A statistical approach sees an image texture as a quantitative measure of the arrangement of intensities in a region. In general this approach is easier to compute and is more widely used, since natural textures are made of patterns of irregular subelements.
Edge detection The use of
edge detection is to determine the number of edge pixels in a specified region, helps determine a characteristic of texture complexity. After edges have been found the direction of the edges can also be applied as a characteristic of texture and can be useful in determining patterns in the texture. These directions can be represented as an average or in a
histogram. Consider a region with N pixels. the gradient-based edge detector is applied to this region by producing two outputs for each
pixel p: the gradient magnitude Mag(p) and the gradient direction Dir(p). The per unit area can be defined by F_{edgeness}=\frac{N} for some threshold T. To include orientation with histograms for both gradient magnitude and gradient direction can be used. Hmag(R) denotes the normalized histogram of gradient magnitudes of region R, and Hdir(R) denotes the normalized histogram of gradient orientations of region R. Both are normalized according to the size NR Then F_{mag,dir}=(H_{mag}(R), H_{dir}(R)) is a quantitative texture description of region R.
Co-occurrence matrices The
co-occurrence matrix captures numerical features of a texture using spatial relations of similar gray tones. Numerical features computed from the co-occurrence matrix can be used to represent, compare, and classify textures. The following are a subset of standard features derivable from a normalized co-occurrence matrix: \begin{align} Angular \text{ } 2nd \text{ } Moment &= \sum_{i} \sum_{j} p[i,j]^{2}\\ Contrast &= \sum_{i=1}^{Ng} \sum_{j=1}^{Ng} n^{2} p[i,j] \text{, where } |i-j|=n\\ Correlation &= \frac{\sum_{i=1}^{Ng} \sum_{j=1}^{Ng}(ij)p[i,j] - \mu_x \mu_y}{\sigma_x \sigma_y} \\ Entropy &= -\sum_{i}\sum_{j} p[i,j] ln(p[i,j])\\ \end{align} where p[i,j] is the [i,j]th entry in a gray-tone spatial dependence matrix, and Ng is the number of distinct gray-levels in the quantized image. One negative aspect of the co-occurrence matrix is that the extracted features do not necessarily correspond to
visual perception. It is used in dentistry for the objective evaluation of lesions [DOI: 10.1155/2020/8831161], treatment efficacy [DOI: 10.3390/ma13163614; DOI: 10.11607/jomi.5686; DOI: 10.3390/ma13173854; DOI: 10.3390/ma13132935] and bone reconstruction during healing [DOI: 10.5114/aoms.2013.33557; DOI: 10.1259/dmfr/22185098; EID: 2-s2.0-81455161223; DOI: 10.3390/ma13163649].
Laws texture energy measures Another approach is to use local masks to detect various types of texture features. Laws originally used four vectors representing texture features to create sixteen 2D masks from the outer products of the pairs of vectors. The four vectors and relevant features were as follows: L5 = [ +1 +4 6 +4 +1 ] (Level) E5 = [ -1 -2 0 +2 +1 ] (Edge) S5 = [ -1 0 2 0 -1 ] (Spot) R5 = [ +1 -4 6 -4 +1 ] (Ripple) To these 4, a fifth is sometimes added: W5 = [ -1 +2 0 -2 +1 ] (Wave) From Laws' 4 vectors, 16 5x5 "energy maps" are then filtered down to 9 in order to remove certain symmetric pairs. For instance, L5E5 measures vertical edge content and E5L5 measures horizontal edge content. The average of these two measures is the "edginess" of the content. The resulting 9 maps used by Laws are as follows: L5E5/E5L5 L5R5/R5L5 E5S5/S5E5 S5S5 R5R5 L5S5/S5L5 E5E5 E5R5/R5E5 S5R5/R5S5 Running each of these nine maps over an image to create a new image of the value of the origin ([2,2]) results in 9 "energy maps," or conceptually an image with each pixel associated with a vector of 9 texture attributes.
Autocorrelation and power spectrum The
autocorrelation function of an image can be used to detect repetitive patterns of textures. ==Texture segmentation==