期刊
IEEE TRANSACTIONS ON IMAGE PROCESSING
卷 27, 期 3, 页码 1214-1229出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIP.2017.2779601
关键词
Fractional calculus; fractional-order partial differential equation; fractional-order steepest descent method; fractional-order Courant-Friedrichs-Lewy condition; fractionalorder retinex
资金
- National Key Research and Development Program Foundation of China [2017YFB0802300]
- National Natural Science Foundation of China [61571312]
- Academic and Technical Leaders Support Foundation of Sichuan province [(2016) 183-5]
- Science and Technology Support Project of Chengdu PU Chip Science and Technology Company, Ltd
This paper discusses a novel conceptual formulation of the fractional-order variational framework for retinex, which is a fractional-order partial differential equation (FPDE) formulation of retinex for the multi-scale nonlocal contrast enhancement with texture preserving. The well-known shortcomings of traditional integer-order computation-based contrastenhancement algorithms, such as ringing artefacts and staircase effects, are still in great need of special research attention. Fractional calculus has potentially received prominence in applications in the domain of signal processing and image processing mainly because of its strengths like long-term memory, nonlocality, and weak singularity, and because of the ability of a fractional differential to enhance the complex textural details of an image in a nonlinear manner. Therefore, in an attempt to address the aforementioned problems associated with traditional integerorder computation-based contrast-enhancement algorithms, we have studied here, as an interesting theoretical problem, whether it will be possible to hybridize the capabilities of preserving the edges and the textural details of fractional calculus with texture image multi-scale nonlocal contrast enhancement. Motivated by this need, in this paper, we introduce a novel conceptual formulation of the fractional-order variational framework for retinex. First, we implement the FPDE by means of the fractional-order steepest descent method. Second, we discuss the implementation of the restrictive fractional-order optimization algorithm and the fractional-order Courant-Friedrichs-Lewy condition. Third, we perform experiments to analyze the capability of the FPDE to preserve edges and textural details, while enhancing the contrast. The capability of the FPDE to preserve edges and textural details is a fundamental important advantage, which makes our proposed algorithm superior to the traditional integer-order computation-based contrast enhancement algorithms, especially for images rich in textural details.
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