The existing methods of selecting threshold based on the maximum entropy criterion involve two or more random variables. They all ignore a constraint that the random variables involved in the overall entropy calculation of a random system should be independent of each other, which directly affects their segmentation accuracy and application scope. In this study, an automatic threshold selection method guided by maximizing single Tsallis entropy under bidirectional sparse probability distribution is proposed, which can naturally circumvent the constraint that multiple random variables should be independent of each other. On two images derived from a multi-scale convolution transformation, the proposed method first constructs a two-dimensional random variable with bidirectional sparse probability distribution, then a two-dimensional Tsallis entropy is defined on the basis of the two-dimensional random variable. After simplifying the calculation of two-dimensional Tsallis entropy to only involve the marginal probability distribution of the two-dimensional random variables, the corresponding threshold when the single Tsallis entropy takes maximal value is selected as the final segmentation threshold. The proposed method is compared with an interactive thresholding method, 4 automatic thresholding methods, and an automatic clustering method on 44 synthetic images and 44 real-world images, and the gray level histograms of these test images are unimodal, bimodal, multimodal or peakless. The experimental results show that the proposed method is not superior to these 5 automatic methods in computational efficiency, but it has a significant enhancement in the adaptability and accuracy of segmentation.