Video Data Compression by Progressive Iterative Approximation

In the present paper, the B-spline curve is used for reducing the entropy of video data. We consider the color or luminance variations of a spatial position in a series of frames as input data points in Euclidean space R or R3. The progressive and iterative approximation (PIA) method is a direct and intuitive way of generating curve series of high and higher fitting accuracy. The video data points are approximated using progressive and iterative approximation for least square (LSPIA) fitting. The Lossless video data compression is done through storing the B-spline curve control points (CPs) and the difference between fitted and original video data. The proposed method is applied to two classes of synthetically produced and naturally recorded video sequences and makes a reduction in the entropy of both. However, this reduction is higher for syntactically created than those naturally produced. The comparative analysis of experiments on a variety of video sequences suggests that the entropy of output video data is much less than that of input video data

Preconditioned geometric iterative methods for cubic B-spline interpolation curves

The geometric iterative method (GIM) is widely used in data interpolation/fitting, but its slow convergence affects the computational efficiency. Recently, much work was done to guarantee the acceleration of GIM in the literature. In this work, we aim to further accelerate the rate of convergence by introducing a preconditioning technique. After constructing the preconditioner, we preprocess the progressive iterative approximation (PIA) and its variants, called the preconditioned GIMs. We show that the proposed preconditioned GIMs converge and the extra computation cost brought by the preconditioning technique is negligible. Several numerical experiments are given to demonstrate that our preconditioner can accelerate the convergence rate of PIA and its variants