3-D B-spline Wavelet-Based Local Standard Deviation (BWLSD): Its application to edge detection and vascular segmentation in magnetic resonance angiography

Extracting reliable image edge information is crucial for active contour models as well as vascular segmentation in magnetic resonance angiography (MRA). However, conventional edge detection techniques, such as gradient-based methods and wavelet-based methods, are incapable of returning reliable detection responses from low contrast edges in the images. In this paper, we propose a novel edge detection method by combining B-spline wavelet magnitude with standard deviation inside local region. It is proved theoretically and demonstrated experimentally in this paper that the new edge detection method, namely BWLSD, is able to give consistent and reliable strengths for edges with different image contrasts. Moreover, the relationship between the size of local region with non-zero wavelet magnitudes and the scale of wavelet function is established. This relationship indicates that if the scale of the adopted wavelet function is s, then the size of a local region, from which the standard deviation is estimated, should be 2s-1. The proposed edge detection technique is embedded in FLUX, namely, BWLSD-FLUX, for vascular segmentation in MRA image volumes. Experimental results on clinical images show that, as compared with the conventional FLUX, BWLSD-FLUX can achieve better segmentations of vasculatures in MRA images under same initial conditions.