Incremental matrix orthogonalization with an application to curve fitting

A new method for fitting implicit curves to scattered data is proposed. The method is based on orthogonal matrix projections and singular value decomposition. The incremental aspect of the algorithm deals with each order of data individually in an incrementing manner, whereby a matrix approximation procedure is applied at each level. This determines the fit quality at each step, and hence provides co-linearity detection of each polynomial order. The best implicit polynomial fit of minimal order is provided, which essentially combines object identification and classification with object fitting.