Cardinal B-spline wavelet based on Canny’s edge detection criteria

Based on Cannypsilas edge detecting criteria, we study two types of the cardinal B-spline wavelets which converge asymptotically to Canny operator and Marr-Hildreth operator respectively, derive the mathematical formulas of the signal-to-noise ratio SNR, the localization L and the nonedge-mean-distance M, and prove that when detecting the object edge, the B-spline wavelet converging to Canny operator is superior to the B-spline wavelet converging to Marr-Hildreth operator. Like the first-derivative of Gauss function, B-spline wavelet converging to Canny operator can satisfy the optimal criteria approximately and detect edges with very high calculation speed.