Generalized Non-rigid Point Set Registration with Hybrid Mixture Models Considering Anisotropic Positional Uncertainties

Min, Zhe; Liu, Li; Meng, Max Q.-H.

doi:10.1007/978-3-030-32254-0_61

Cited by 11 publications

(5 citation statements)

References 13 publications

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“…The expression of in (13), we can get J C P,mn ,dt in (11). The updated rigid transformation R q , t q are computed as follows, R q = dRR q−1 , t q = dRt q−1 + dt.…”

Section: Derivation Of ∂C Pmn ∂Dtmentioning

confidence: 99%

Generalized Point Set Registration with the Kent Distribution

Min

Zhu

Meng

2021

2021 IEEE International Conference on Robotics and Automation (ICRA)

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Point set registration (PSR) is an essential problem in communities of computer vision, medical robotics and biomedical engineering. This paper is motivated by considering the anisotropic characteristics of the error values in estimating both the positional and orientational vectors from the PSs to be registered. To do this, the multi-variate Gaussian and Kent distributions are utilized to model the positional and orientational uncertainties, respectively. Our contributions of this paper are three-folds: (i) the registration problem using the normal vectors is formulated as a maximum likelihood problem, where the anisotropic characteristics in both positional and normal vectors are considered; (ii) the matrix forms of the objective function and its associated gradients with respect to the desired parameters are provided, which can facilitate the computational process; (iii) two approaches of computing the normalizing constant in the Kent distribution are compared. We verify our proposed registration method on various pre-operative and intra-operative PSs (pelvis and femur bones) in computer-assisted surgery (CAS). Extensive experimental results demonstrate that our proposed method outperforms the state-of-the-art methods in terms of the registration accuracy and the robustness.

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“…The expression of in (13), we can get J C P,mn ,dt in (11). The updated rigid transformation R q , t q are computed as follows, R q = dRR q−1 , t q = dRt q−1 + dt.…”

Section: Derivation Of ∂C Pmn ∂Dtmentioning

confidence: 99%

Generalized Point Set Registration with the Kent Distribution

Min

Zhu

Meng

2021

2021 IEEE International Conference on Robotics and Automation (ICRA)

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“…The most common type of motion coherence is based on the proximity between points. The motion coherence of this type is typically introduced by imposing local rigidity on a shape surface [4], [5] and the penalty on a non-smooth deformation field [6], [7], [8], [9], [10], [11], [12]. Apart from the coherent moves based on proximity, nonrigid registration techniques impose the coherence based on prior knowledge to register shapes involving more specific deformations, such as human face [13], [14], human hand shape and pose [15], and human body pose [16], [17], [18], [19], [20].…”

Section: Introductionmentioning

confidence: 99%

Geodesic-Based Bayesian Coherent Point Drift

Hirose

2022

IEEE Trans. Pattern Anal. Mach. Intell.

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Coherent point drift is a well-known algorithm for non-rigid registration, i.e., a procedure for deforming a shape to match another shape. Despite its prevalence, the algorithm has a major drawback that remains unsolved: It unnaturally deforms the different parts of a shape, e.g., human legs, when they are neighboring each other. The inappropriate deformations originate from a proximity-based deformation constraint, called motion coherence. This study proposes a non-rigid registration method that addresses the drawback. The key to solving the problem is to redefine the motion coherence using a geodesic, i.e., the shortest route between points on a shape's surface. We also propose the accelerated variant of the registration method. In numerical studies, we demonstrate that the algorithms can circumvent the drawback of coherent point drift. We also show that the accelerated algorithm can be applied to shapes comprising several millions of points.

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“…Under the iterative closest point (ICP) framework, the NICP [24] and G-IMOP [25], [26] methods incorporate the estimated surface normal vectors into both correspondence and registration stages of their algorithms. In both orthopedic and cardiac surgeries, both position vectors and normal vectors are utilized to enable intra-operative guidance in both pair-wise [27]- [29] and group-wise generalized PSR problems [30]- [32], and in both rigid [33] and non-rigid PSR problems [27], [28], [30]- [32], [34]. In neurosurgery, the extracted features from the multi-modal brain images could be utilized to screen the outliers [14], [35].…”

mentioning

confidence: 99%

“…However, the intra-operative PS usually only forms a curve, from which features such as normal vectors cannot be accurately estimated. Hence, most existing feature-based [24], [26], [28], [31], [34], [45] or deep-learning based methods [36]- [38] cannot be readily adopted in the CAOS application. In addition, in many surgical procedures such as the ACL reconstruction, the intra-operative data only covers a partial region of the whole interested organ, and is often corrupted with noise and outliers.…”

mentioning

confidence: 99%

“…Differences from Our Previous Work We have previously proposed several rigid and non-rigid registration methods, which utilize the normal vectors estimated from both PSs to be registered [29], [34], [45], [48], [49]. In those methods, von-Mises Fisher (vMF) distribution was used to model the error distributions between one model normal vector and one data normal vector [29].…”

mentioning

confidence: 99%

See 1 more Smart Citation

Aligning 3D Curve With Surface Using Tangent and Normal Vectors for Computer-Assisted Orthopedic Surgery

Min

Zhu

Liu

et al. 2021

IEEE Trans. Med. Robot. Bionics

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Registration that aligns different views of one interested organ together is an essential technique and outstanding problem in medical robotics and image-guided surgery (IGS). This work introduces a novel rigid point set registration (PSR) approach that aims to accurately map the pre-operative space with the intra-operative space to enable successful image guidance for computer-assisted orthopaedic surgery (CAOS). The normal vectors and tangent vectors are first extracted from the pre-operative and intra-operative point sets (PSs) respectively, and are further utilized to enhance the registration accuracy and robustness. The contributions of this article are threefolds. First, we propose and formulate a novel distribution that describes the error between one normal vector and the corresponding tangent vector based on the von-Mises Fisher (vMF) distribution. Second, by modelling the anisotropic position localization error with the multi-variate Gaussian distribution, we formulate the PSR considering anisotropic localization error as a maximum likelihood estimation (MLE) problem and then solve it under the expectation maximization (EM) framework. Third, to facilitate the optimization process, the gradients of the objective function with respect to the desired parameters are computed and presented. Extensive experimental results on the human femur and pelvis models verify that the proposed approach outperforms the state-of-the-art methods, and demonstrate potential clinical values for relevant surgical navigation applications.

show abstract

Generalized Non-rigid Point Set Registration with Hybrid Mixture Models Considering Anisotropic Positional Uncertainties

Cited by 11 publications

References 13 publications

Generalized Point Set Registration with the Kent Distribution

Generalized Point Set Registration with the Kent Distribution

Geodesic-Based Bayesian Coherent Point Drift

Aligning 3D Curve With Surface Using Tangent and Normal Vectors for Computer-Assisted Orthopedic Surgery

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