Abstract: False corners will emerge in the corner detection of the image with high texture complexity by Harris algorithm, and when fractional differential is applied to image processing, the order needs to be specified by human. This paper analyzed the reason that caused the false corners and suggested to replace the integral order in the algorithm with fractional order to operate differential coefficient so as to improve the algorithm. The paper also brought forward an approach regarding fractal dimension as a parameter which came from the order in choosing differential coefficient. So the marginal information of image can be saved when operating the differential coefficient of the image, and this approach makes the fractional differential be applied in occasions with high real-time requirements such as video target tracing and video image stabilization. The tests show that the modified algorithm has higher precision in the corner detection.

Key words: fractional differential, Harris algorithm, corner detection, fractal dimension, texture complexity

摘要： 针对Harris算法在对纹理复杂程度高的图像进行角点检测时会出现大量伪角点,以及分数阶微分应用到图像处理中需要人为地指定阶数的缺点。分析了伪角点大量产生的原因,并提出以分数阶替换原算法中的整数阶对图像进行微分的改进方法,以及一种以图像的分形维数作为参数来自适应地选择微分所需要的阶数的方法。从而使图像做微分运算时能更好地保留图像中的边缘信息,使分数阶微分可以应用于视频目标追踪、视频稳像等实时性要求较高的场合。实验表明,改进算法在进行角点检测时具有更高的精确度。

关键词: 分数阶微分, Harris算法, 角点检测, 分形维数, 纹理复杂度