Uncertainty Modeling and Geometric Inference
Uncertainty Modeling and Geometric Inference
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DOI：
10.1007/3-540-28247-5_14
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发表时间：
2005
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影响因子：
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通讯作者：
K. Kanatani
中科院分区：
文献类型：
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作者：
K. Kanatani
我们探讨了基于图像特征点的几何推理的“统计方法”的含义。本文将特征不确定性的起源追溯到图像处理操作，讨论了渐近分析在”几何拟合”和”几何模型选择”中的意义，指出标准统计分析与几何推理问题之间存在着对应关系。我们还比较了“几何AIC”和“几何MDL”在检测简并方面的能力。接下来，我们回顾了线性约束的几何拟合技术的最新进展，描述了“FNS方法”，“HEIV方法”，“重整化方法”，以及其他相关技术。最后，我们讨论了与几何推理有关的“Neyman-Scott问题”和“半参数模型”。我们的结论是，统计方法的应用需要仔细考虑的问题的性质。
We investigate the meaning of" statistical methods" for geometric inference based on image feature points. Tracing back the origin of feature uncertainty to image processing operations, we discuss the implications of asymptotic analysis in reference to" geometric fitting" and" geometric model selection", We point out that a correspondence exists between the standard statistical analysis and the geometric inference problem. We also compare the capability of the" geometric AIC" and the" geometric MDL'in detecting degeneracy. Next, we review recent progress in geometric fitting techniques for linear constraints, describing the" FNS method", the" HEIV method", the" renormalization method", and other related techniques. Finally, we discuss the" Neyman-Scott problem" and" semiparametric models" in relation to geometric inference. We conclude that applications of statistical methods requires careful considerations about the nature of the problem in question.