Modeling 2D image data by robust M-estimation

Abstract

The conventional least squared distance method of fitting a model t o a set of data points gives unreliable results when the amount of noise in the input is significani compared with the amount of data correlated io the model itself. The iheory of robust staiistics formally addresses these problems and is used in this work io develop a method of separation of ihe data of interest from noise. It is based on iteraiively reweighied least squares algorithm where Hampel redescending function is applied f o r weighting data. The method has been eficienily tested in modeling synthetic and real ZD image data with second order curves.

Automatic reconstruction of 3D human arm motion from a monocular image sequence

“…Taking into consideration that arm segments can appear in different sizes, orientations and shapes, we need a procedure that is robust to local deformations and outliers (data parts from other parts, or just noise), as well as stable to global transformations (rotation, translation and scaling). Robust M-estimation technique based on the Hampel redescending function turned out to be good in both aspects [4]. This section proceeds with the mathematical background of the robust parameter estimation technique.…”

“…It was chosen because of the property that ψ(x) = 0 for |x| > c, where c is a preselected cutoff value, also known as the finite rejection point, which allows rejection of outliers. Experimental results on synthetical data [4] demonstrated a high convergence speed of the robust M-estimator, and therefore the reweighting in the experiments with real data was limited to few iterations. The final solution depends on the initial fit (L2 estimate) and the scale estimate s.…”