TY - JOUR
T1 - Ellipse fitting via low-rank generalized multidimensional scaling matrix recovery
AU - Liang, Junli
AU - Yu, Guoyang
AU - Li, Pengliang
AU - Sui, Liansheng
AU - Wu, Yuntao
AU - Kong, Weiren
AU - Liu, Ding
AU - So, H. C.
PY - 2018/1
Y1 - 2018/1
N2 - 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.
AB - 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.
KW - Alternating direction method of multiplier (ADMM)
KW - Ellipse fitting algorithm
KW - Generalized multidimensional scaling matrix
KW - Givens transform
KW - Low rank
KW - Nuclear norm minimization
KW - Unknown auxiliary parameter (UAP)
UR - http://www.scopus.com/inward/record.url?scp=84988322695&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84988322695&origin=recordpage
U2 - 10.1007/s11045-016-0452-x
DO - 10.1007/s11045-016-0452-x
M3 - RGC 21 - Publication in refereed journal
SN - 0923-6082
VL - 29
SP - 49
EP - 75
JO - Multidimensional Systems and Signal Processing
JF - Multidimensional Systems and Signal Processing
IS - 1
ER -