Name
Abstract | ||
|---|---|---|
This paper develops a novel ellipse fitting algorithm by recovering a low-rank generalized multidimensional scaling (GMDS) matrix. The main contributions of this paper are: i) Based on the derived Givens transform-like ellipse equation, we construct a GMDS matrix characterized by three unknown auxiliary parameters (UAPs), which are functions of several ellipse parameters; ii) Since the GMDS matrix will have low rank when the UAPs are correctly determined, its recovery and the estimation of UAPs are formulated as a rank minimization problem. We then apply the alternating direction method of multipliers as the solver; iii) By utilizing the fact that the noise subspace of the GMDS matrix is orthogonal to the corresponding manifold, we determine the remaining ellipse parameters by solving a specially designed least squares problem. Simulation and experimental results are presented to demonstrate the effectiveness of the proposed algorithm. |
Year | DOI | Venue |
|---|---|---|
2018 | https://doi.org/10.1007/s11045-016-0452-x | Multidim. Syst. Sign. Process. |
Keywords | Field | DocType |
Generalized multidimensional scaling matrix,Givens transform,Low rank,Nuclear norm minimization,Ellipse fitting algorithm,Alternating direction method of multiplier (ADMM),Unknown auxiliary parameter (UAP) | Least squares,Fitting algorithm,Mathematical optimization,Multidimensional scaling,Subspace topology,Matrix (mathematics),Solver,Ellipse,Mathematics,Manifold | Journal |
Volume | Issue | ISSN |
29 | 1 | 0923-6082 |
Citations | PageRank | References |
0 | 0.34 | 16 |
Authors | ||
8 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Junli Liang | 1 | 370 | 25.91 |
| Guoyang Yu | 2 | 26 | 2.11 |
| Pengliang Li | 3 | 0 | 0.34 |
| Liansheng Sui | 4 | 1 | 1.05 |
| Yuntao Wu | 5 | 71 | 12.57 |
| Weiren Kong | 6 | 0 | 0.34 |
| Ding Liu | 7 | 611 | 32.97 |
| H. C. So | 8 | 1787 | 161.44 |