**Conclusion **

The smoothing operator we have proposed acts as a modified 'á trous' filter. The method is quite flexible. As we can choose the degree of the interpolation for the input image and the degree and size of the smoothing spline. A nice feature of the algorithm is that the computational cost is independent of the scaling factor. This property is the one that makes feasible the design of an adaptive smoothing algorithm. The implementation is relatively fast as the values of the 'á trous' filter are pre-calculated and stored in a look-up table. The number of applications of the adaptive smoothing algorithm are huge and many of them, still for discover. As part of the project work, we have applied the method to denoising and feature detection.