Using the logarithm of odds to define a vector space on probabilistic atlases
Using the logarithm of odds to define a vector space on probabilistic atlases
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DOI：
10.1016/j.media.2007.06.003
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发表时间：
2007-10-01
影响因子：
10.9
通讯作者：
Wells, William M.
中科院分区：
文献类型：
--
作者：
Pohl, Kilian M.;Fisher, John;Wells, William M.
比值比的对数（LogOdds）经常用于人工神经网络，经济学和生物学等领域，作为概率的替代表示。在这里，我们使用LogOdds将概率地图集放置在线性向量空间中。该表示具有用于医学成像的几个有用的性质。例如，它不仅对多个解剖结构的形状进行编码，而且还捕获一些关于不确定性的信息。我们证明了向量空间的加法和标量乘法运算具有自然的概率解释。我们讨论了几个将标签映射放置到LogOdds空间的例子。首先，我们将符号距离图（一种广泛使用的隐式形状表示）与LogOdds相关联，并将其与基于空间高斯平滑的替代方案进行比较。我们发现，LogOdds的方法更好地保留在一个复杂的多个对象设置的形状。在第二个例子中，我们通过将同一对象的多个标签映射到LogOdds空间来捕获边界位置的不确定性。第三，我们定义了一个非凸插值的地图集，捕捉人口老化过程中的不同时间点之间的框架。我们通过生成一个可变形的形状地图集，捕捉人口的解剖形状的变化来评估我们的表示的准确性。可变形图谱是LogOdds空间内的主成分分析的结果。该图谱被集成到现有的MR图像分割方法中。我们比较了分割20个测试用例的执行性能的一个类似的方法，使用一个更标准的形状模型，是基于签署的距离图。在这个数据集上，贝叶斯分类模型与我们的新表示在分割皮层下结构优于其他方法。(C)2007 Elsevier B.V.保留所有权利。
The logarithm of the odds ratio (LogOdds) is frequently used in areas such as artificial neural networks, economics, and biology, as an alternative representation of probabilities. Here, we use LogOdds to place probabilistic atlases in a linear vector space. This representation has several useful properties for medical imaging. For example, it not only encodes the shape of multiple anatomical structures but also captures some information concerning uncertainty. We demonstrate that the resulting vector space operations of addition and scalar multiplication have natural probabilistic interpretations.We discuss several examples for placing label maps into the space of LogOdds. First, we relate signed distance maps, a widely used implicit shape representation, to LogOdds and compare it to an alternative that is based on smoothing by spatial Gaussians. We find that the LogOdds approach better preserves shapes in a complex multiple object setting. In the second example, we capture the uncertainty of boundary locations by mapping multiple label maps of the same object into the LogOdds space. Third, we define a framework for non-convex interpolations among atlases that capture different time points in the aging process of a population.We evaluate the accuracy of our representation by generating a deformable shape atlas that captures the variations of anatomical shapes across a population. The deformable atlas is the result of a principal component analysis within the LogOdds space. This atlas is integrated into an existing segmentation approach for MR images. We compare the performance of the resulting implementation in segmenting 20 test cases to a similar approach that uses a more standard shape model that is based on signed distance maps. On this data set, the Bayesian classification model with our new representation outperformed the other approaches in segmenting subcortical structures. (C) 2007 Elsevier B.V. All rights reserved.