Tsallis entropy in scale-spaces

Recently an interesting image analysis by scale-space method is given by Sporring and Weickert.(20) They considered Renyi entropy at each scale to estimate the extents of the lighter pattern and the darker pattern in a given image. On the other hand, there is another generalized entropy such as Tsallis entropy, which has a physical meaning like Boltzmann entropy and is also famous for its usefulness in physics. In this paper, after giving a brief review of Tsallis entropy, we adopt Tsallis entropy as an information measure at each level for the scale-space method to elucidate what the difference between Renyi entropy and Tsallis entropy causes in result. It is also shown that Tsallis entropy is a more natural information measure than Renyi entropy.