What is it about?

Local patterns play an important role in statistical physics as well as in image processing. Two-dimensional ordinal patterns were studied by Ribeiro et al. who determined permutation entropy and complexity in order to classify paintings and images of liquid crystals. Starting from the observation that 2 × 2 patterns come in three types, this paper develops a different approach. Two parameters expressing the frequency of types define the smoothness and branching structure of an image. It is shown that the parameters consistently describe textures and are well-suited to distinguish different structures.

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Why is it important?

There is a huge demand for fast methods of evaluating textures. An unbelievable amount of image data is produced each day, ranging from microscopic pictures in cancer and virus detection to multispectral satellite images. They have to be screened automatically to fix regions where valuable information could be. Computers must find similar phenomena and do some classification before men and women will see the picture. There are many tools for studying local structures. Ordinal parameters, such as permutation entropy, have been shown to be fast, simple, and robust in one dimension. It is tempting to transfer them to two dimensions where quadratic data size requires just these properties.


We introduced two very simple ordinal parameters describing smoothness and branching structure in images. They could become part of the big toolbox of image processing. Applications range from virus detection to the analysis of satellite images.

Katharina Wittfeld
University Medicine Greifswald

Read the Original

This page is a summary of: Two new parameters for the ordinal analysis of images, Chaos An Interdisciplinary Journal of Nonlinear Science, April 2023, American Institute of Physics, DOI: 10.1063/5.0136912.
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