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Monte Carlo Methods
Published in Matthew N.O. Sadiku, Computational Electromagnetics with MATLAB®, 2018
For any absorbing Markov chain, I–Q has an inverse. This is usually referred to as the fundamental matrix N=(I−Q)−1 where Nij is the average number of times the random-walking particle starting from node i passes through node j before being absorbed. The absorption probability matrix B is B=NRwhere Bij is the probability that a random-walking particle originating from a non-absorbing node i will end up at the absorbing node j. B is an nf × np matrix and is stochastic like the transition probability matrix, that is, ∑j=1npBij=1,i=1,2,…,nf
Derivative-based Optimization: Lie Algebra Method
Published in Kenichi Kanatani, 3D Rotations, 2020
The fundamental matrix is determined by the intrinsic parameters of the two cameras and their relative pose. If the intrinsic parameters are known, it reduces to a matrix with a smaller degree of freedom, i.e., more constraints, called the essential matrix. The Lie algebra method can also be applied to its computation [43].
Objective evaluation of fabric pilling based on multi-view stereo vision
Published in The Journal of The Textile Institute, 2021
Lulu Liu, Na Deng, Binjie Xin, Yiliang Wang, Wenzhen Wang, Yan He, Shuaigang Lu
This process needs to use the data structure of kd-tree to calculate the nearest neighbor matching. If the ratio of d1 and d2 is less than a certain threshold value, it can be judged that the matching is successful. However, mismatches still occur, so geometry constraint is used to detect whether the primary matching pair is reliable. Using fundamental matrix F to calculate the epipolar geometry, F matrix can relate pixel coordinates between two images and contain the intrinsic camera parameters. Each matching pair of pixel coordinates must meet the following requirements: