本文提出簡化平面類複眼架構，作為估測平移運動參數的技巧。此架構主要包括基本的並列三眼和擴展的單列類複眼。首先利用平行三眼系統架構和最小平方演算法，所提的作法可克服當利用雙眼架構求取平移運動參數時所遭遇的矩陣奇異性的問題。為了進ㄧ步降低求解運動過程的計算複雜性，本研究也提出估算平移運動參數的一個簡潔封閉解。此封閉解不但消除矩陣奇異性問題，而且可避免矩陣運算。因此，它具有低複雜性運算，因而是在複雜且實際視覺影像應用時，為執行運動估算的一個理想解。經由理想情況和擾動環境下，各種大小的平移運動和方向的一系列數值模擬。一般而言，只要深度不大，均可驗證出精確的回復運動參數。
由平行三眼擴展其應用到昆蟲複眼可精確和快速抓取獵物，此種有趣的問題不以生物的角度，而以電腦視覺來探討。利用單列平面類複眼架構，主要在運動回復的抗雜訊性能評估。此種平面類複眼具有昆蟲複眼中，大量的小眼組成的特殊對稱架構，因而模擬雜訊在四周環境不確定下或CCD裝置低解析度下產生的可能模糊影像型態，並進一步模擬，其結果指出，無論雜訊大小，此種特殊視覺架構均可提供優越的運動性能估算，甚至當雜訊干擾是非常嚴重時，此種類複眼不需要任何型態濾波器下，也能大量的降低平移運動的回復誤差。
總之，依據三眼視覺系統的最小平方演算法，擴展到單列平面類複眼，此種多重視覺偵測裝置的類複眼對於可能的雜訊具有統計上均勻化的優勢，此發現正是以工程的觀點解開昆蟲複眼之謎的基本依據。

This dissertation presents a technique for recovering translational motion parameters using two simplified planar compound-like eye schemes, namely a parallel trinocular system and a single-row Superposition-type Planar Compound-like Eye (SPCE).
In the parallel trinocular scheme, a least squares estimation algorithm is developed for recovering the translational motion parameters. The proposed approach resolves the matrix singularity problem encountered when attempting to recover motion parameters using a conventional binocular scheme. To further reduce the computational complexity of the motion estimation process, a compact closed-form scheme is also proposed to estimate the translational motion parameters. The closed-form algorithm not only resolves the matrix singularity problem, but also avoids the requirement for matrix manipulation. As a result, it has a low computational complexity and is therefore an ideal solution for performing motion estimation in complex, real-world visual imaging applications following an initial image filtering process. The performance of the closed-form algorithm is evaluated by performing a series of numerical simulations in which translational displacements of various magnitudes in three-dimensional space are recovered in both noise-free and perturbed environments. In general, the results demonstrate that the translational motion parameters can be reconstructed with a high degree of accuracy provided that the motion in the depth direction is limited to small displacements only.
Having developed a motion estimation scheme for a parallel trinocular system, additional charge coupled device (CCD) cameras are added in the horizontal direction to create a single-row SPCE. Translational motion models for the SPCE are then constructed by stacking the optical flow equations in the horizontal direction. The ego-translational parameters are then extracted using a simple least squares estimation algorithm. The simulation results reveal that the introduction of additional cameras to the machine vision system ensures an excellent motion estimation performance without the need for filters of any kind even when the viewing field is characterized by significant noise or the CCD deployment within the SPCE configuration has a non-uniform distribution.
Overall, the parallel binocular scheme and single-row SPCE configuration presented in this dissertation demonstrate a high degree of robustness toward noise and enable the motion estimation process to be performed in a rapid and computationally efficient manner using a simple least squares approximation approach. Whilst science can not realistically hope to improve upon the visioning capabilities found in the insect world, the techniques presented in this dissertation nonetheless provide a sound foundation for the development of artificial planar-array compound-like eyes which mimic the mechanisms at work in biological compound eyes and attain an enhanced visioning performance as a result.

List of Tables v
List of Figures vi
Chinese Abstract viii
English Abstract ix
Chapter 1 Introduction 1
1.1 Background 1
1.2 Motivation 7
1.3 Organization of the dissertation 11
Chapter 2 Parallel Trinocular and Motion Parameters 12
2.1 Recovery of translational motion parameters 12
2.2 Model A (the complete model) 15
2.3 Model B (the simplified model) 16
2.4 Model C (the compromise model) 17
Chapter 3 Acquisition of Translational Motion by the Parallel Trinocular 19
3.1 Limitations of binocular imaging systems 19
3.2 Compact closed-form solution 20
3.3 Validation of closed-form solution 21
3.3.1 Translational motion parameters estimation 22
3.3.2 Effects of Z-axis displacement and baseline distances between cameras 24
3.4 Motion estimation in perturbed environments 25
3.5 Performance comparison 29
3.6 Discussions 31
Chapter 4 Motion Estimation Using Single-Row SPCE 33
4.1 Compound-like eye and computer vision 33
4.2 Translational motion model of single-row SPCE 36
4.3 Motion estimation using single-row SPCE 38
4.3.1 Validation of three models 44
4.3.1.1 Accuracy 44
4.3.1.2 Computational efficiency 46
4.3.2 Effects of variation in noise level 48
4.3.3 Effects of irregular arrangement cameras 49
4.4 Discussions 51
Chapter 5 Conclusions 52
5.1 Contributions 53
5.2 Future research topics 55
Appendix A Product of disparities 57
Appendix B Determinant of ATA for Model C 58
Appendix C Data of 50 non-coplanar test points 60
Appendix D Determinant of ATA for Model A 62
Appendix E Orders of image matrix and optical flow vector 63
Appendix F Study on the elapsed time 64
Bibliography 66

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