Peak-error-constrained optimal shape representation

B-spline approximation is an efficient tool for shape representation. Recently, the B-spline technique has also been employed for shape coding with regard to MPEG-4. The traditional B-spline method is a least-squared-error (LS) approach which inevitably may bring about certain undesirable peak errors. To alleviate this error, we arrange to incorporate the minimax constraint into the design goal. The resulting method, called peak-error-constrained optimal shape-representation (PECOS), is a balance between the pure LS and pure minimax design. With the aid of the peak-error-constraint, it, is easy to reduce the magnitude of the peak error at a relatively much lower cost of the root-mean-squared (rms) error. For instance, an example of 32% decrease in peak error is easily obtained at the cost of only 3.6% increase of the rms error! Two algorithms are proposed to solve the PECOS problem. Both of them run very fast and basically converge in a very small number of iterations (typically below 5 iterations).