scholarly journals Rotation Estimation: A Closed-Form Solution Using Spherical Moments

Sensors ◽  
2019 ◽  
Vol 19 (22) ◽  
pp. 4958
Author(s):  
Hicham Hadj-Abdelkader ◽  
Omar Tahri ◽  
Houssem-Eddine Benseddik
Keyword(s):  
Image Processing ◽  
Closed Form ◽  
Synthetic Data ◽  
Closed Form Solution ◽  
Form Solution ◽  
Unified Model ◽  
Experimental Results ◽  
Motion Information ◽  
Vision Sensors ◽  
Spherical Projection

Photometric moments are global descriptors of an image that can be used to recover motion information. This paper uses spherical photometric moments for a closed form estimation of 3D rotations from images. Since the used descriptors are global and not of the geometrical kind, they allow to avoid image processing as features extraction, matching, and tracking. The proposed scheme based on spherical projection can be used for the different vision sensors obeying the central unified model: conventional, fisheye, and catadioptric. Experimental results using both synthetic data and real images in different scenarios are provided to show the efficiency of the proposed method.

A unified model for synchronous and asynchronous FDL buffers allowing closed-form solution

2009 ◽  
Vol 66 (7) ◽  
pp. 343-355 ◽  
Author(s):  
W. Rogiest ◽  
J. Lambert ◽  
D. Fiems ◽  
B. Van Houdt ◽  
H. Bruneel ◽  
...  
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Unified Model

scholarly journals An Efficient Algorithm for Overcomplete Sparsifying Transform Learning with Signal Denoising

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Beiping Hou ◽  
Zhihui Zhu ◽  
Gang Li ◽  
Aihua Yu
Keyword(s):  
Closed Form ◽  
Efficient Algorithm ◽  
Synthetic Data ◽  
Closed Form Solution ◽  
Form Solution ◽  
Signal Denoising ◽  
Alternating Minimization ◽  
Computation Complexity ◽  
Learning Problem ◽  
Computation Efficiency

This paper deals with the problem of overcomplete transform learning. An alternating minimization based procedure is proposed for solving the formulated sparsifying transform learning problem. A closed-form solution is derived for the minimization involved in transform update stage. Compared with existing ones, our proposed algorithm significantly reduces the computation complexity. Experiments and simulations are carried out with synthetic data and real images to demonstrate the superiority of the proposed approach in terms of the averaged representation and denoising errors, the percentage of successful and meaningful recovery of the analysis dictionary, and, more significantly, the computation efficiency.

A Dishing Model for STI CMP Process

2005 ◽  
Vol 867 ◽  
Author(s):  
Shih-Hsiang Chang
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Closed Form ◽  
Contact Mechanics ◽  
Closed Form Solution ◽  
Form Solution ◽  
Experimental Results ◽  
Quantitative Prediction ◽  
Comparison With Experimental Data

AbstractIt is well known that oxide dishing occurring in STI CMP leads to considerable sidewall and edge-parasitic conduction. Thus, a closed-form solution for quantitative prediction of oxide dishing is needed. A contact-mechanics-based approach to describe the steady-state oxide dishing occurring in STI CMP process is presented. The theory is validated through comparison with experimental data in the literature. Once validated, the model is used to quantify the effect of pattern geometry on oxide dishing. It is shown that the predictions of the model agree reasonably well with the experimental results measured in overpolishing time.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

scholarly journals A Closed-Form Solution to Planar Feature-Based Registration of LiDAR Point Clouds

2021 ◽  
Vol 10 (7) ◽  
pp. 435
Author(s):  
Yongbo Wang ◽  
Nanshan Zheng ◽  
Zhengfu Bian
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Point Clouds ◽  
Form Solution ◽  
Spatial Transformation ◽  
Dual Quaternions ◽  
Feature Based ◽  
Planar Feature

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper. Based on the Plücker coordinate-based representation of linear features in three-dimensional space, a quad tuple-based representation of planar features is introduced, which makes it possible to directly determine the difference between any two planar features. Dual quaternions are employed to represent spatial transformation and operations between dual quaternions and the quad tuple-based representation of planar features are given, with which an error norm is constructed. Based on L2-norm-minimization, detailed derivations of the proposed solution are explained step by step. Two experiments were designed in which simulated data and real data were both used to verify the correctness and the feasibility of the proposed solution. With the simulated data, the calculated registration results were consistent with the pre-established parameters, which verifies the correctness of the presented solution. With the real data, the calculated registration results were consistent with the results calculated by iterative methods. Conclusions can be drawn from the two experiments: (1) The proposed solution does not require any initial estimates of the unknown parameters in advance, which assures the stability and robustness of the solution; (2) Using dual quaternions to represent spatial transformation greatly reduces the additional constraints in the estimation process.

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