To perform geometric transforms on discrete images such as a rotation or zooming we need to first fit the discrete data to a continuous function. This can be done using splines. B-splines can be used to interpolate and form the continuous image from the discrete samples.
B-splines form a simple set of scaling functions satisfying the dilation equation with binomial filter coefficients. However B-Splines other than the zeroth order B-spline (the Haar function) are not orthogonal to its own shifts. Hence to form a perfect reconstruction(PR) filter bank system, biorthogonal scaling functions are used. Also semiorthogonal filter banks can be used to form a PR filter bank system.
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