Gray level size zone matrix

The gray level size zone matrix (SZM) is the starting point of Thibault matrices. It is an advanced statistical matrix used for texture characterization.

For a texture image f with N gray levels, it is denoted and provides a statistical representation by the estimation of a bivariate conditional 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 is equal to the number of zones of size and of gray level . The resulting 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 (COM). However, it has been empirically proved that the degree of gray level 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 × 4 with four gray levels.

Matrix filling examples
gollark: Hmm, they might just use a pi digits formula using arbitrary-precision decimals or whatever then multiply it by two.I doubt it though.
gollark: I'm fairly sure they probably won't actually be operating on them as numbers, but digit-wise, somehow.
gollark: No.
gollark: There is a 10000 digits of tau thing up on the tauday page, but they don't list how they get it.
gollark: For Pi, you have magic formula like these for getting digits. I'm annoyed that there are none I can find easily for Tau.

References
  • Guillaume Thibault; Bernard Fertil; Claire Navarro; Sandrine Pereira; Pierre Cau; Nicolas Levy; Jean Sequeira; Jean-Luc Mari (2009). "Texture Indexes and Gray Level Size Zone Matrix. Application to Cell Nuclei Classification". Pattern Recognition and Information Processing (PRIP): 140–145.
  • Guillaume Thibault; Bernard Fertil; Claire Navarro; Sandrine Pereira; Pierre Cau; Nicolas Levy; Jean Sequeira; Jean-Luc Mari (2013). "Shape and Texture Indexes, Application to Cell Nuclei Classification". Pattern Recognition and Artificial Intelligence (IJPRAI).
  • Guillaume Thibault; Jesus Angulo; Fernand Meyer (2011). "Advanced Statistical Matrices for Texture Characterization: Application to DNA Chromatin and Microtubule Network Classification". IEEE International Conference on Image Processing (ICIP): 53–56.
  • Guillaume Thibault; Izhak Shafran (2016). "Fuzzy Statistical Matrices for Cell Classification". arXiv:1611.06009 [cs.CV].
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