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研究生: 李冠俊
Lee, Kuan-Chun
論文名稱: 合成式視覺與推論:應用吉式抽樣於脈絡敏感的擾動建構
Compositional Vision and Inference: Perturbation Formulation for Context Sensitivity with Gibbs Sampler
指導教授: 陳國璋
Chen, Kuo-Chang
張洛賓
Chang, Lo-Bin
口試委員: 翁久幸
Weng, Chiu-Hsing
學位類別: 碩士
Master
系所名稱: 理學院 - 數學系
Department of Mathematics
論文出版年: 2014
畢業學年度: 102
語文別: 英文
論文頁數: 26
中文關鍵詞: 貝氏影像分析脈絡敏感擾動方法吉式抽樣合成性
外文關鍵詞: Bayesian image analysis, context-sensitive, perturbation Method, Gibbs sampler, compositionality
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  • 本文將會討論一貝氏影像分析的生成模型。模型部分,我們考慮兩點:根據「合成性(compositioanlity)」的想法,建構一個關於影像解釋並具有脈絡訊息的先驗分布以及建構給定特定解釋下,影像像素的機率分布。我們也會介紹一個馬可夫鏈蒙地卡羅的推論算法---吉式抽樣。最後,我們將應用此模型與吉式方法進行五官樣態估計的實驗。


    In this thesis, we discuss a generative model for Bayesian image analysis. In this model, we focus on building a prior of pares of an image with context information based on compositionality and a conditional model of image pixels given a particular interpretation.
    Also, a MCMC inference algorithm, Gibbs sampler, is introduced. Finally,
    Gibbs sampler and our model will be applied to a facial pose estimation experiment.

    1 Introduction 1 1.1 Bayesian Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Bayesian Inference as image parsing . . . . . . . . . . . . . . . . . . 1 2 Inference Algorithms 2 2.1 Markov Chain Monte Carlo Sampling: The Gibbs Sampler . . . . . 2 3 Building The Prior: Hierarchical Modelling 5 3.1 Interpretation and Basic Notation . . . . . . . . . . . . . . . . . . . 6 3.2 Context-Free Grammar: Markove Backbone . . . . . . . . . . . . . 8 3.3 Context-Sensitive Grammar: The Perturbation Method . . . . . . . 8 3.4 Discussion: Existence of KL Distance Minimizer . . . . . . . . . . . 10 4 An Experiment of Pose Inference 12 4.1 The Model: Prior of the Poses . . . . . . . . . . . . . . . . . . . . . 12 4.2 The Model: Likelihood Term . . . . . . . . . . . . . . . . . . . . . . 14 4.3 Parameters Estimation . . . . . . . . . . . . . . . . . . . . . . . . . 16 4.4 Model Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 22 5 Conclusion 23

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