Proceedings PaperRecognition of digital algebraic surfaces by large collections of inequalities
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It has been shown that digital algebraic surfaces can be characterized by inequality conditions that follow from Helly's Theorem on convex sets. As a result, we can recognize digital algebraic surfaces by examining the validity of large collections of inequalities. These inequality conditions can be regarded as a natural extension of the chord property which has been proved by Rosenfeld for digital straight lines. In this paper we show that these inequalities can also be used to measure an absolute value distance. They can be used for example, to measure how far a digital set is from being digitally straight. Since the collection of measurements that must be performed to measure the absolute value distance can be very large, it makes sense to study the mathematical structure of such a collection. We show that it has the structure of a polynomial ideal. For digital straight lines this ideal is generated by a single polynomial.