Granular computing in visual haze-free task

In the past decade, granular computing (GrC) has been an active topic of research in machine learning and computer vision. However, the granularity division is itself an open and complex problem. Deep learning, at the same time, has been proposed by Geoffrey Hinton, which simulates the hierarchical structure of human brain, processes data from lower level to higher level and gradually composes more and more semantic concepts. The information similarity, proximity and functionality constitute the key points in the original insight of granular computing proposed by Zadeh. Many GrC researches are based on the equivalence relation or the more general tolerance relation, either of which can be described by some distance functions. The information similarity and proximity depended on the samples distribution can be easily described by the fuzzy logic. From this point of view, GrC can be considered as a set of fuzzy logical formulas, which is geometrically defined as a layered framework in a multi-scale granular system. The necessity of such kind multi-scale layered granular system can be supported by the columnar organization of the neocortex. So the granular system proposed in this paper can be viewed as a new explanation of deep learning that simulates the hierarchical structure of human brain. In view of this, a novel learning approach, which combines fuzzy logical designing with machine learning, is proposed in this paper to construct a GrC system to explore a novel direction for deep learning. Unlike those previous works on the theoretical framework of GrC, our granular system is abstracted from brain science and information science, so it can be used to guide the research of image processing and pattern recognition. Finally, we take the task of haze-free as an example to demonstrate that our multi-scale GrC has high ability to increase the texture information entropy and improve the effect of haze-removing.