從單一RGB圖像中，解決由物體的對稱性或遮擋所造成的姿態模糊性，並精準預測物體的6D姿態是一個重大的挑戰。為了應對這一挑戰，我們提出了一種新穎的基於特殊歐幾里得三維群 SE(3) 的分數擴散模型。這是首次將基於 SE(3) 的分數擴散模型應用到圖像領域中解決姿態估計問題。實驗數據顯示，該方法在處理姿態模糊性與減輕影像透視引起的模糊性上能達到卓越的效果，同時也展示我們對 SE(3) 提出的替代斯坦分數公式具有很好的穩健性。這種公式不僅提高了朗之萬動力學方程式在 SE(3) 上的收歛性，也增強了斯坦分數的計算效率。因此，我們開發出一種有潛力的6D物體姿態估計方法。

Addressing accuracy limitations and pose ambiguity in 6D object pose estimation from single RGB images presents a significant challenge, particularly due to object symmetries or occlusions. In response, we introduce a novel score-based diffusion method applied to the SE(3) group, marking the first application of diffusion models to SE(3) within the image domain, specifically tailored for pose estimation tasks. Extensive evaluations demonstrate the method's efficacy in handling pose ambiguity, mitigating perspective-induced ambiguity, and showcasing the robustness of our surrogate Stein score formulation on SE(3). This formulation not only improves the convergence of Langevin dynamics but also enhances computational efficiency. Thus, we pioneer a promising strategy for 6D object pose estimation.

摘要 i
Abstract ii
1 Introduction 1
2 Related Work 5
2.1 Methodologies for Dealing with Pose Ambiguity Issues . . . . . . . . . . . . . 5
2.2 Previous Diffusion Probabilistic Models and Their Application Domains . . . . 6
3 Background 7
3.1 Lie Groups and Their Application in Pose Estimation . . . . . . . . . . . . . . 7
3.2 Parametrization of SE(3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.3 Score­Based Generative Modeling . . . . . . . . . . . . . . . . . . . . . . . . 8
4 Preliminaries 11
4.1 Comparative Analysis of Diffusion Models on Lie Groups . . . . . . . . . . . 11
4.2 The Benefits of SE(3) over R3SO(3) in Perspective­Affected Pose Estimation 12
5 Methodology 13
5.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
5.2 Efficient Computation of Stein Score . . . . . . . . . . . . . . . . . . . . . . . 14
5.3 Surrogate Stein Score Calculation on SE(3) . . . . . . . . . . . . . . . . . . . 15
5.4 Proposed Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
6 Experimental Results 19
6.1 Experimental Hypotheses and Validation Objectives . . . . . . . . . . . . . . . 19
6.2 Datasets and Baselines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
6.3 Quantitative Results on SYMSOL . . . . . . . . . . . . . . . . . . . . . . . . 21
6.4 Quantitative Results on SYMSOL­T . . . . . . . . . . . . . . . . . . . . . . . 22
6.5 Analysis of SE(3) and R3SO(3) in the Presence of Image Perspective Ambiguity 23
6.6 Performance Analysis: Surrogate Score versus Automatically Differentiated
True Score . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
6.7 Comparison with Other Diffusion Models . . . . . . . . . . . . . . . . . . . . 25
7 Limitations and Future Directions 27
8 Conclusion 29
iii
9 Appendix 31
9.1 Additional Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . 31
9.1.1 Calculation of Stein Scores Using Automatic Differentiation in JAX . . 31
9.1.2 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
9.1.3 Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
9.1.4 Hyperparameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
9.1.5 Evaluation Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
9.1.6 Visualization of SYMSOL­T Results . . . . . . . . . . . . . . . . . . 34
9.2 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
9.2.1 Closed­Form of Stein Scores . . . . . . . . . . . . . . . . . . . . . . . 35
9.2.2 Left and Right Jacobians on SO(3) . . . . . . . . . . . . . . . . . . . 36
9.2.3 Eigenvector of The Jacobians . . . . . . . . . . . . . . . . . . . . . . 36
9.2.4 Closed­Form of Stein Scores on SE(3) . . . . . . . . . . . . . . . . . 37
References 41

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