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摘要翻译：
基于原始数据的变形模板生成模型的定义和估计问题对于建模受各种几何变异性影响的非对齐数据具有特别重要的意义。在计算机视觉社区的形状建模或计算解剖学(CA)的概率图谱构建中尤其如此。Allassonni\'ere、Amit和Trouv\'e(JRSS2006)提出了第一个将几何变异性建模为隐变量的相干统计框架。在贝叶斯背景下，他们证明了MAP估计的相合性，并给出了一个简单的具有EM风格的迭代确定性算法，从而在低噪声条件下得到了MAP估计的合理逼近。本文在SAEM算法的基础上，提出了一种近似MAP估计量的随机算法。以手写体数字图像为例，证明了它收敛于观测似然的一个临界点。
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英文标题：
《Construction of Bayesian Deformable Models via Stochastic Approximation
Algorithm: A Convergence Study》
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作者：
St\'ephanie Allassonni\`ere (CMAP), Estelle Kuhn (LAGA), Alain
Trouv\'e (CMLA)
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最新提交年份：
2009
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分类信息：
一级分类：Statistics 统计学
二级分类：Computation 计算
分类描述：Algorithms, Simulation, Visualization
算法、模拟、可视化
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英文摘要：
The problem of the definition and the estimation of generative models based on deformable templates from raw data is of particular importance for modelling non aligned data affected by various types of geometrical variability. This is especially true in shape modelling in the computer vision community or in probabilistic atlas building for Computational Anatomy (CA). A first coherent statistical framework modelling the geometrical variability as hidden variables has been given by Allassonni\`ere, Amit and Trouv\'e (JRSS 2006). Setting the problem in a Bayesian context they proved the consistency of the MAP estimator and provided a simple iterative deterministic algorithm with an EM flavour leading to some reasonable approximations of the MAP estimator under low noise conditions. In this paper we present a stochastic algorithm for approximating the MAP estimator in the spirit of the SAEM algorithm. We prove its convergence to a critical point of the observed likelihood with an illustration on images of handwritten digits.
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PDF链接：
https://arxiv.org/pdf/706.0787
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