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What is the difference between BSpline transformation based image registration and Polynomial transformation based image registration?

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PSPLINE is an expansion. It takes a variable as input and produces more than one variable as output. The difference between PSPLINE and BSPLINE is that PSPLINE produces a piecewise polynomial, whereas BSPLINE produces a B-spline.

The is a misuse of the word polynomial for transformation. B-splines are localized piecewise polynomial functions with conveniently adjustable (non)-continuous derivatives

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