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On the complete convergence of randomly weighted sums of random fields

Gdula A. M., Krajka A.

Demonstratio Mathematica

2014

Vol. 47, nr 1

232--252

Let (…) be a d-dimensional random field indexed by some subset V of lattice Nd, which are stochastically dominated by a random variable X. Let (…) be a 2d-dimensional random field independent of (…) and such that (…) for some constant M. In this paper, we give conditions under which the following series (…), is convergent for some real t, some fixed p > 0 and all ε > 0. Here |n| is used for (…). The randomly indexed sums of field (…) are considered too.

Detecting and matching interest points in relative scale

Islam M. S., Sluzek A., Zhu L.

Machine Graphics and Vision

2005

Vol. 14, No. 3

259-283

The same object seen in two different images can be geometrically and photometrically transformed. In this paper, a method of interest point detection and matching is described for the same object in different images. One of the main considerations is the change in the object scale. In this method, a reference scale is assigned to a particular instance of the object, and the change of scale is represented by a relative scale. Then, Harris' relative scale method is used for interest point detection. This method is robust to linear geometric transformations. A heuristic method for threshold selection is also described for robustness to intensity changes in a cluttered environment with partial occlusions. The repeatability rate of interest points for this method is higher then that for the existing methods. For the matching process, a local invariant descriptor is computed in the relative scale for each of the detected interest points. A hashing technique is applied to find the matches efficiently. The matching method enables finding a good number of correct matches for different types of transformations in a cluttered environment and one with partial occlusions. The proposed single scale detection and matching method could be effectively used for many practical applications, where the relative scale of the object can be predicted in advance.

Fast Index Filtering in Vector Approximation File

Skarbek W., Sikora T., Galinski G.

Fundamenta Informaticae

2004

Vol. 61, nr 3,4

335--349

Several fast filtering attributes are analysed for vector interval (cell) pruning while querying the vector approximation file. Beside distance range, sum and median features their deviation forms are introduced. Range and K-NN queries are considered and appropriate acceptance intervals are designed. The impact of feature space dimensionality on index design is discussed, too.