. Author manuscript; available in PMC: 2013 Oct 1.

Published in final edited form as: Acad Radiol. 2012 Oct;19(10):1241–1251. doi: 10.1016/j.acra.2012.04.020

TABLE 2.

Gray-level Run-length and Gap-length Features Used for Texture Analysis

Run-length Features

Formula

Gap-length Features

Formula

Average run length

\frac{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{r}} {j R}_{i j}}{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{r}} R_{i j}}

Average gap length

\frac{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{g}} {j G}_{i j}}{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{g}} G_{i j}}

Average gray level

\frac{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{r}} i R_{i j}}{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{r}} R_{i j}}

Average gray level

\frac{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{g}} {i G}_{i j}}{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{g}} G_{i j}}

Short run emphasis

\frac{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{r}} R_{i j} / j^{2}}{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{r}} R_{i j}}

Short gap emphasis

\frac{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{g}} G_{i j} / j^{2}}{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{g}} G_{i j}}

Long run emphasis

\frac{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{r}} j^{2} R_{i j}}{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{r}} R_{i j}}

Long gap emphasis

\frac{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{g}} j^{2} G_{i j}}{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{g}} G_{i j}}

Bright color emphasis

\frac{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{r}} i^{2} R_{i j}}{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{r}} R_{i j}}

Bright color emphasis

\frac{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{g}} i^{2} G_{i j}}{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{g}} G_{i j}}

Dark color emphasis

\frac{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{r}} R_{i j} / i^{2}}{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{r}} R_{i j}}

Dark color emphasis

\frac{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{g}} G_{i j} / i^{2}}{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{g}} G_{i j}}

Gray-level nonuniformity

\frac{\sum_{i = 1}^{N_{l}} {(\sum_{j = 1}^{N_{r}} R_{i j})}^{2}}{{(\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{r}} R_{i j})}^{2}}

Gray level nonuniformity

\frac{\sum_{i = 1}^{N_{l}} {(\sum_{j = 1}^{N_{g}} G_{i j})}^{2}}{{(\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{g}} G_{i j})}^{2}}

Run-length nonuniformity

\frac{\sum_{i = 1}^{N_{r}} {(\sum_{j = 1}^{N_{l}} R_{i j})}^{2}}{{(\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{r}} R_{i j})}^{2}}

Gap-length nonuniformity

\frac{\sum_{i = 1}^{N_{g}} {(\sum_{j = 1}^{N_{l}} G_{i j})}^{2}}{{(\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{g}} G_{i j})}^{2}}

Gray-level distribution

\frac{\sum_{i = 1}^{N_{l}} {(\sum_{j = 1}^{N_{r}} R_{i j})}^{2}}{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{r}} R_{i j}}

Gray-level distribution

\frac{\sum_{i = 1}^{N_{l}} {(\sum_{j = 1}^{N_{g}} G_{i j})}^{2}}{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{g}} G_{i j}}

Run-length distribution

\frac{\sum_{i = 1}^{N_{r}} {(\sum_{j = 1}^{N_{l}} R_{i j})}^{2}}{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{r}} R_{i j}}

Gap-length distribution

\frac{\sum_{i = 1}^{N_{g}} {(\sum_{j = 1}^{N_{l}} G_{i j})}^{2}}{\sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{g}} G_{i j}}

Run percentage

\frac{1}{n} \sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{r}} R_{i j}

Gap percentage

\frac{1}{n} \sum_{i = 1}^{N_{l}} \sum_{j = 1}^{N_{g}} G_{i j}

R and G are the run-length and gap-length matrices, respectively; N_r and N_g represent the numbers of run and gap lengths considered, respectively; N_l is the number of gray levels in the binned image; and n is the number of pixels in the image or region of interest.