Recognition and characterization of digitized curves

Abstract We consider the graphs of functions representable in the form h ( x ) = Σ j =1 n a j f j ( x ) where the f j constitute a linearly independent set of functions over R . These graphs are digitized by the set of lattice points ( i , ⌊ h ( i )⌋). An algorithm is presented to determine if a given set of lattice points is part of such a digitization. We also study the digitization of polynomials. An important tool used is the set of differences of the y -coordinates (digital derivatives). For example, if h ( x ) is a polynomial of degree n , then its n -th digital derivative is cyclic and its ( n + 1)st digital derivative has a bound which depends only on n .

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