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1

Distance between two Keplerian orbits

Mohamed Ayman Homda, Dwidar Hany Ramdan, Adham Inal, Bakry Abd-Elazaz, El-Raffie Ahmed

Artificial Satellites : Journal of Planetary Geodesy

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2021

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Vol. 56, No. 3

57--77

EN

In this paper, constrained minimization for the point of closest approach of two conic sections is developed. For this development, we considered the nine cases of possible conics, namely, (elliptic-elliptic), (elliptic-parabolic), (elliptic–hyperbolic), (paraboli-elliptic), (paraboli-parabolic), (parabolic–hyperbolic), (hyperbolic-elliptic), (hyperbolic-parabolic), and (hyperbolic–hyperbolic). The developments are considered from two points of view, namely, analytical and computational. For the analytical developments, the literal expression of the minimum distance equation (S) and the constraint equation (G), including the first and second derivatives for each case, are established. For the computational developments, we construct an efficient algorithm for calculating the minimum distance by using the Lagrange multiplier method under the constraint on time. Finally, we compute the closest distance S between two conics for some orbits. The accuracy of the solutions was checked under the conditions that L|solution ≤ε1G||solution ≤ε2, where ε1,2 < 10 -10. For the cases of (paraboli-parabolic), (paraboli-hyperbolic), and (hyperbolic-hyperbolic), we studied thousands of comets, but the condition of the closest approach was not met.

2

Extraction of centre line from curvilinear objects

Rokicki J., Matiukas V., Ušinskas A., Adaškevičius R.

Opto-Electronics Review

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2011

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Vol. 19, No. 1

22-29

EN

This tutorial paper surveys three methods designed to detect the centre line in curvilinear structures. These are the iterative thinning, Steger's and derivatives' methods. We aim to illustrate the effectivness of the chosen methods for processing laser-trace images and magnetic resonance slices of human head. The essence of each three methods is presented and important parameters are discussed. Experiments have been carried out and results are discussed in the light of the quality of the centre line produced and work time of all three methods.

3

Efektywność wykrywania punktów charakterystycznych w obrazach stereoskopowych za pomocą wartości własnych hesjanu

Korohoda P.

Automatyka / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie

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2009

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T. 13, z. 3/2

1233-1243

PL

W artykule opisano eksperyment obliczeniowy, przeprowadzony dla stereoskopowej pary obrazów, mający na celu zbadanie różnic i podobieństw w efektywności wykrywania punktów charakterystycznych z wykorzystaniem trzech metod bazujących na wartościach własnych hesjanu. Stosując gaussowską czteropoziomową piramidę, wyznaczono punkty charakterystyczne wspólne dla wszystkich poziomów, porównano wizualnie i statystycznie ich lokalizację, a następnie wyznaczono mapy dysparycji. W badaniach wykorzystano korelacyjną technikę wyznaczania dysparycji. Wykazano różnice między teoretycznie podobnymi metodami wykorzystującymi iloraz wartości własnych oraz potwierdzono korzystne cechy metody bazującej na różnicy wartości własnych.

EN

In the paper a computational experiment performed for the stereoscopic image pair has been described. The aim of the designed experiment was to investigate the similarities and differences between three methods used to localize the keypoints, basing on the Hessian matrix eigenvalues. The keypoints were obtained for the four-level Gaussian pyramid, and then the ones common for all levels were selected. Afterwards their locations were visually and statistically compared and then the disparity maps were computed. The disparity in that task was calculated with use of the correlation coefficient. The results indicate noticeable differences between theoretically similar techniques utilizing the eigenvalues ratio. The advantegous properties of the third method, based on the difference between eigenvalues, have been confirmed.