A Review of Point Set Registration: From Pairwise Registration to Groupwise Registration
Abstract
:1. Introduction
2. Pairwise Point Set Registration
2.1. Distance-Based Methods
2.2. Filtering-Based Methods
2.3. Probability-Based Methods
- (1)
- Selecting a suitable non-rigid transformation function: In the CPD method, only one non-rigid transformation function is considered. Therefore, multiple kernel functions were used to represent non-rigid transformations in [72]. By automatically adjusting the kernel weights, this method can prune the ineffective kernels and evaluate the importance of each kernel. Considering the multi-layer motion between two sets of points, a robust point set registration using the GMM model was proposed in [73].
- (2)
- Choosing the distribution of point set: In [74], the Student’s-t distribution was used to replace the Gaussian distribution for tackling the outliers in the point set registration. Similar to the CPD method, one point set is treated as Student’s-t mixture model centroids, while another point set is fitted to those of the Student’s-t mixture model centroids by moving coherently.
- (3)
- Setting the membership probabilities: In the CPD method, equal membership probabilities were used. To improve the performance of point set registration, the shape context was proposed to assign the membership probabilities of the mixture model in [1].
- (4)
- Developing the local structure descriptors: In the CPD method, the GMM centroids were forced to move coherently to fit the data points by maximizing the likelihood, which only encodes the global structure of the two point sets. To preserve the local structure of point sets, the idea of local linear embedding (LLE) was proposed. The local neighbors in the point set could be preserved after the non-rigid transformed. Each point can be represented by a weighted linear of its neighbors. Then, an EM algorithm was derived for the ML optimization constrained with both CPD and LLE terms [75]. Similar to the LLE, the locally linear transforming (LLF) was developed for constructing the local structure [76]. In [1], the local features were used to assign the membership probabilities of the GMM. A non-rigid point set registration, which preserves both global and local structures, was developed. In [78], the shape context and LLF were proposed to the nonrigid point set registration. In [17], a non-rigid point set registration using spatially constrained Gaussian fields (SCGF) was developed. The shape context was also used for the membership probabilities initialization. A graph Laplacian regularized Gaussian fields was proposed to preserve the local structure of point sets. Furthermore, two local structure descriptors were embedded in the CPD framework in [79]. The first descriptor was LLE. The Laplacian coordinate was used in the second descriptor to keep the size of neighborhood structure. Therefore, the objective function of point set registration was composed of the global distance item, non-rigid transformation constraint item and two local structure constraints items.
- (5)
- Extraction the feature of point sets: The spatial location of point sets is a traditional feature for registration. In [86], the color information of point sets was used to extend the CPD algorithm. In [87], the correlation of color information and spatial location information was formulated. Then, a probabilistic point set registration framework with color information and spatial location information was given.
- (6)
- Performing algorithm: The disadvantage of the traditional CPD algorithm is that the CPD method has a high computation cost. Therefore, In [88], an accelerated CPD (ACPD) method was proposed to register a 3-D point cloud. In ACPD, a global squared iterative EM algorithm was developed to speed up the process of likelihood maximization. The dual-tree improved fast Gauss transform method was used to accelerate the process of Gaussian summation. In [92], the regression and clustering for performing point set registration in a Bayesian framework were presented. The coarse-to-fine variational inference algorithm was used to estimate the unknown parameters.
2.4. Discussion
3. Groupwise Point Set Registration
- the construction of the mean point set.
- the estimation of the transformation between the multiple point sets and mean point set.
4. Experiments
5. Conclusions
- (1)
- Object localization for the purpose of autonomous vehicles and in health systems requires point set registration over massive and high-dimensional point sets. One direction for alleviating this problem relies on point or feature selection. Clustering algorithms can then be used to cope with such challenges. Sparse Bayesian learning methods are also capable of identifying the suitable features for point set registration.
- (2)
- There is a need for more benchmark examples and large scale datasets with ground truth for thorough performance evaluation of the developed approaches.
- (3)
- Point set registration is an essential step towards target tracking and pattern recognition. There is a scope of assessing its impact on the entire monitoring system of interest, with different levels of autonomy.
Author Contributions
Funding
Conflicts of Interest
References
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Research Study | Pairwise/Groupwise | Method | Rigid/Non-Rigid | Parametric/Non-Parametric Model | Characteristics |
---|---|---|---|---|---|
Besl and McKay [23] | Pairwise | Distance-based method | Rigid | Parametric Model | (1) Sensitive to the initialization (2) Trapping into local minima |
Gold et al. [34] | Pairwise | Distance-based method | Rigid | Parametric Model | (1) Combining deterministic annealing and softassign optimization (2) Restricting to perform the rigid-body transformation |
Chui et al. [35] | Pairwise | Distance-based method | Non-rigid | Parametric Model | Difficult to extend to perform higher dimension |
Tsin et al. [36] | Pairwise | Distance-based method | Rigid and Non-rigid | Parametric Model | Maximizing the KC of point sets |
Jian et al. [38] | Pairwise | Distance-based method | Rigid and Non-rigid | Parametric Model | Minimizing the Euclidean distance of two GMMs |
Leordeanu et al. [46] | Pairwise | Distance-based method | Rigid and Non-rigid | Non-Parametric Model | Convexifying the QAP problem by spectral relaxation method |
Cour et al. [47] | Pairwise | Distance-based method | Rigid and Non-rigid | Non-Parametric Model | Convexifying the QAP problem by semidefinite-programming relaxation |
Almohamad et al. [50] | Pairwise | Distance-based method | Rigid and Non-rigid | Non-Parametric Model | Convexifying the QAP problem by doubly stochastic relaxation |
Zhou et al. [22] | Pairwise | Distance-based method | Rigid and Non-rigid | Non-Parametric Model | Factorizing the large pairwise affinity matrix into some smaller matrices |
Sandhu et al. [67] | Pairwise | Filter-based method | Rigid | Non-Parametric Model | Using a particle filter to register the point sets |
Li et al. [16] | Pairwise | Filter-based method | Rigid | Non-Parametric Model | (1) Using a cubature Kalman filter to register the point sets (2) The correspondence should be computed in advance |
Myronenko et al. [25] | Pairwise | Probability-based method | Rigid and Non-rigid | Parametric Model | (1) Using a GMM model to formulate the distribution of the point sets (2) Maximizing the likelihood of GMM |
Ma et al. [76] | Pairwise | Probability-based method | Rigid and Non-rigid | Parametric Model | Developing a locally linear transforming for local structure constrict |
Wang et al. [104] | Groupwise | Information theoretic measure | Rigid and Non-rigid | Parametric Model | Proposing a CDF-JS divergence as the cost function |
Chen et al. [105] | Groupwise | Information theoretic measure | Rigid and Non-rigid | Parametric Model | Developing a CDF-HC divergence as the cost function |
Giraldo et al. [106] | Groupwise | Information theoretic measure | Rigid and Non-rigid | Parametric Model | Using a Rényi’s second order entropy divergence as the cost function |
Rasoulian et al. [108] | Groupwise | Probability-based method | Non-rigid | Parametric Model | Assumed that the multiple point sets are the noisy observations of mean point set |
Evangelidis et al. [2,3] | Groupwise | Probability-based method | Rigid | Parametric Model | Assumed that the multiple point sets are transformed realizations of mean point set |
Method | KC | ICP | TPS-RPM | CPD | CPD-GL | SCGF |
---|---|---|---|---|---|---|
Fish | 0.41 s | 0.47 s | 2.37 s | 0.22 s | 0.42 s | 37.04 s |
Chinese | 0.39 s | 0.50 s | 2.38 s | 0.22 s | 0.73 s | 27.64 s |
Method | CDF-HC | JRMPC | TMM | Rényi’s |
---|---|---|---|---|
Fish | 58.34 s | 20.06 s | 27.11 s | 60.06 s |
Chinese | 77.70 s | 20.17 s | 31.70 s | 72.72 s |
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Zhu, H.; Guo, B.; Zou, K.; Li, Y.; Yuen, K.-V.; Mihaylova, L.; Leung, H. A Review of Point Set Registration: From Pairwise Registration to Groupwise Registration. Sensors 2019, 19, 1191. https://doi.org/10.3390/s19051191
Zhu H, Guo B, Zou K, Li Y, Yuen K-V, Mihaylova L, Leung H. A Review of Point Set Registration: From Pairwise Registration to Groupwise Registration. Sensors. 2019; 19(5):1191. https://doi.org/10.3390/s19051191
Chicago/Turabian StyleZhu, Hao, Bin Guo, Ke Zou, Yongfu Li, Ka-Veng Yuen, Lyudmila Mihaylova, and Henry Leung. 2019. "A Review of Point Set Registration: From Pairwise Registration to Groupwise Registration" Sensors 19, no. 5: 1191. https://doi.org/10.3390/s19051191
APA StyleZhu, H., Guo, B., Zou, K., Li, Y., Yuen, K. -V., Mihaylova, L., & Leung, H. (2019). A Review of Point Set Registration: From Pairwise Registration to Groupwise Registration. Sensors, 19(5), 1191. https://doi.org/10.3390/s19051191