Bidimensional Distribution Entropy to Analyze the Irregularity of Small-Sized Textures

Abstract

Abstract-Two-dimensional sample entropy (SampEn 2D ) has been recently proposed to quantify the irregularity of textures. However, when dealing with small-sized textures, SampEn 2D may lead to either undefined or unreliable values. Moreover, SampEn 2D is too slow for most real-time applications. To alleviate these deficiencies, we introduce bidimensional distribution entropy (DistrEn 2D ). We evaluate DistrEn 2D on both synthetic and real texture datasets. The results indicate that DistrEn 2D can detect different amounts of white Gaussian and salt and pepper noise, and discriminate periodic from synthesized textures. The results also show that DistrEn 2D distinguishes different kinds of textured surfaces. In addition, DistrEn 2D , unlike SampEn 2D , does not lead to undefined values. Moreover, DistrEn 2D is noticeably faster than SampEn 2D . Overall, DistrEn 2D -as an insensitive feature extraction method to rotation -is expected to be very useful for the analysis of real image textures.

Texture Feature Extraction Methods: A Survey

“…Moreover, DistEn 2D is more rapid than SampEn 2D [254]. DistEn 2D is also rotation-invariant [253], [254].…”

“…In order to overcome the drawbacks of SampEn 2D (undefined values or unreliable values for small-sized textures, long computation time), Azami et al [254] recently proposed the bi-dimensional distribution entropy (DistEn 2D ). Its algorithm for an image I with width W and height H is the following [254] 1) Normalize I between 0 and 1. Create all twodimensional matrices (template matrices) X m kl , (k = 1, 2, .…”

“…, W −(m w −1)) with size m h ×m w as described in [254] It has been shown that DistEn 2D is not very sensitive to its parameter values [254] and gives values even for low image sizes, by opposition to SampEn 2D [254]. Moreover, DistEn 2D is more rapid than SampEn 2D [254]. DistEn 2D is also rotation-invariant [253], [254].…”

“…DistEn 2D is able to detect different amounts of noise, and distinguish periodic from synthetized textures [254].…”

On Structural Entropy and Spatial Filling Factor Analysis of Colonoscopy Pictures

“…Stantchev based the probabilities on the number of connections of a given node in a graph. The entropy from [ 13 , 46 ] calculates probabilities from distances between neighboring vertexes and connections weights; Humeau-Heurtier and her co-workers generalized the sample entropy, which uses probabilities consisting of the ratio of the number of cases when two sample vectors froming a series have sufficiently small distance, and a similar number for their shortened versions [ 36 , 47 , 48 , 49 ]. All these methods introduce quite complicated concepts, which are scale-dependent.…”