"A Multiscale Bi-Gaussian Filter for Adjacent Curvilinear Structures Detection With Application to Vasculature Images"
Changyan Xiao, Marius Staring, Yaonan Wang, Denis P. Shamonin and Berend C. Stoel
The intensity or gray-level derivatives have been widely used in image segmentation and enhancement. Conventional derivative filters often suffer from an undesired merging of adjacent objects, due to their intrinsic usage of an inappropriately broad Gaussian kernel; as a result neighboring structures cannot be properly resolved. To avoid this problem, we propose to replace the low-level Gaussian kernel with a bi-Gaussian function, which allows independent selection of scales on foreground and background. By selecting a narrow neighborhood for the background relative to the foreground, the proposed method will reduce interference from adjacent objects, while preserving the ability of intra-region smoothing. Our idea is inspired by a comparative analysis of existing line filters, where several traditional methods including the vesselness, gradient flux and medialness models are integrated into a uniform framework. The comparison subsequently aids in understanding the principles of the different filtering kernels, which is also a contribution of the paper. Based on some axiomatic scale-space assumptions, the full representation of our bi-Gaussian kernel is deduced. The popular γ-normalization scheme for multi-scale integration is extended to the bi-Gaussian operators. Finally, combined with a parameter-free shape estimation scheme, a derivative filter is developed for the typical applications of curvilinear structure detection and vasculature image enhancement. It is verified in experiments using synthetic and real data that the proposed method outperforms several conventional filters in separating closely located objects as well as being robust to noise.