Arkadiusz Orłowski

Finding Line Segments in the Ulam Square with the Hough Transform

The regularities present in the Ulam spiral provided an incentive for interesting observations in the number theory. Therefore, we have made the Ulam square an object of analysis from the image processing perspective. A version of the Hough transform designed specially for detecting sequences of pixels forming segments of straight lines with the slope defined by an irreducible fraction was used to find line segments in the Ulam spiral. Angles which described the slopes of the segments had tangents p / q expressed by integers p from 0 to 10 and q from \(-10\) to 10 (0 excluded). Due to storage limitations the squares with the side of length up to 5001 points which correspond to the largest prime \(25\,009\,991\) were analyzed at present. In such a square the longest segment has 16 primes and its tangent is 3 (3 up and 1 to the right). Segments of length 14 and 15 were absent. The number of shorter segments varied strongly, from one for a 13-point segment to tens of thousands for shorter ones.

A Decentralized System for Load Balancing of Containerized Microservices in the Cloud

Microservice architecture is a cloud application design pattern which shifts the complexity away from the traditional monolithic application into the infrastructure. Each microservice is a small containerized application that has a single responsibility in terms of functional requirement, and that can be deployed, scaled and tested independently using automated orchestration systems. We propose a simple swarm-like decentralized load balancing system for microservices running inside OpenVZ containers. It can potentially offer performance improvements with respect to the existing centralized container orchestration systems.

Defect Detection in Furniture Elements with the Hough Transform Applied to 3D Data

Defects in furniture elements were detected using data from a commercially available structured light 3D scanner. Out-of-plane deviations down to 0.15 mm were analyzed successfully. The hierarchical, iterated version of the Hough transform was used. The calculation of position of the plane could be separated from that of its direction due to the assumption of nearly horizontal location of the plane, which is natural when the tested elements lie on a horizontal surface.

A Study on Directionality in the Ulam Square with the Use of the Hough Transform

A version of the Hough transform in which the direction of the line is represented by a pair of co-prime numbers has been used to investigate the directional properties of the Ulam spiral. The method reveals the detailed information on the intensities of the lines which can be found in the square and on the numbers of primes contained in these lines. This makes it possible to make quantitative assessments related to the lines. The analysis, among others, confirms the known observation that one of the diagonal directions is more populated with lines than the other one. The results are compared to those made for a square containing randomly located points with a density close to that for the Ulam square of a corresponding size. Besides its randomness, such square also has a directional structure resulting from the square shape of the pixel lattice. This structure does not depend significantly on the size of the square. The analysis reveals that the directional structure of the Ulam square is both quantitatively and qualitatively different from that of a random square. Larger density of lines in the Ulam square along one of the diagonal directions in comparison to the other one is confirmed.

Detection of Surface Defects of Type 'orange skin' in Furniture Elements with Conventional Image Processing Methods

An attempt was made to differentiate between surfaces of furniture elements having the orange skin defect and those free from it. As the detectors, the directional derivative of the image intensity along the dominating light direction and the modulus of the image intensity gradient were used. The detectors were tested on series of images with the small and large light incident angles. In case of both detectors, there existed sufficiently wide ranges of thresholds for which both sensitivity and specificity were

Pattern Recognition in the Japanese Candlesticks

100\,\%

A four-level “Ξ-system”: Exact solvability and effective evolution operators via multiple scales

for all the 19i¾źimages tested. The ranges of thresholds were wider for the light closer to tangential, and for the detector using the gradient modulus, than for the other cases. The optimum scale of the detectors was found different for each light conditions.

Detecting Changes with the Robust Competitive Detector

The planar digital terrain model to be used in the analysis of forest measurements made with terrestrial LIDAR scanning is proposed for regions dominated by plains. The structure of the data suggests that the iterated version of the Hough transform is a suitable method. This makes it possible to reduce the time and memory requirements of the method. Randomization with the fraction of data used varying with distance to the scanner is proposed to address the biasing of the result towards the measurements which are made with higher density in the central part of the stand. Using this method instead of weighted voting reduces the time of analysis. Hierarchical approach leads to further reduction of time. The method can be extended to models formed from more than one plane.