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The visibility of outdoor images is usually significantly degraded by haze. Existing dehazing algorithms, such as dark channel prior (DCP) and colour attenuation prior (CAP), have made great progress and are highly effective. However, they all suffer from the problems of dark distortion and detailed information loss. This paper proposes an improved algorithm for single-image haze removal based on dark channel prior with weighted guided coefficient and union self-adaptive image enhancement. First, a weighted guided coefficient method with sampling based on guided image filtering is proposed to refine the transmission map efficiently. Second, the k-means clustering method is adopted to calibrate the original image into bright and non-bright colour areas and form a transmission constraint matrix. The constraint matrix is then marked by connected-component labelling, and small bright regions are eliminated to form an atmospheric light constraint matrix, which can suppress the halo effect and optimize the atmospheric light. Finally, an adaptive linear contrast enhancement algorithm with a union score is proposed to optimize restored images. Experimental results demonstrate that the proposed algorithm can overcome the problems of image distortion and detailed information loss and is more efficient than conventional dehazing algorithms.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Modeling data relation as a hierarchical structure has proven beneficial for many learning scenarios, and the hyperbolic space, with negative curvature, can encode such data hierarchy without distortion. Several recent studies also show that the representation power of the hyperbolic space can be further improved by endowing the kernel methods. Unfortunately, the known kernel methods, developed in hyperbolic space, are limited by the adaptation capacity or distortion issues. This paper addresses the issues through a novel embedding function. To this end, we propose a curvature-aware isometric embedding, which establishes an isometry from the Poincar\'e model to a special reproducing kernel Hilbert space (RKHS). Then we can further define a series of kernels on this RKHS, including several positive definite kernels and an indefinite kernel. Thorough experiments are conducted to demonstrate the superiority of our proposals over existing-known hyperbolic and Euclidean kernels in various learning tasks, e.g., graph learning and zero-shot learning.