or outputs, taking into consideration the fact that the operative scale of sensed data determines the final result of the elaboration and the output of the information quality, because each of them was sensitive to specific shapes in each input image, we had mapped linear and nonlinear objects, updating archaeological cartography, automatic change detection analysis for the Babylon site. The discussion of these techniques has the objective to provide the archaeological team with new instruments for the orientation and the planning of a remote sensing application. & 2009 Elsevier Ltd. All rights reserved