Box Spline Wavelet Frames for Image Edge Analysis

We present a new box spline wavelet frame and apply it for image edge analysis. The wavelet frame is tight and constructed based on a box spline of eight directions which is seldom used for application before. Due to the eight different directions, it can find edges of various types in detail quite well. In addition to step edges (local discontinuities in intensity), it is able to locate Dirac edges (momentary changes of intensity) and hidden edges (local discontinuity in intensity derivatives). The method is simple and robust to noise. Many numerical examples are presented to demonstrate the effectiveness of this method. Quantitative and qualitative comparison with other edge detection techniques are given to show the advantage of this wavelet frame. Our test images include synthetic ones with known ground truth and natural, medical images with rich geometric information.