We consider the digital plane of integer points equipped with the Khalimsky topology. We suggest a digitization of straight lines such that the digitized image is homeomorphic to the Khalimsky line and a digitized line segment is a Khalimsky arc. It is demonstrated that a Khalimsky arc is the digitization of a straight line segment if and only if it satisfies a generalized version of the chord ...

We investigate homeomorphisms of a compact interval, applied randomly. We consider this system as a skew product with the two-sided Bernoulli shift in the base. If on the open interval there is a metric in which almost all maps are contractions, then (with mild additional assumptions) there exists a global pullback attractor, which is a graph of a function from the base to the fiber. It is also...

An orientation-preserving recurrent homeomorphism of the twosphere which is not the identity is shown to admit exactly two fixed points. A recurrent homeomorphism of a compact surface with negative Euler characteristic is periodic.

In this survey, we consider several questions pertaining to homeomorphisms, including criteria for their existence in certain circumstances, and obstructions to their existence.

♦ Sampling density along the contours Interpolation of the irregular set of data points to a regular grid Valid theorems for sampling density have only recently been developed. Interpolation methods have to deal with the 'flat triangle' problem, as well as preservation of the accuracy of slope. Meaningful slopes are increasingly important in applications such as soil erosion and run-off modelli...

We prove that solutions of stochastic differential equations driven by fractional Brownian motion for H > 1/2 define flows of homeomorphisms on R. AMS Subject Classification: 60H05, 60H07

In this paper we characterize all possible sets of periods of homeomorphisms defined on some classes of finite connected compact graphs.

We propose a probabilistic algorithm able to detect the curves that are unexpectedy smooth in a set of digital curves. The only parameter is a false alarme rate, influencing the detection only by its logarithm. We experiment the good continuation criterion on image level lines. One of the conclusion is that, accordingly to Gestalt Theory, one can detect egdes in a way that is widely independent...