A weighted least-squares approach for B-spline shape representation

B-spline functions have been widely used in shape analysis and modeling for years. Conventional methods for B-spline shape representation are based on the least-squares (LS) design principle. The key disadvantage of LS approaches is its incapability to deal with corners. To reduce this effect, in this article we propose a weighted LS technique that puts more emphasis on data points with larger errors. Through this mechanism, significant reduction of peak reconstruction errors can be achieved. The weight matrix is chosen by first detecting error peaks and then assigning more weights to only those few points with extraordinarily high approximation errors. The effectiveness of the proposed approach is demonstrated through experiments on real image examples with considerably different characteristics.