Knut Kvaal. Norwegian University for Life Sciences NMBU,

**[Kvaal et al]** Texture may be described as a pattern that is spatially repeated, either deterministically or stochastically. Thus a pattern may be completely deterministic (e.g. a chessboard) or completely random (e.g. a fractal surface or the surface of children’s sand box). Naturally, many types of intermediate degrees of random- ness will occur, for example textures like tree bark, clouds and surfaces of sandstone, textile cloth and laminates. In the present context, texture is classified in a continuum – from completely isotropic (displaying no preferred orientation) to strongly anisotropic (images with strong structure). A fac¸ade stone (e.g. granite) could serve as an isotropic illustration while a texture comprised of rock layers (e.g. sandstone, schist) is strongly anisotropic. A well-known, useful systematization of texture classes is proposed by the Herriot Watt University Texture Lab [1]: ’Image texture (also termed visual texture) – is what you see in a photograph or on a screen; Topological texture – that which you can feel (i.e. a local variation of surface height); Albedo texture – this may be a printed pattern on a flat surface and Reflectance function variation – local variations from, say, full gloss to dull matte finishes. Image texture is a function of surface texture, illumination conditions and the imaging system.’ We shall here use the word ’texture’ as a common term for image texture.

A texture very often exhibits different properties at different scales. The Angle Measure Technique (AMT) algorithm has been found useful to characterize textures in gray-level images at all scales in almost the entire continuum from isotropic images to middle-structured images; AMT is not designed to be applied to significantly anisotropic imagery [2–6]. AMT has shown greatpropensity for information rich characterization of such textures within the gamut of fine microscopic structures, large(r) meso- and macroscale structures, open structures, coarse structures and for many more features. In our work with AMT over the last decade, we have now reached the stage where we have been able to implement the definitive version of the software needed for further research, and especially with respect to general user applications. The AMT plugin described on this page will be a useful contribution to the work in the field where texture is a topic.

1. Heriot-Watt. Texture Lab. [Online] 2008. http://www.macs.hw.ac.uk/ texturelab/resources/.

2. Huang J, Esbensen KH. Applications of AMT (Angle Measure Tech- nique) in image analysis. Part II: Prediction of powder functional properties and mixing components using Multivariate AMT Regression (MAR). Chemometr. Intell. Lab. Sys. 2001; 57(1): 37–56.

3. Huang J, Esbensen KH. Applications of Angle Measure Technique (AMT) in image analysis - Part I.A. new methodology for in situ powder characterization. Chemometr. Intell. Lab. Sys. 2000; 54(1): 1–19.

4. Kvaal K, Wold JP, Indahl UG, Baardseth P, Næs T. Multivariate feature extraction from textural images of bread. Chemometr. Intell. Lab. Sys. 1998; 42(1): 141–158.

5. Kucheryavski S. Using hard and soft models for classification of medical images. Chemometr. Intell. Lab. Sys. 2007; 88(1): 100–106. 6. Dahl CK, Esbensen KH. Image analytical determination of particle size

distribution characteristics of natural and industrial bulk aggregates.
Chemometr. Intell. Lab. Sys. 2007; 89(1): 9–25.

[**Kucheryavski** et al] The angle measure technique, AMT, is a powerful tool for analysis of one- and two-dimensional isotropic signals. Developed in 1994 by Robert Andrle [1] for description of complex geomorphic lines, it was later introduced into chemometrics as a general approach for textural analysis of generic ‘measurement series’ by Esbensen et al. [2]. The most important AMT information is the mean angle spectrum (MA) (or median angle) that reflects signal complexity on all possible scales simultaneously. All details of the AMT spectrum method and algorithm are given in References [1–3] and will be only introduced very briefly here. Below a two- dimensional digitized image is used as an example; as such imagery is always unfolded in AMT (see further below), one- dimensional signals can be treated in identical fashion without loss of generality.

In Figure 1 is shown an unfolded image. Unfolded isotropic imagery constitutes a one-dimensional signal. Unfolding can be achieved in three principal ways, operationally called ‘chop-chop’, ‘snake’ and ‘spiral’, respectively, all of which are treated in detail in Reference [3]—where it was concluded that only the outward-in spiral unfolding successfully negates all unfolding artefacts previously encountered; below this spiral unfolding is used exclusively.

The default AMT algorithm randomly selects a user-defined number of points, A, along the unfolded signal measurement series (for 1-D series usually 500, for unfolded imagery preferentially at least 2–5% of the total number of original image pixels) — other options are systematic — and stratified random selection. Circles with given radius s, centred on each of the selected set of points are constructed and intersections with the ‘connecting line’ between all signals (measurements) are found. The radius s is a measure of scale in the domain of the measurement series. In Figure 1 one centre point, A and its associated two intersections, B and C can be observed. The supplement to angle CAB is calculated and stored for all A points, following which their mean can be obtained, appropriately termed the MA, pertaining to scale s (below an alternative median angle concept is examined). By repeating these calculations for all scales of possible interest in the interval [1, . . . N/2] (N: number of original measurements/pixels], one can construct the so-called AMT complexity-spectrum [1–3]. AMT’s MA spectrum is simultaneous characterization of the textural complexity for the entire measurement series for all scales. From a chemometric point of view this spectrum can either be used independently (rare) or typically as a feature vector, x, for example, as a row in an X-matrix in a PLS-regression context, to be calibrated with respect to a functional property, y, pertaining to the original image or 1-D series.

One of the important features of signal processing and analysis methods is their robustness relative to the effects of different pre-processing operations, for example, geometric rectification (for images: rotation or secant direction, re-sizing) as well as to signal acquisition effects, especially digitization and quantification. Robustness here means that the analytical results are relatively stable w.r.t. the possible pre-processing operations, that is, the AMT spectrum remains essentially the same regardless of the possible pre-processing options that might be invoked.

1. Andrle R. The angle measure technique: a new method for character- ising the complexity of geomorphic lines. Math. Geol. 1994; 16: 83–79.

2. Esbensen KH, Kvaal K, Hjelmen KH. The AMT approach in chemo- metrics - first forays. J. Chemometrics 1996; 10: 569–590.

3. Mortensen PP, Esbensen KH. Optimization of the Angle Measure Technique for image analytical sampling of particulate matter. Che- mometrics. Intell. Lab. Sys. 2005; 75: 219–229.

**Ref: Sergei V. Kucheryavski, Knut Kvaal, Maths Halstensen, Peter Paasch Mortensen, Casper K. Dahl, Pentti Minkkinen & Kim H. Esbensen: Optimal Corrections for Digitization and Quantification Effects in Angle Measure Technique (AMT) Texture Analysis. J. Chemometrics 22:2008, 72**

**Ref: Knut Kvaal, Sergei V. Kucheryavski, Maths Halstensen, Simen Kvaal, Andreas S. Flø, Pentti Minkkinen & Kim H. Esbensen: eAMTexplorer – A Software Package for Texture and Signal Characterization using Angle Measure Technique. J. Chemomentrics 2008:22,717-721**

Please send a request to the authors to get the latest versions of the AMT and Texture plugins.

Published by the AMT Consortium 2006-2014, Knut Kvaal. ACABS research group Aalborg University, Esbjerg. Norwegian University for Life Sciences NMBU,

NMBU 2014