Browsing by Author "Lavine, David"
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Item An Enumeration Problem In Digital Geometry.(1986) Berenstein, Carlos A.; Lavine, David; ISRWe prove that the number L(N) of digital line segments of length N(corresponding to the line y=ax+b <= a < 1, 0 < b < 1) has the asymptotic expansion: L(N)=N^3/PI^2+0(N^2 log N) This expression has applications in image registration problems and originated in a question posed by NASA.Item On the Number of Digital Straight Line Segments.(1987) Berenstein, Carlos A.; Lavine, David; ISRLet L_N be the number of digital line segments of length N that correspond to lines of the form y = ax + BETA, 0 <= a, BETA <=1. In a previous paper [4], a closed form expression for the quantity L_N was obtained. We prove an asymptotic estimate for L_N that might prove useful for many applications. Namely,