分数阶微分的图像滤波和增强方法多数通过尝试不同的分数阶得到结果,并以固定分数阶进行纹理细节提取,这种方法对于复杂环境难以鲁棒地增强整幅图像中的纹理细节。为此,提出了一种自适应的分数阶微分的复合双边滤波算法。通过分析纹理特性,建立幅值频率非线性联合指数模型自适应选择分数阶微分阶数检测图像纹理细节,有效克服图像中纹理细节的变化;在双边滤波的框架下,引入自适应分数阶微分构建的引导图像,借助细节转移方法,确保在图像去噪的同时保持/增强纹理图像细节。实验结果表明,自适应分数阶微分的复合双边滤波算法在图像滤波、去雾、细节增强等计算机视觉应用方面具有良好的效果。

The majority of methods based on fractional order differentiation for image enhancement always try to select different fractional orders and they fix the optimal one all the pixels in one image. However, these methods have difficulties in robustly enhancing images in complex environments. Therefore, a multi-bilateral filtering algorithm based on adaptive fractional order differentiation is proposed. The amplitude-frequency nonlinear joint model is established to adaptively select fractional order by analyzing the texture's characters, which can effectively overcome texture changes in images with complex environment. In the framework of bilateral filtering, introducing the guided image by adaptively selecting fractional order and detail transfer method makes sure that the texture details of an image are maintained/enhanced during denoising. Experiment results show that the proposed algorithm has better performance in computer vision and graphics, such as image filtering, dehazing and detail enhancement.