An Approach to the Feature-Based Comparisons for the Rational Curves

In image processing, the curve comparisons can be achieved by extracting the curve information from the bitmapped images. The revealed curves are represented in the forms of the sets of pixel information. Thus, the determination of curve matching is to compare pixel by pixel, which is time consuming. On the contrary, for vector graphics images, there have been no methods written in the literatures referred about directly comparing the parametric curves either in the rational or non-rational (polynomial) forms. In this paper, the relationships between two curves can be classified into 4 main categories: curve congruence, curve proportion, curve similarity and curve difference. The comparison algorithms for two given parametric curves either non-rational or rational curves are then established. These algorithms can be simply determined by verifying some important geometric features, e.g., the blending functions, the locations of their control points and their weights. In this connection, since a rational curve can be transformed into a non-rational one, the curve comparison algorithms for polynomial curves can also be applied for the cases of the rational curves.