Browsing by Subject "Discrete points"

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Open Access
Calculation of the scalar diffraction field from curved surfaces by decomposing the three-dimensional field into a sum of Gaussian beams
(Optical Society of America, 2013) Şahin, E.; Onural, L.
We present a local Gaussian beam decomposition method for calculating the scalar diffraction field due to a twodimensional field specified on a curved surface. We write the three-dimensional field as a sum of Gaussian beams that propagate toward different directions and whose waist positions are taken at discrete points on the curved surface. The discrete positions of the beam waists are obtained by sampling the curved surface such that transversal components of the positions form a regular grid. The modulated Gaussian window functions corresponding to Gaussian beams are placed on the transversal planes that pass through the discrete beam-waist position. The coefficients of the Gaussian beams are found by solving the linear system of equations where the columns of the system matrix represent the field patterns that the Gaussian beams produce on the given curved surface. As a result of using local beams in the expansion, we end up with sparse system matrices. The sparsity of the system matrices provides important advantages in terms of computational complexity and memory allocation while solving the system of linear equations.
Open Access
Employing active contours and artificial neural networks in representing ultrasonic range data
(IEEE, 2008-08) Altun, Kerem; Barshan, Billur
Active snake contours and Kohonen's self-organizing feature maps (SOM) are considered for efficient representation and evaluation of the maps of an environment obtained with different ultrasonic arc map (UAM) processing techniques. The mapping results are compared with a reference map acquired with a very accurate laser system. Both approaches are convenient ways of representing and comparing the map points obtained with different techniques among themselves, as well as with an absolute reference. Snake curve fitting results in more accurate maps than SOM since it is more robust to outliers. The two methods are sufficiently general that they can be applied to discrete point maps acquired with other mapping techniques and other sensing modalities as well. copyright by EURASIP.