NNetEn2D: Two-Dimensional Neural Network Entropy in Remote Sensing Imagery and Geophysical Mapping

Andrei Velichko, Matthias P. Wagner, Alireza Taravat, Bruce Hobbs, Alison Ord

Research output: Contribution to journalArticlepeer-review


Measuring the predictability and complexity of 2D data (image) series using entropy is an essential tool for evaluation of systems’ irregularity and complexity in remote sensing and geophysical mapping. However, the existing methods have some drawbacks related to their strong depend-ence on method parameters and image rotation. To overcome these difficulties, this study proposes a new method for estimating two-dimensional neural network entropy (NNetEn2D) for evaluating the regularity or predictability of images using the LogNNet neural network model. The method is based on an algorithm for converting a 2D kernel into a 1D data series followed by NNetEn2D cal-culation. An artificial test image was created for the study. We demonstrate the advantage of using circular instead of square kernels through comparison of the invariance of the NNetEn2D distribution after image rotation. Highest robustness was observed for circular kernels with a radius of R = 5 and R = 6 pixels, with a NNetEn2D calculation error of no more than 10%, comparable to the dis-tortion of the initial 2D data. The NNetEn2D entropy calculation method has two main geometric parameters (kernel radius and its displacement step), as well as two neural network hyperparame-ters (number of training epochs and one of six reservoir filling techniques). We evaluated our method on both remote sensing and geophysical mapping images. Remote sensing imagery (Senti-nel-2) shows that brightness of the image does not affect results, which helps keep a rather con-sistent appearance of entropy maps over time without saturation effects being observed. Surfaces with little texture, such as water bodies, have low NNetEn2D values, while urban areas have con-sistently high values. Application to geophysical mapping of rocks to the northwest of southwest Australia is characterized by low to medium entropy and highlights aspects of the geology. These results indicate the success of NNetEn2D in providing meaningful entropy information for 2D in remote sensing and geophysical applications.

Original languageEnglish
Article number2166
JournalRemote Sensing
Issue number9
Publication statusPublished - 1 May 2022


Dive into the research topics of 'NNetEn2D: Two-Dimensional Neural Network Entropy in Remote Sensing Imagery and Geophysical Mapping'. Together they form a unique fingerprint.

Cite this