Discrete Splines and Vision - Bezier and Splines in Image Processing and Machine Vision - page 155

where A is the Laplacian matrix of D i , M − 1 = diag ( A − 1 ,A − 1 ). As A − 1 is

irregular, there is no method for multiplying A − 1 eciently by any vector.
•

We cannot say anything about the optimality of λ . Interested readers can
consult the topic [79].

7.7 Concluding Remarks

This chapter provides a theoretical background for discrete splines, which can
be used effectively in designing a high quality surface. Resolution of a surface
can be increased with the addition of knots in steps. This is the process of
repeated refinement. The impact of discrete smoothing spline in computer
vision shows that it is only possible to have a range of the regularization
parameter for which an iterative algorithm can be devised to explore the
shape of a physical surface from its image brightness values.
As splines are a powerful tool, their capability in different aspects should
be re-investigated thoroughly. This tool is equally useful both in analysis and
synthesis.