Skip to content

Latest commit

 

History

History
117 lines (75 loc) · 3.73 KB

f_gldm.rst

File metadata and controls

117 lines (75 loc) · 3.73 KB
Raw

Texture features / GLDM

A Gray Level Dependence Matrix (GLDM) quantifies gray level dependencies in an image. A gray level dependency is defined as a the number of connected voxels within distance \delta that are dependent on the center voxel. A neighbouring voxel with gray level j is considered dependent on center voxel with gray level i if |i-j|\le\alpha. In a gray level dependence matrix \textbf{P}(i,j) the (i,j)-th element describes the number of times a voxel with gray level i with j dependent voxels in its neighbourhood appears in image.

As an example, consider the following 5x5 ROI image having 5 gray levels:

\textbf{G} = \begin{bmatrix}
5 & 2 & 5 & 4 & 4\\
3 & 3 & 3 & 1 & 3\\
2 & 1 & 1 & 1 & 3\\
4 & 2 & 2 & 2 & 3\\
3 & 5 & 3 & 3 & 2 \end{bmatrix}

For \alpha=0 and \delta = 1, the GLDM then becomes:

\textbf{P} = \begin{bmatrix}
0 & 1 & 2 & 1 \\
1 & 2 & 3 & 0 \\
1 & 4 & 4 & 0 \\
1 & 2 & 0 & 0 \\
3 & 0 & 0 & 0 \end{bmatrix}

Let:

  • N_g be the number of discrete intensity values in the image
  • N_d be the number of discrete dependency sizes in the image
  • N_z be the number of dependency zones in the image, which is equal to \sum^{N_g}_{i=1}\sum^{N_d}_{j=1}{\textbf{P}(i,j)}
  • \textbf{P}(i,j) be the dependence matrix
  • p(i,j) be the normalized dependence matrix, defined as p(i,j) = \frac{\textbf{P}(i,j)}{N_z}

Small Dependence Emphasis

GLDM_SDE = \frac{\sum^{N_g}_{i=1}\sum^{N_d}_{j=1}{\frac{\textbf{P}(i,j)}{i^2}}}{N_z}

Large Dependence Emphasis

GLDM_LDE = \frac{\sum^{N_g}_{i=1}\sum^{N_d}_{j=1}{\textbf{P}(i,j)j^2}}{N_z}

Gray Level Non-Uniformity

GLDM_GLN = \frac{\sum^{N_g}_{i=1}\left(\sum^{N_d}_{j=1}{\textbf{P}(i,j)}\right)^2}{N_z}

Dependence Non-Uniformity

GLDM_DN = \frac{\sum^{N_d}_{j=1}\left(\sum^{N_g}_{i=1}{\textbf{P}(i,j)}\right)^2}{N_z}

Dependence Non-Uniformity Normalized

GLDM_DNN = \frac{\sum^{N_d}_{j=1}\left(\sum^{N_g}_{i=1}{\textbf{P}(i,j)}\right)^2}{N_z^2}

Gray Level Variance

GLDM_GLV = \sum^{N_g}_{i=1}\sum^{N_d}_{j=1}{p(i,j)(i - \mu)^2}

where,

\mu = \sum^{N_g}_{i=1}\sum^{N_d}_{j=1}{ip(i,j)}

Dependence Variance

GLDM_DV = \sum^{N_g}_{i=1}\sum^{N_d}_{j=1}{p(i,j)(j - \mu)^2} where \mu = \sum^{N_g}_{i=1}\sum^{N_d}_{j=1}{jp(i,j)}

Dependence Entropy

GLDM_DE = -\sum^{N_g}_{i=1}\sum^{N_d}_{j=1}{p(i,j)\log_{2}(p(i,j)+\epsilon)}

Low Gray Level Emphasis

GLDM_LGLE = \frac{\sum^{N_g}_{i=1}\sum^{N_d}_{j=1}{\frac{\textbf{P}(i,j)}{i^2}}}{N_z}

High Gray Level Emphasis

GLDM_HGLE = \frac{\sum^{N_g}_{i=1}\sum^{N_d}_{j=1}{\textbf{P}(i,j)i^2}}{N_z}

Small Dependence Low Gray Level Emphasis

GLDM_SDLGLE = \frac{\sum^{N_g}_{i=1}\sum^{N_d}_{j=1}{\frac{\textbf{P}(i,j)}{i^2j^2}}}{N_z}

Small Dependence High Gray Level Emphasis

GLDM_SDHGLE = \frac{\sum^{N_g}_{i=1}\sum^{N_d}_{j=1}{\frac{\textbf{P}(i,j)i^2}{j^2}}}{N_z}

Large Dependence Low Gray Level Emphasis

GLDM_LDLGLE = \frac{\sum^{N_g}_{i=1}\sum^{N_d}_{j=1}{\frac{\textbf{P}(i,j)j^2}{i^2}}}{N_z}

Large Dependence High Gray Level Emphasis

GLDM_LDHGLE = \frac{\sum^{N_g}_{i=1}\sum^{N_d}_{j=1}{\textbf{P}(i,j)i^2j^2}}{N_z}