Abstract: The existing Tsallis cross entropy can measure the difference between the original image and
its segmentation result, but it has the drawback of complex formula and low computational efficiency.
Thus two-dimensional asymmetric Tsallis cross entropy threshold selection method based on
decomposition is proposed. Firstly, the asymmetric Tsallis cross entropy is defined and a
one-dimensional threshold selection method based on the asymmetric Tsallis cross entropy is put
forward. Then it is extended to the two-dimensional space, and the corresponding threshold selection
formulae are derived. Finally, the decomposition algorithm of two-dimensional asymmetric Tsallis cross
entropy thresholding is proposed on this basis. As a result, the computations of two-dimensional
asymmetric Tsallis cross entropy thresholding method are converted into two one-dimensional spaces.
The computational complexity is greatly reduced from O(L4) to O(L). A large number of experimental results show that, compared with two-dimensional maximum Tsallis gray entropy method based on
chaos particle swarm optimization, symmetric cross entropy method based on two-dimensional
histogram oblique segmentation, symmetric Tsallis cross entropy method based on two-dimensional
histogram oblique segmentation and so on, the proposed method has superior image segmentation
performance and short running time, which can meet the real-time processing requirement of
segmentation in the practical application systems.

Key words: image segmentation, threshold selection, asymmetric Tsallis cross entropy;
two-dimensional histogram, decomposition