Angle Measurement Technique
This website focuses on the analysis of images using AMT. This technique is commonly used to extract features from images of the same type. Through advanced statistical methods and machine learning, AMT demonstrates significant potential in image classification tasks. It has found applications across various fields in both research and industry. Explore its capabilities for enhanced image analysis.
(WEBSITE UNDER MAINTENANCE. PLEASE REFRESH THE PAGE)
Textural Patterns
Texture can be defined as a repetitive pattern that occurs in space, whether in a deterministic or stochastic manner. Patterns can range from being completely deterministic, like a chessboard, to entirely random, such as a fractal surface or a child's sandbox. In reality, many textures exhibit varying degrees of randomness, like tree bark, clouds, sandstone surfaces, textile cloth, and laminates. Within this context, texture is classified along a spectrum – from completely isotropic (showing no preferred orientation) to strongly anisotropic (exhibiting a distinct structure).
A facade stone like granite represents isotropic texture, while textures formed by rock layers such as sandstone or schist are highly anisotropic. The Herriot Watt University Texture Lab offers a well-known categorization of texture classes: 'Image texture (or visual texture) – what is visible in a photograph or on a screen; Topological texture – variations in surface height that can be felt; Albedo texture – patterns printed on flat surfaces; Reflectance function variation – local changes from gloss to matte finishes. Our discussion here uses 'texture' as a general term encompassing image texture.
Textures often display different characteristics at various scales. The Angle Measure Technique (AMT) algorithm is valuable for characterizing gray-level image textures across scales, from isotropic to moderately structured images. While AMT is not ideal for significantly anisotropic imagery, it excels in providing detailed texture characterization for a range of features spanning microscopic to macroscopic structures.
After a decade of work with AMT, we have successfully developed a definitive software version for further research, particularly in user applications. The AMT plugin referenced on this page will be a valuable asset for those working in the field of texture analysis.
AMT description
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.
References and litterature:
1. Heriot-Watt. Texture Lab. [Online] 2020. http://www.macs.hw.ac.uk/texturelab/resources/databases/
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.
6. Andrle R. The angle measure technique: a new method for character- ising the complexity of geomorphic lines. Math. Geol. 1994; 16: 83–79.
7. Esbensen KH, Kvaal K, Hjelmen KH. The AMT approach in chemo- metrics - first forays. J. Chemometrics 1996; 10: 569–590.
8. 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.
9. 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
10. 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