Smoothing splines with discontinuities for image analysis.

Smoothing splines are very popular in practice, including machine vision. However, they exhibit poor performance along the edges and boundaries. To cope with discontinuities in image analysis, we study more general smoothing splines, which preserve corners and discontinuities. Cubic splines are investigated in detail since they are easy to implement and provide satisfactory results for most applications. To determine discontinuities at data points, we introduce a discrete regularization method.