so-called X84 rule [17, 40]. More recently, statistical analysis has been introduced into the general registration problem (Eq. (6.1)) by proposing a new error function named Fractional Root Mean Squared Distance [67].

Additional Information The basic ICP algorithm computes the correspondences by taking into account only the proximity of points. However, corresponding points should be similar with respect to other aspects. Several studies have attempted to exploit additional information available from the acquisition process or from the analysis of the surface properties. In practice, the distance formulation is modified to integrate this information, such as local surface properties [36], intensity derived from the sensor [36, 98], or color [72]. In [45] the authors proposed to use color and texture information. In [85] the so-called ICP using invariant features (ICPIF) was introduced where several geometric features are employed, namely curvatures, moments invariants and Spherical Harmonics Invariants. In [14] additional information was integrated in the point descriptors using the spin-image with color.

Probabilistic Methods In order to improve the robustness of the registration, several probabilistic version of the standard ICP have been proposed [38, 73, 74]. In [73, 74] the idea of multiple weighted matches justified by a probabilistic version of the matching problem is introduced. A new matching model is proposed based on Gaussian weights (SoftAssign [74]) and Mutual Information [73], leading to a smaller number of local minima and thus presenting the most convincing improvements. In [38] the authors introduced a probabilistic approach based on the Expectation Maximization (EM) paradigm, namely EM-ICP. Hidden variables are used to model the point matching. Specifically, in the case of Gaussian noise, the proposed method corresponds to ICP with multiple matches weighted by normalized Gaussian weights. In practice, the variance of the Gaussian is interpreted as a scale parameter. At high scales EM-ICP gets many matches, while it behaves like standard ICP at lower scales.

6.3 Advanced Techniques

Although registration is one of the most studied problems in computer vision, several cases are still open and new issues have emerged in the recent years. In this section we focus on some scenarios where registration becomes more challenging: registration of more than two views, registration in cluttered scenes and registration of deformable objects. We also describe some emerging techniques based on machine learning to solve the registration problem. Figure 6.7 illustrates the proposed taxonomy for advanced registration techniques.