Abstract
The main goal of the adaptive local strategy consists in reducing the complexity of computational problems. We propose a new approach to curve approximation and smoothing based on 4-point transformations or Discrete Projective Transform (DPT). In the framework of DPT, the variable point is related to three data points (accompanying points). The variable y-ordinate is expressed via the convolution of accompanying y-ordinates and weight functions that are defined as cross-ratio functions of four x-coordinates. DPT has some attractive properties (natural norming, scale invariance, threefold symmetry, and “4-point” orthogonality), which are useful in designing new algorithms. Diverse methods and algorithms based on DPT have been developed.
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Dikoussar, N.D. Four-point transformation methods in approximation and the smoothing problems. Phys. Part. Nuclei Lett. 5, 317–323 (2008). https://doi.org/10.1134/S1547477108030382
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DOI: https://doi.org/10.1134/S1547477108030382