Invariant matching and identification of curves using B-splines curve representation

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.