Abstract In this study, we construct a smoothing term structure, which is an essential part of the energy function in binocular matching. However, the existing energy models are mainly deterministic, which cannot adapt to processing low-quality images, especially when there exists a large proportion of vague areas. In order to perform better in processing these low-quality images, in this paper, we construct the smoothing term based on a fuzzy model, which includes fuzzy segmentation, the fuzzy network between the superpixels and the fuzzy relationship between the pixels. These can be compatible with the uncertainty in the image. In addition, to explain the rationality of the calculation of the degree of correlation between superpixels and further elaborate on the property of these degrees between each superpixel, we propose five corresponding theorems with proofs. After we solve the energy model combined with our proposed smoothing term, we compare our disparity results with the corresponding deterministic model and several state-of-the-art algorithms in the experiment. The results verify the effectiveness of the proposed algorithm.

We consider the problem of constructing asymptotically valid confidence intervals for the change point in a high-dimensional covariance shift setting. A novel estimator for the change point parameter is developed, and its asymptotic distribution under high dimensional scaling obtained. We establish that the proposed estimator exhibits a sharp $O_p(\psi^{-2})$ rate of convergence, wherein $\psi$ represents the jump size between model parameters before and after the change point. Further, the form of the asymptotic distributions under both a vanishing and a non-vanishing regime of the jump size are characterized. In the former case, it corresponds to the argmax of an asymmetric Brownian motion, while in the latter case to the argmax of an asymmetric random walk. We then obtain the relationship between these distributions, which allows construction of regime (vanishing vs non-vanishing) adaptive confidence intervals. Easy to implement algorithms for the proposed methodology are developed and their performance illustrated on synthetic and real data sets.