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 ${\displaystyle GS_{f}}$ 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 ${\displaystyle GS_{f}(s_{n},g_{m})}$ is equal to the number of zones of size ${\displaystyle s_{n}}$ and of gray level ${\displaystyle g_{m}}$. 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.