Granular Computing in Visual Haze-Free Task Hong Hu, Liang Pang, Dongping Tian, Zhongzhi Shi Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Science, Beijing 100080, China, Email: huhong@ict.ac.cn, {pangl, tiandp, shizz}@ics.ict.ac.cn Abstract—In the past decade, granular computing (GrC) has been an active topic of research in machine learning and com- puter 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. Index Terms—Granular Computing; Leveled Granular Sys- tem; Fuzzy Logic; Deep Learning; Haze Free;brain-like comput- er I. I NTRODUCTION Just as the scholars summarized in the IEEE-GrC2006 con- ference ”though the label is relatively recent, the basic notions and principles of GrC, though under different names, have appeared in many related fields, such as information hiding in programming, granularity in artificial intelligence, divide and conquer in theoretical computer science, interval computing, cluster analysis, fuzzy and rough set theories, neutrosophic computing, quotient space theory, belief functions, machine learning, databases, and many others[1]. The above definition of GrC is too augmental and the subjects about classes, clusters, subsets, groups and intervals have already studied by artificial intelligence or mathematics for a long time. What is really new point for GrC ? We think that the new or main point of the GrC lies in the original insight of GrC proposed by Zadeh, in which there are three basic concepts that underlie human cognition: granulation, organization and causation, and informally, granulation involves decomposition of whole into parts; organization involves integration of parts into whole; and causation involves association of causes with effects. Granulation of an object A leads to a collection of granules of A, with a granule being a clump of points (objects) drawn together by indistinguishability, similarity, proximity or functionality[9]. Many granular computing researches neglect information transformation and feature abstraction,this is very important for deep learning. In this paper, we propose a novel framework of granular system, which has ability to process information transformation and object-background separation. At last of our paper, we take the haze-free task as an example to show the ability of our granular system. II. HYBRID DESIGNING OF LEVELED PERCEPTION GRANULAR SYSTEM BASED ON FUZZY LOGIC AND PSVM For the sake of pages, the detailed definition of Granular system based on tolerance Relation is listed in [4]. Owing to the limitation of the scope, in this paper only nested layered GrC is discussed. A nested layered GrC is defined by the input and output relation of a granular computing on a granular system. There are three kinds relations between nearby layers (layers k and k +1) of a nested GrC: (1) binary logic; (2)fuzzy logic; (3) alogical relation. Because fuzzy logic and binary logic are all created by the sigmoid function, so back propagation method can be used to modify weights of all layers. In order to speed up the learning process, for a layered GrC, we combine logical designing with PSVM [2], such kind novel approach is called as ”Logical support vector machine (LPSVM)”. For nested layered GrC, parameters in the binary logical layers can be directly designated according to the binary relation; for the fuzzy logical layers, parameters can also be set according to these layers’functions, but a suitable small adjustment by back propagation is necessary, this is similar to the deep learning proposed by Geoffrey Hinton such that a many-layered neural network could be effectively 147 2013 IEEE International Conference on Granular Computing (GrC) 978-1-4799-1282-7/13/$31.00 ©2013 IEEE