Abstract
Abstract. The paper presents a robust version of a recent anisotropic orthogonal Procrustes algorithm that has been proposed to solve the socalled camera exterior orientation problem in computer vision and photogrammetry. In order to identify outliers, that are common in visual data, we propose an algorithm based on Least Median of Squares to detect a minimal outliers-free sample, and a Forward Search procedure, used to augment the inliers set one sample at a time. Experiments with synthetic data demonstrate that, when the percentage of outliers is greater than 30% or the data size is small, the proposed method is more accurate in detecting outliers than the customary detection based on median absolute deviation.
Highlights
In a recent paper (Garro et al, 2012) a new method for the exterior orientation problem solution of a calibrated camera has been proposed
We present a robust version of the above mentioned algorithm, that can tolerate a minority of arbitrarily large outliers
We propose to refine the clean subset produced by the Least Median of Squares (LMedS) procedure with Forward Search (FS); the resulting robust procrustean exterior orientation procedure is summarized in Algorithm 2
Summary
In a recent paper (Garro et al, 2012) a new method for the exterior orientation problem solution of a calibrated camera has been proposed. Orthogonal Procrustes Analysis (OPA) is a very useful tool to perform the direct least squares solution of similarity transformation problems in any dimensional space At first, it was used for the multidimensional rotation and scaling of different matrix configuration pairs (Schonemann, 1966, Schonemann and Carroll, 1970). The iterative algorithm proposed by (Garro et al, 2012) applies instead anisotropic scaling for each measurement and is based on the same kind of relaxation techniques This algorithm proved to reach a good trade-off between speed and accuracy, it has the drawback of a Procrustes method, i.e. it is a least squares estimation technique failing to cope with outliers. Up to 20% outliers, MAD and FS produce comparable results, but when the percentage of outliers increases, FS becomes more reliable for outliers detection
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