Image edges detection through B-Spline filters

B-Spline signal processing was used to detect the edges of a digital image. This technique is based upon processing the image in the Spline transform domain, instead of doing so in the space domain (classical processing). The transformation to the Spline transform domain means finding out the real coefficients that makes it possible to interpolate the grey levels of the original image, with a B-Spline polynomial. There exist basically two methods of carrying out this interpolation, which produces the existence of two different Spline transforms: an exact interpolation of the grey values (direct Spline transform), and an approximated interpolation (smoothing Spline transform). The latter results in a higher smoothness of the gray distribution function defined by the Spline transform coefficients, and is carried out with the aim of obtaining an edge detection algorithm which higher immunity to noise. Finally the transformed image was processed in order to detect the edges of the original image (the gradient method was used), and the results of the three methods (classical, direct Spline transform and smoothing Spline transform) were compared. The results were that, as expected, the smoothing Spline transform technique produced a detection algorithm more immune to external noise. On the other hand the direct Spline transform technique, emphasizes more the edges, even more than the classical method. As far as the consuming time is concerned, the classical method is clearly the fastest one, and may be applied whenever the presence of noise is not important, and whenever edges with high detail are not required in the final image. (author). 9 refs., 17 figs., 1 tab