On Structural Entropy and Spatial Filling Factor Analysis of Colonoscopy Pictures

Abstract

Colonoscopy is the standard device for diagnosing colorectal cancer, which develops from little lesions on the bowel wall called polyps. The Rényi entropies-based structural entropy and spatial filling factor are two scale- and resolution-independent quantities that characterize the shape of a probability distribution with the help of characteristic curves of the structural entropy–spatial filling factor map. This alternative definition of structural entropy is easy to calculate, independent of the image resolution, and does not require the calculation of neighbor statistics, unlike the other graph-based structural entropies.The distant goal of this study was to help computer aided diagnosis in finding colorectal polyps by making the Rényi entropy based structural entropy more understood. The direct goal was to determine characteristic curves that can differentiate between polyps and other structure on the picture. After analyzing the distribution of colonoscopy picture color channels, the typical structures were modeled with simple geometrical functions and the structural entropy–spatial filling factor characteristic curves were determined for these model structures for various parameter sets. A colonoscopy image analying method, i.e., the line- or column-wise scanning of the picture, was also tested, with satisfactory matching of the characteristic curve and the image.

Entropy in Image Analysis

“…Nagy et al, in their article concerning the imaging of colonoscopy [ 17 ], propose a research with its framework in the methods based on the structural Rényi entropy. The aim of their work is to contribute to computer-aided diagnoses in finding colorectal polyps.…”

Application of Structural Entropy and Spatial Filling Factor in Colonoscopy Image Classification

“…In the future we plan to change the method of prepairing tiles, we would like to introduce overlaps between the tiles as too small polyp percentage is not beneficial for the detection efficiency. Also, The results presented in [29] showed that the sliding windows can uncover such properties that can be used for distinguishing between bowel wall and polyp-like structures.…”

“…In image processing, based on the shape of the trend lines associated with the Bonyár introduced the notion of the localisation factor α [38], which he used for characterising roughness of micro and nano surfaces [39]. The above Rényi entropy based quantities are used in detecting the shape and the pattern on the surface of the polyp [29]. We found significant difference between the responses of corrugated bowel wall and the semisphere-like polyps with or without shadow.…”

“…In image processing and computer vision, entropies are proven to be useful features [29]. Beside the usual von Neumann [30] and Shannon [31] entropies, there are many other generalizations and these are also in use in the mentioned disciplines [32,33].…”

“…As the structural entropy and the spatial filling factor seemed to be promising in this type of classification [29], therefore we decided to check, whether using only these variables from the image tiles and their four wavelet transformed versions can lead to more probable decisions. When this approach was followed then the histogram fitted results improved significantly.…”