Computing the Characteristics of a SubSegment of a Digital Straight Line in Logarithmic Time

We address the problem of computing the exact characteristics of any subsegment of a digital straight line with known characteristics. We present a new algorithm that solves this problem, whose correctness is proved. Its principle is to climb the Stern-Brocot tree of fraction in a bottom-up way. Its worst-time complexity is proportionnal to the difference of depth of the slope of the input line and the slope of the output segment. It is thus logarithmic in the coefficients of the input slope. We have tested the effectiveness of this algorithm by computing a multiscale representation of a digital shape, based only on a digital straight segment decomposition of its boundary.

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