View source for Gray level size zone matrix

{{short description|Advanced statistical matrix}}
The '''gray level size zone matrix''' (SZM) is the starting point of Thibault matrices. It is an advanced [[Statistics|statistical]] matrix used for texture characterization.

For a texture image '''f''' with '''N''' gray levels, it is denoted <math>GS_f</math> and provides a statistical representation by the estimation of a bivariate conditional [[Physics:Probability density function|probability density function]] of the image distribution values. It is calculated according to the pioneering run length matrix principle (RLM): the value of the matrix <math>GS_f(s_n, g_m)</math> is equal to the number of zones of size <math>s_n</math> and of gray level <math>g_m</math>. The resulting [[Matrix (mathematics)|matrix]] has a fixed number of lines equal to '''N''', the number of gray levels, and a dynamic number of columns, determined by the size of the largest zone as well as the size quantization.

The more homogeneous the texture, the wider and flatter the matrix. SZM does not required computation in several directions, contrary to RLM and [[Co-occurrence matrix|co-occurrence matrix]] (COM). However, it has been empirically proved that the degree of gray level [[Quantization (signal processing)|quantization]] still has an important impact on the texture classification performance. For a general application it is usually required to test several gray-level quantization to find the optimal one with respect to a training dataset.

==Examples==
Two examples of matrix filling for textures 4&nbsp;×&nbsp;4 with four gray levels.

[[File:GlszmExamples.pdf|thumb|center|Matrix filling examples]]

==References==
* {{ cite journal
 |author1=Guillaume Thibault |author2=Bernard Fertil |author3=Claire Navarro |author4=Sandrine Pereira |author5=Pierre Cau |author6=Nicolas Levy |author7=Jean Sequeira |author8=Jean-Luc Mari | year = 2009
 | title = Texture Indexes and Gray Level Size Zone Matrix. Application to Cell Nuclei Classification
 | journal = Pattern Recognition and Information Processing (PRIP)
 | pages = 140–145
 }} [http://www.thibault.biz/Doc/Publications/TextureIndexesAndGrayLevelSizeZoneMatrixApplicationToCellNucleiClassification_PRIP2009.pdf]

* {{ cite journal
 |author1=Guillaume Thibault |author2=Bernard Fertil |author3=Claire Navarro |author4=Sandrine Pereira |author5=Pierre Cau |author6=Nicolas Levy |author7=Jean Sequeira |author8=Jean-Luc Mari | year = 2013
 | title = Shape and Texture Indexes, Application to Cell Nuclei Classification
 | journal = Pattern Recognition and Artificial Intelligence (IJPRAI)
 }} [http://www.thibault.biz/Doc/Publications/ShapeAndTextureIndexesIJPRAI2013.pdf]

* {{ cite journal
 |author1=Guillaume Thibault |author2=Jesus Angulo |author3=Fernand Meyer | year = 2011
 | title = Advanced Statistical Matrices for Texture Characterization: Application to DNA Chromatin and Microtubule Network Classification
 | journal = IEEE International Conference on Image Processing (ICIP)
 | pages = 53–56
 }} [http://www.thibault.biz/Doc/Publications/AdvancedStatisticalMatrices_ICIP_2011.pdf]

* {{ cite arxiv
 |author1=Guillaume Thibault |author2=Izhak Shafran | year = 2016
 | title = Fuzzy Statistical Matrices for Cell Classification
 | eprint=1611.06009
|class=cs.CV }}

==External links==
* [http://www.thibault.biz/Research/ThibaultMatrices/ThibaultMatrices.html Software and Thibault matrices]
* [http://www.thibault.biz/Research/ThibaultMatrices/GLSZM/GLSZM.html Gray Level Size Zone Matrix]
* [http://www.thibault.biz/Research/ThibaultMatrices/FSZM/FSZM.html Fuzzy Size Zone Matrix]
* [http://www.thibault.biz/Research/ThibaultMatrices/MGLSZM/MGLSZM.html Multiple Gray Level Size Zone Matrix]

[[Category:Image processing]]

{{Sourceattribution|Gray level size zone matrix|1}}