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

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.