Towards a coherent statistical framework for dense deformable template estimation
Towards a coherent statistical framework for dense deformable template estimation
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DOI：
10.1111/j.1467-9868.2007.00574.x
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发表时间：
2007-02
期刊：
影响因子：
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通讯作者：
S. Allassonnière;Y. Amit;A. Trouvé
中科院分区：
文献类型：
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作者：
S. Allassonnière;Y. Amit;A. Trouvé
总结。估计计算机视觉领域的概率可变形模板模型或计算解剖学领域的概率地图集的问题尚未得到一致的统计公式，仍然是一个挑战。我们为可变形对象的灰度图像提供了一个基于密集可变形模板的定义良好的统计模型的仔细定义和分析。我们提出了一个严格的贝叶斯框架，我们证明了最大后验估计的渐近一致性，并导致了小样本设置下几何和光度参数的有效迭代估计算法。该模型被扩展到有限数量的这类成分的混合物，从而对一类物体的光度和几何变化进行精细描述。我们用手写数字的图像说明了一些想法，并通过最大似然将估计模型应用于分类。
Summary. The problem of estimating probabilistic deformable template models in the field of computer vision or of probabilistic atlases in the field of computational anatomy has not yet received a coherent statistical formulation and remains a challenge. We provide a careful definition and analysis of a well‐defined statistical model based on dense deformable templates for grey level images of deformable objects. We propose a rigorous Bayesian framework for which we prove asymptotic consistency of the maximum a posteriori estimate and which leads to an effective iterative estimation algorithm of the geometric and photometric parameters in the small sample setting. The model is extended to mixtures of finite numbers of such components leading to a fine description of the photometric and geometric variations of an object class. We illustrate some of the ideas with images of handwritten digits and apply the estimated models to classification through maximum likelihood.