This paper presents a new algorithm that is capable of extracting circles from complicated and heavily corrupted images. The algorithm uses a least-squares fitting algorithm for arc segments. The arcs are segmented by using the short straight lines which are extracted by a fast line extraction algorithm. The arc segments are used to yield accurate circle parameters. Tests performed on synthetic...

We prove a general Borg-type result for reflectionless unitary CMV operators U associated with orthogonal polynomials on the unit circle. The spectrum of U is assumed to be a connected arc on the unit circle. This extends a recent result of Simon in connection with a periodic CMV operator with spectrum the whole unit circle. In the course of deriving the Borg-type result we also use exponential...

A Hamilton circle in an infinite graph is a homeomorphic copy of the unit circle S1 that contains all vertices and all ends precisely once. We prove that every connected, locally connected, locally finite, claw-free graph has such a Hamilton circle, extending a result of Oberly and Sumner to infinite graphs. Furthermore, we show that such graphs are Hamilton-connected if and only if they are 3-...

We prove a general Borg-type result for reflectionless unitary CMV operators U associated with orthogonal polynomials on the unit circle. The spectrum of U is assumed to be a connected arc on the unit circle. This extends a recent result of Simon in connection with a periodic CMV operator with spectrum the whole unit circle. In the course of deriving the Borg-type result we also use exponential...

In the present paper, we introduced an arc recognition technique suitable for irregular isothetic object. It is based on the digital inter-pixel (DIP) circle model, a pixel-based representation of the Kovalevsky’s circle. The adaptation to irregular image structurations allows us to apply DIP models for circle recognition in noisy digital contours. More precisely, the noise detector from Keraut...

A graph is balanced if its clique-vertex incidence matrix is balanced, i.e., it does not contain a square submatrix of odd order with exactly two ones per row and per column. Interval graphs, obtained as intersection graphs of intervals of a line, are well-known examples of balanced graphs. A circular-arc graph is the intersection graph of a family of arcs on a circle. Circular-arc graphs gener...

An algorithm to generate the locus of a circle using the intersection points of straight lines is proposed. The pixels on the circle are plotted independent of one another and the operations involved in finding the locus of the circle from the intersection of straight lines are parallelizable. Integer only arithmetic and algorithmic optimizations are used for speedup. The proposed algorithm mak...

in the complex z = e -2H plane, where H is the reduced external magnetic field. At infinite temperature (T = m) the spins are noninteracting and the partition function reduces to (z 1í2 + z-ìë)~, where N is the total number of spins. The zeros are therefore N-fold degenerate at 8 = a. As the temperature is lowered, the zeros spread into an arc segment of the unit circle centered about 8 = 7r an...

Orthogonal polynomials on the unit circle are completely determined by their reflection coefficients through the Szegő recurrences. We assume that the reflection coefficients converge to some complex number a with 0 < |a| < 1. The polynomials then live essentially on the arc { e : α ≤ θ ≤ 2π−α } where cos α 2 def = √ 1− |a|2 with α ∈ (0, π). We analyze the orthogonal polynomials by comparing th...