Transforming Least Squares to Weighted Least Squares for Accurate Range Image Registration

Abstract

The traditional ICP algorithm is a de facto standard approach for range image registration. While it assumes that one data set is a subset of another, this assumption is often violated in practice. As a result, a number of algorithms have been developed to first eliminate false matches due to occlusion, appearance and disappearance of points and then estimate the camera motion parameters in the least squares sense. Instead of eliminating outliers in the process of image registration, we in this paper use the generalised entropy to estimate the probability of correspondences established using the traditional closest point criterion, leading camera motion parameters to be estimated in the weighted least squares sense. For more accurate registration results, we also learn from the probability of correspondences estimated in the past. Since one point in one data set can only correspond to a single point in another, the two way constraint is also imposed. Finally the camera motion parameters are optimized using the powerful mean field annealing scheme. A comparative study based on real images has shown that the proposed algorithm produces promising automatic range image registration results.

Replicator Dynamics in the Iterative Process for Accurate Range Image Matching

“…For a comparative study of performance, we duplicated the experimental results of the GA in Silva (2005) and the feature extraction and matching of local surface patches (LSP) (Chen and Bhanu 2007) and implemented the extended version, SoftICP (Liu 2005;Liu 2006), of the SoftAssign algorithm (Gold et al 1998) and the GenICP algorithm described in Liu et al (2006b). To deal with main concerns of performance of the proposed EvolICP algorithm, the comparative study is conducted from the following eight aspects: probability evolution, ICP variants for relatively small motions, ICP variants for relatively large motions, image orders, image resolutions, ICP variants and GA, EvolICP and LSP, and overall analysis.…”

“…They all have an advantage of easy implementation; • The classification based ICP variants (Turk and Levoy 1994;Zhang 1992;Pulli 1999;Liu and Wei 2004;Rusinkiewicz and Levoy 2001) are usually not robust, since it is often difficult for them to develop universally effective classification rules. In contrast, the probability based ICP variants (Liu 2005;Liu 2006;Liu et al 2006b), as is the case for both the SoftICP and GenICP algorithms, often succeed in explicitly modelling outliers, applying the entropy maximization principle (Gold et al 1998) for the estimation of the probabilities of possible correspondences being real, and globally optimizing them using the powerful deterministic annealing scheme (Puzicha et al 1997) and thus, are generally more robust; and • The dynamics these two algorithms describe in the iterative process for automatic overlapping range image matching is closely related to that the proposed EvolICP algorithm does. The actual relations are outlined in the next section.…”

“…For a comparative study of performance, we duplicated the experimental results of the genetic algorithm (GA) in Silva (2005) and the feature extraction and matching of local surface patches (LSP) (Chen and Bhanu 2007) and implemented the extended version, SoftICP (Liu 2005;Liu 2006), of the SoftAssign algorithm (Gold et al 1998) and the GenICP algorithm proposed in Liu et al (2006b). These four algorithms were selected respectively from the three different classes of methods discussed above in Sect.…”

“…While the SoftAssign algorithm applies the traditional Shannon entropy to estimate the probabilities of possible correspondences being real, the GenICP algorithm (Liu et al 2006b) employs the generalised Tsallis entropy:…”