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

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Abstract
Two-dimensional sample entropy (SampEn2D) has been recently proposed to quantify the irregularity of textures. However, when dealing with small-sized textures, SampEn2D may lead to either undefined or unreliable values. Moreover, SampEn2D is too slow for most real-time applications. To alleviate these deficiencies, we introduce bidimensional distribution entropy (DistrEn2D). We evaluate DistrEn2D on both synthetic and real texture datasets. The results indicate that DistrEn2D can detect different amounts of white Gaussian and salt and pepper noise, and discriminate periodic from synthesized textures. The results also show that DistrEn2D distinguishes different kinds of textured surfaces. In addition, DistrEn2D , unlike SampEn2D, does not lead to undefined values. Moreover, DistrEn2D is noticeably faster than SampEn2D. Overall, DistrEn2D—as an insensitive feature extraction method to rotation—is expected to be very useful for the analysis of real image textures.

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