Image Approximation by Variable Knot Bicubic Splines

This paper presents a degree of freedom or information content analysis of images in the context of digital image processing. As such it represents an attempt to quantify the number of truly independent samples one gathers with imaging devices. The degrees of freedom of a sampled image itself are developed as an approximation problem. Here, bicubic splines with variable knots are employed in an attempt to answer the question as to what extent images are finitely representable in the context of digital sensors and computers. Relatively simple algorithms for good knot placement are given and result in spline approximations that achieve significant parameter reductions at acceptable error levels. The knots themselves are shown to be useful as an indicator of image activity and have potential as an image segmentation device, as well as easy implementation in CCD signal processing and focal plane smart sensor arrays. Both mathematical and experimental results are presented.