A REPRESENTATION OF DIGITAL HYPERBOLAS Y=1 X ALPHA+BETA/

It is proved that digital hyperbola segments and their least squares h yperbola fits are in one-to-one correspondence. This enables a constan t space representation of a digital hyperbola segment inscribed into t he integer grid. Such a representation is (x(1) n, a, b), where x(1) i s the x-coordinate of the left endpoint of the digital hyperbola segme nt, n is the number of its integer points, while a and b are the coeff icients of the least squares hyperbola fit Y=1/x a+b of the given digi tal hyperbola segment. An O(n max {log n,log x(1)}) algorithm for obta ining a digital hyperbola segment from its least squares hyperbola fit is described.