基于有理数阶偏微分的图像增强新模型
Image enhancement new model based on rational-order Partial Differential

为了在锐化图像边缘的同时增强纹理细节特征，将分数阶微积分与整数阶微积分理论有效结合，推导出有理数阶微分的差分表达式，构建了基于空间有理数阶偏微分的图像增强模型，并利用有理数阶偏微分掩模算子实现增强模型的数值计算。实验结果表明，该方法对图像可以得到连续变化的增强效果，不仅图像纹理得到很好的增强，图像边缘增强效果也比分数阶微分方法有所提高。客观上，采用了信息熵和平均梯度等图像边缘纹理特征评价参数做定量分析和实验验证，结果显示明新模型融合了整数阶微分与分数阶微分各自的优点，弥补了各自的不足，很好地达到了图像增强的目的。
In order to sharpen the image edge features while enhancing texture detail, the image enhancement model based on space rational-order derivative was constructed by the effective combination of integer-order theory and fractional-order calculus theory to derive the differential expression of rational-order partial differential, and the numerical of enhanced model was achieved using rational-order partial differential mask operator. The experimental results showed that compared with the fractional-order differential method , the image enhancement model can be obtained the effect of continuous variation, that not only enhanced image texture well, but also improved the edge enhancement effect. Objectively, using image edge evaluation parameters of texture features such as information entropy and average gradient for quantitative analysis and experimental verification shown that the new model combined the advantages of integer and fractional order differential to make up for their lack of own and achieved a good image enhancement results