Robust Generalized Point Cloud Registration Using Hybrid Mixture Model

Joint Rigid Registration of Multiple Generalized Point Sets With Anisotropic Positional Uncertainties in Image-Guided Surgery

“…After that b q j has been calculated, then [dR q j , dt q j ] can be easily restored using the Rodrigues formula in (9) again. With [dR q j , dt q j ], the updated rotation matrice R q j ∈ SO(3) and the updated translation vector t q j ∈ R 3 in the current q step are computed as that in [2]: R q j = dR q j R q−1 j , t q j = dR q j t q−1 j + dt q j , where R q−1 j ∈ SO(3) and t q j ∈ R 3×1 are the rotation matrix and translation vector associated with D j in the (q −1)-th step.…”

“…P OINT set registration (PSR) is a fundamental and challenging problem in the fields of medical robotics, medical image analysis (MIA) and computer-assisted surgery (CAS) [1]- [15]. The aim of the rigid PSR problem is to accurately compute the rigid transformation matrix between point sets (PSs) [2]. In CAS, both fiducial-based registration and surface registration (or generally speaking PSR) can be used to align the pre-operative volumetric image space to the intra-operative patient space [16]- [18].…”

“…The possible clinical applications of the registration problem to be dealt with in this article are summarized as follows. (1) Pre-operative to intra-operative space alignment in CAS [2], [17], [23], [24]. (2) Statistical shape modelling (SSM).…”

“…(1) In order to significantly improve the registration accuracy and robustness, we utilize the orientation-al information (i.e., the normal vectors) that can be extracted from the raw PS with various methods [2], [28], [29]. (2) The second motivation is to consider the anisotropic characteristic in the position localization error, which is common in many CAS applications [29]- [32]. (3) The third motivation is to remove the bias towards one specific PS in the PSR algorithm.…”

Registration of vascular structures using a hybrid mixture model

“…To overcome this limitation, [25] proposed a probabilistic point set registration approach based on Student's t-distributions (TMM), which confers the property of localized robustness to the registration process, via estimation of a unique shape parameter for each mixture component in the TMM. Numerous recent studies have employed hybrid shape representations [26,19,18,20,17,23], in order to increase the discriminative capacity of probabilistic point set registration approaches. In [26] for example, spatial positions and their associated surface normal vectors were modeled with Student's t-distributions, and Von-Mises-Fisher (vmF) distributions, respectively.…”