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Handbook of Image Processing and Computer Vision pp 261–314Cite as

Texture Analysis

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Abstract

Texture is an important component for the recognition of objects. In the field of image processing, it has been consolidated with the term texture, any geometric and repetitive arrangement of the gray levels or color of an image. In this context, the texture becomes an additional strategic component to solve the problem of object recognition, the segmentation of images, and the problems of synthesis. Some of the described algorithms are based on the mechanisms of human visual perception of texture. They are useful for the development of systems for the automatic analysis of the information content of an image, obtaining a partitioning of the image in regions with different textures (segmentation). Texture description methods are classified into statistical, syntactical, spatial and spectral transform, structural, and model-based.

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Notes

  1. 1.

    Stimulus processing does not always require the use of attentional resources. Many experiments have shown that the elementary characteristics of a stimulus derived from the texture (as happens for color, shape, movement) are detected without the intervention of attention. The processing of the stimulus is, therefore, defined as pre-attentive. In other words, the pre-attentive information process allows to detect the most salient features of the texture very quickly, and only at a second time the focused attention completes the recognition of the particular texture (or of an object in general).

  2. 2.

    It is assumed that L is a random variable that expresses the gray level of an image deriving from a stochastic process.

  3. 3.

    Recall the 2D convolution operator g(x, y) between two functions f(x, y) and h(x, y) is defined as: \(g(x,y)=f(x,y) \star h(x,y)=\sum _{r}\sum _{c}f(r,c)h(x-r,y-c)\).

  4. 4.

    Lacunarity, originally introduced by Mandelbrot cite Mandelbrot, is a term in fractal geometry that refers to a measure of how patterns fill space. Geometric objects appear more lacunar if they contain a wide range of empty spaces or holes (gaps). Consequently, the lacunarity can be thought of as a measure of “gaps” present, for example, in an image. Note that high lacunarity images that are heterogeneous at small scales can be quite homogeneous at larger scales or vice versa. In other words, lacunarity is a scale-dependent measure of the spatial complexity of patterns. In the fractal context the lacunarity, being also a measure of spatial heterogeneity, can be used to distinguish between images that have similar fractal dimensions but look different from the other.

  5. 5.

    Psychovisual redundancy studies indicate that the human visual system processes images at different scales. In the early stages of vision, the brain performs a sort of analysis in different spatial frequencies, and consequently, the visual cortex is composed of different cells that correspond to different frequencies and orientations. It has also been observed that the responses of these cells are similar to those of the Gabor functions. This multiscale process, which successfully takes place in the human vision for texture perception, has motivated the development of texture analysis methods that mimic the mechanisms of human vision.

  6. 6.

    We recall that it is customary to divide the bands with constant percentage amplitudes. Each band is characterized by a lower frequency \( f_i \) and a higher frequency \( f_s \) and a central frequency \( f_c \). The most frequently used bandwidths are the octave where the lower and upper extremes are in the ratio 1 : 2, or \( f_s = 2F_i \). The bandwidth percentage is given by \((f_s-d_i)/d_c=constant\), and \(f_c=\sqrt{f_i\cdot f_s}\). We also have 1/3 octave bands \(f_s=\root 3 \of {2}\cdot f_i\), where the width of each band is narrower, equal to 23.2% of the central nominal frequency of each band.

  7. 7.

    Primal sketch indicates the first information that the human visual system extracts from the scene and in the context of image processing are the first features extracted such as borders, corners, homogeneous regions, etc. A primal sketch image we can think of as equivalent to the significant traits that an artist draws as his expression of the scene.

  8. 8.

    Normally the evaluation of a distribution is evaluated with respect to the normal distribution considering two indexes that of asymmetry (or skewness) \(\gamma _1=\frac{\mu _3}{\mu _2^{3/2}}\) and kurtosis index \(\gamma _2=\frac{\mu _4}{\mu _2^2}-3\) where \( \mu _n \) indicates the central moment of order n. From the analysis of the two indexes we detect the deviation of a distribution compared to normal:

    \(\bullet \)  \(\gamma _1<0\): Negative asymmetry, which is the left tail of the very long distribution;

    \(\bullet \)  \(\gamma _1>0\): Positive asymmetry, which is the right tail of the very long distribution;

    \(\bullet \)  \(\gamma _2<0\): The distribution is platykurtic, which is very flat compared to the normal;

    \(\bullet \)  \(\gamma _2>0\): The distribution is leptokurtic, which is much more pointed than normal;

    \(\bullet \)  \(\gamma _2=0\): The distribution is mesokurtic, meaning that this distribution has kurtosis statistic similar to that of the normal distribution.

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  1. Institute of Applied Sciences and Intelligent Systems, Consiglio Nazionale delle Ricerche, Lecce, Italy

    Arcangelo Distante & Cosimo Distante

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Distante, A., Distante, C. (2020). Texture Analysis. In: Handbook of Image Processing and Computer Vision. Springer, Cham. https://doi.org/10.1007/978-3-030-42378-0_3

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