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Hough transform for lines with slope defined by a pair of co-primes

Chmielewski Leszek J., Orlowski Arkadiusz

Machine Graphics and Vision

2013

Vol. 22, No. 1/4

17--25

Data structure and Hough-type algorithm suitable for ﬁnding the lines having the slope exactly speciﬁed by the ratio of small co-prime numbers is proposed. It is suitable for analysing images like the Ulam square in which the points representing prime numbers form such structures as contiguous lines and other regular sequences of points. This analysis is diﬀerent from that in the case of images in which the real-world objects are represented approximately. Until now in the Ulam square the horizontal and vertical sequences, and those inclined by 45 deg were typically analysed. With the proposed method the sequences having slopes represented by such tangents like 1/3, 2/3, 3/4 etc. can be looked for.

Szego's First Limit Theorem in Terms of a Realization of a Continuous-Time Time-Varying System

Iglesias P. A., Zang G.

International Journal of Applied Mathematics and Computer Science

2001

Vol. 11, no 6

1261-1276

It is shown that the limit in an abstract version of Szego's limit theorem can be expressed in terms of the antistable dynamics of the system. When the system dynamics are regular, it is shown that the limit equals the difference between the antistable Lyapunov exponents of the system and those of its inverse. In the general case, the elements of the dichotomy spectrum give lower and upper bounds.