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The article deals with the problem of matching and recognizing planar curves that are modeled by B-splines, independently of possible affine transformations to which the original curve has been subjected (for example, rotation, translation, scaling, orthographic, and semiperspective projections), and possible occlusion. It presents a fast algorithm for estimating the B-spline control points that is robust to nonuniform sampling, noise, and local deformations. Curve matching is achieved by using a similarity measure based on the B-spline knot points introduced by Cohen et al. (1991). This method, however, can neither handle the affine transformation between the curves nor the occlusion. Solutions to these two problems are presented through the use of a new class of weighted B-spline curve moments that are well defined for both open and closed curves. The method has been applied to classifying affine-transformed aircraft silhouettes, and appears to perform well.

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There have been many techniques for curve shape representation and analysis, ranging from Fourier descriptors, to moments, to implicit polynomials, to differential geometry features, to time series models, to B-splines, etc. The B-splines stand as one of the most efficient curve (surface) representations and possess very attractive properties such as spatial uniqueness, boundedness and continuity, local shape controllability, and invariance to affine transformations. These properties made them very attractive for curve representation, and consequently, they have been extensively used in computer-aided design and computer graphics. Very little work, however, has been devoted to them for recognition purposes. One possible reason might be due to the fact that the B-spline curve is not uniquely described by a single set of parameters (control points), which made the curve matching (recognition) process difficult when comparing the respective parameters of the curves to be matched. This paper is an attempt to find matching solutions despite this limitation, and as such, it deals the problem of using B-splines for shape recognition and identification from curves, with an emphasis on the following applications: affine invariant matching and classification of 2-D curves with applications in identification of aircraft types based on image silhouettes and writer-identification based on handwritten text.