Vahid Mohammadi

Hamid Fsian, Vahid Mohammadi, Pierre Gouton et al.

Stereo Matching is one of the classical problems in computer vision for the extraction of 3D information but still controversial for accuracy and processing costs. The use of matching techniques and cost functions is crucial in the development of the disparity map. This paper presents a comparative study of six different stereo matching algorithms including Block Matching (BM), Block Matching with Dynamic Programming (BMDP), Belief Propagation (BP), Gradient Feature Matching (GF), Histogram of Oriented Gradient (HOG), and the proposed method. Also three cost functions namely Mean Squared Error (MSE), Sum of Absolute Differences (SAD), Normalized Cross-Correlation (NCC) were used and compared. The stereo images used in this study were from the Middlebury Stereo Datasets provided with perfect and imperfect calibrations. Results show that the selection of matching function is quite important and also depends on the images properties. Results showed that the BP algorithm in most cases provided better results getting accuracies over 95%.

Vahid Mohammadi, Mehdi Dehghan, Amirreza Khodadadian et al.

In this work, we apply two meshless methods for the numerical solution of the time-dependent transport equation defined on the sphere in spherical coordinates. The first technique, which was introduced by Mirzaei (BIT Numerical Mathematics, 54 (4) 1041-1063, 2017) in Cartesian coordinates is a generalized moving least squares approximation, and the second one, which is developed here, is moving kriging least squares interpolation on the sphere. These methods do not depend on the background mesh or triangulation, and they can be implemented on the transport equation in spherical coordinates easily using different distribution points. Furthermore, the time variable is approximated by a second-order backward differential formula. The obtained fully discrete scheme is solved via the biconjugate gradient stabilized algorithm with zero-fill incomplete lower-upper (ILU) preconditioner at each time step. Three well-known test problems namely solid body rotation, vortex roll-up, and deformational flow are solved to demonstrate our developments.