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In mathematics, splines are piecewise continuous functions, such as polynomials, defined in successive subintervals. They are often used to represent one- or multidimensional data set (e.g., a curve or a surface) in the applications requiring interpolation, smoothing or nonrigid transformation [1]. For example, a spline curve is a piecewise collection of curve segments defined in polynomials that are connected end to end to form a single continuous curve. A curve in L-dimensional space can be simply defined by the following form:
where function S takes variables from an interval [a,b] and maps them to an L-dimensional real number. If the interval [a,b] is divided into k ordered disjoint subintervals t i , ti+1 with
then in each subinterval [t i , ti+1] there is a polynomial defined as
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Zheng, B. (2014). Splines. In: Ikeuchi, K. (eds) Computer Vision. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-31439-6_419
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DOI: https://doi.org/10.1007/978-0-387-31439-6_419
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