Chapter 5 Experimental Results
5.3 Results of 3D Image Alignment
In the current section, a vehicle model depicted in Fig. 4.5 is selected as a reference model.
The reference model is constructed by 4907 point clouds which are uniformly distributed on its surface. Thus, the aim of the 3D surface alignment task defined in the experiment is to align the arbitrary input 3D images (i.e. point clouds) with the reference model.
The experimental results comprise two parts. The first part uses the synthesized point cloud sets to test the proposed TNFN-based coarse alignment approach. In the second part, real 3D point cloud data scanned by a 3D imaging laser scanner are used to validate the alignment accuracy of the proposed fine alignment method. In both parts of the experiments, the alignment algorithm is compared with the neural network method (NNM) [46] and ICP [45] to demonstrate superior performance of the proposed coarse-to-fine scheme.
A. Testing using synthesized 3D point cloud data
To perform the coarse alignment learning, 2000 synthesized point cloud sets are generated randomly within the range described in Table 5.14. For training the TNFN, 50% of point clouds (1000) are prepared for training data set and the remaining 50% of point clouds (1000) are prepared for testing data set. The learning parameters for the TNFN training are defined in the left side of Table 5.15. Thus, after the coarse alignment learning completes, the output of TNFN is an estimated pose that coarsely aligns the input points with the reference model.
In TNFN-based surface modeling, we produce a cube model with the size of 5m×5m×5m that encloses the entire reference model. Within the cube model, 64000 point clouds are uniformly sampled according the resolution setting (0.125 m). Thus, the sampled point clouds are utilized for training TNFN to model the reference surface. The learning parameters of the TNFN-based surface modeling are defined in the right side of Table 5.15. Once the training of TNFN-based surface modeling is completed, the TNFN modeling is combined with the downhill simplex optimization method to execute the fine alignment of 3D surface.
Table 5.15: Learning parameters for the TNFN training.
Value for coarse alignment Value for surface modeling Parameters of training
the TNFN PLE SLE PLE SLE
Psize 40 25 80 25
Nc 20 none 20 none
Selection_Times 50 none 50 none
NormalTimes 10 none 10 none
Minimum_Support TransactionNum/2 none TransactionNum/2 none
Minimum_Confidence 60% none 60% none
RGLS parameter (λ) 0.0001 0. 0001 0.0005 0.0005
N-bin for MVFH 36 36 none none
Because the execution time and alignment accuracy are two major issues for a 3D image alignment system, these elements are taken as the evaluation conditions to examine the proposed alignment system.
(1) Alignment accuracy
To evaluate the alignment accuracy, the proposed TNFN-based coarse-to-fine system is compared with NNM [46] and ICP [45], two methods that use PCA for coarse alignment.
Thus, based on the 1000 testing sets of point clouds, the alignment errors of the coarse and fine alignments are listed in Table 5.16 where RMSE indicates the root mean square error.
From this table, the proposed system exhibits the lowest coarse and fine alignment errors among all systems. In addition, the proposed method improves the PCA coarse alignment, as shown in the table. Figure 5.18(a) and (b) presents a coarse alignment example of PCA and the proposed TNFN-based method, where the blue and red point clouds represent the testing and reference model data, respectively. From this figure, the proposed method exhibits less alignment error than PCA.
To compare RGLS with the pseudo inverse method, this paper uses the same 1000 testing sets of point clouds on the pseudo inverse method. The RMSE of the pseudo inverse method for the coarse phase is 0.2619, which is larger than RGLS (0.1042). Thus, in the 3D image alignment task, RGLS would be better than the pseudo inverse method. In short, from
example 1 to example 3, we conclude that RGLS would be more suitable than the pseudo inverse method for constructing a TNTN.
(2) Alignment speed
In consideration of alignment speed, the average execution time for aligning 1000 testing sets of point clouds is calculated. The results of the alignment speed are also listed in Table 5.16. From the table, the execution time of the proposed system is shorter than those of NNM and ICP.
Table 5.16: Results of alignment accuracy and execution time.
Average RMSE (m) Method
Coarse alignment error Fine alignment error
Average execution Time (sec)
TNFN-based
coarse-to-fine alignment 0.1042m 0.0627m 3.29s PCA coarse alignment
NNM fine alignment 0.2846m 0.1423m 4.53s
PCA coarse alignment
ICP fine alignment 0.2846m 0.0688m 49.48s
(a) (b)
Figure 5-18: Examples of two coarse alignment methods: (a) PCA and (b) TNFN-based coarse alignment.
B. Validation of real 3D point cloud data alignment
Figure 5.19 presents a real case of 3D point cloud data scanned by a 3D imaging laser
method. In this figure, the coarse alignment errors of PCA and the proposed method are 0.262 and 0.106m, respectively. Thus, this result again proves that the proposed method is superior to PCA. In the case of fine alignment, Fig. 5.21(a)-(c) depicts the fine alignment results of proposed TNFN-based fine alignment system, NNM, and ICP. From this figure, the fine alignment errors of the proposed system, NNM, and ICP are 0.0558, 0.1121, and 0.0569m, respectively. These results indicate that the proposed TNFN-based method can achieve high accuracy in real 3D point cloud data. Furthermore, regarding the alignment speed, the execution time of the proposed system, NNM, and ICP are 1.71, 2.13, and 7.93s, respectively.
Therefore, the proposed system demonstrates higher alignment speed compared to NNM and ICP. In short, the proposed TNFN-based coarse-to-fine 3D image alignment system can align 3D point cloud data with the reference model accurately at high speed.
Figure 5-19: Real case of 3D point cloud data scanned by a 3D imaging laser scanner.
Figure 5-20: Coarse alignment results: (a) PCA and (b) TNFN-based coarse alignment.
(a) (b)
(a)
(b) (c)
Figure 5-21: Fine alignment results: (a) TNFN-based fine alignment, (b) NNM, and (c) ICP.
Chapter 6
Conclusions and Future Works
The purpose of this dissertation is to develop a methodology to automatically design TSK-type neural fuzzy networks (TNFNs) such that the developed networks can be applied to real world problems. To make TNFNs to be useful, the learning algorithm must be powerful to evolve networks in simulation that are robust enough to transfer to the real world. Toward this end, two components have been involved to achieve this goal: regularized least square based cooperative coevolutionary algorithm (RGLS-HCCA) and image alignment applications. The RGLS-HCCA model can evolve the structure and parameters of TNFN and the evolved TNFN can be taken to transfer the problem from simulation to the real world applications.
This chapter summarizes the conclusions of these two components in Section 6.1 and discusses future works to extend the proposed algorithm in Section 6.2.
6.1 Conclusions
This dissertation concludes two key components to the fields of evolutionary computation and its applications. Regarding the first component, the proposed RGLS-HCCA encodes an antecedent part of a TSK-type fuzzy rule into a chromosome and utilizes RGLS to estimate the consequent part of a TSK-type fuzzy rule. Such combination not only reduces the number of parameters that must be trained but also controls HCCA to adapt the network to more complex tasks. In HCCA, it proposes parameter level evolution (PLE) and structure level evolution (SLE) to solve the problem of the random group selection, preserve the good combinations of fuzzy rules, and make the parameters and structure of network be evolved locally and globally, respectively. In addition, this dissertation proposes VAC, VAM, and SRM such that the variable length of chromosomes can be evaluated and the number of fuzzy
rules can be self-adjusted. The experimental results show that by applying RGLS-HCCA to the prediction of Mackey-Glass time series, RGLS-HCCA would demonstrate faster the algorithm convergence rate and lower estimating error than those of other learning algorithms.
Regarding the second component, two image alignment applications, which are 2D and 3D image alignment problems, are used to demonstrate the applicability of RGLS-HCCA. For 2D image alignment application, RGLS-HCCA is used to construct a CNFN-based 2D image alignment system. The CNFN utilizes the multi-stage of TNFN to solve problems that one-stage neural network have difficulty in applying a large range of affine parameters. This evidence can be found in the experimental results of both synthesized and real-images cases.
The results show that the performance of the proposed scheme is superior to the traditional neural network methods on accuracy and robustness. For 3D image alignment application, the use of RGLS-HCCA can benefit the training of the TNFN-based coarse-to-fine 3D image alignment system. In the coarse alignment procedure, utilizing RGLS-HCCA to train a TNFN to model the relationship between the input feature and output pose can solve the problem of the high alignment error caused by PCA. In fine alignment procedure, using RGLS-HCCA to train a TNFN to model the reference surface can improve the heavy computational cost caused by ICP. In addition, by combining the surface modeling with the downhill simplex optimization, the distance from the input image to the reference model can be reduced iteratively. The evidence can be found in the experimental results to demonstrate the superior performance of the proposed 3D image alignment system over existing systems.
are discussed as follows:
To discuss the proposed RGLS-HCCA, the number of hierarchical level is only two to execute the training of structure and parameters of neural fuzzy networks. As the application problem become more complex, there is a need to increase the hierarchical level to match the complex problem. Thus, in the future work, the multi hierarchical level is taken into consideration of further investigation of how to cooperate these hierarchical levels to adapt the model to a complex problem.
For the image alignment applications, two tasks are considered: 2D image alignment and 3D image alignment. For the 2D image alignment task, although the proposed system can demonstrate high performance, it still has some limitations. Specifically, as the application problem becomes more complicated, the number of cooperative neural fuzzy networks would increase. Such condition leads the proposed model to suffer from the difficulty of choosing the suitable number of cooperative networks. If the unsuitable number of networks is chosen, the overall system will yield large estimated errors. Therefore, future works should identify a well-defined method to determine the number of cooperative neural fuzzy networks automatically.
For the 3D image alignment task, in spite of combing the surface modeling with the downhill simplex optimization can obtain good results in fine alignment phase, the downhill simplex optimization may suffer from getting in local minima. Toward this end, the on-line parallel search techniques may be the solution for preventing the local minima happened. The on-lien parallel search techniques should be fast and keep the proper accuracy for applying to the fine alignment task. Therefore, the future work would modify the proposed RGLS-HCCA model to satisfy the design of the fine alignment phase.
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