Abstract: A boundary curve or line pattern is recognized by using iterative parametrization and transformation to develop a Fourier descriptor set that is mutually independent and of minimal size and then applying a classification procedure to the Fourier descriptor set to obtain a recognition result. The Fourier descriptor set so obtained has properties that enable effective recognition and compression.

Abstract: A piecewise parametric polynomial curve-fitting method using an iterative transformation-reparametrization technique is used to compress information describing lines, such as those formed by handwritten lines, for storage in a compressed form in a computer. The curve-fitting method is applied iteratively with adaptive segmenting of curve segments to optimize piecewise approximations of complex curves. Each piecewise segment is iteratively lengthened, parameterized with an updatable parametrization table, and approximated using a cosine-type transform. To minimize approximation errors, both the accuracy and the trend of the approximation errors are monitored. In order to match end-point positions of the piecewise approximation segments, the cosine coefficients representing each piecewise segment are modified in view of the edge conditions so the segments properly abut one another upon reconstruction.