Baloch Sajjad, Verma Ragini, Davatzikos Christos
University of Pennsylvania, Philadelphia, PA, USA.
Inf Process Med Imaging. 2007;20:594-606. doi: 10.1007/978-3-540-73273-0_49.
Existing approaches to computational anatomy assume that a perfectly conforming diffeomorphism applied to an anatomy of interest captures its morphological characteristics relative to a template. However, biological variability renders this task extremely difficult, if possible at all in many cases. Consequently, the information not reflected by the transformation, is lost permanently from subsequent analysis. We establish that this residual information is highly significant for characterizing subtle morphological variations and is complementary to the transformation. The amount of residual, in turn, depends on transformation parameters, such as its degree of regularization as well as on the template. We, therefore, present a methodology that measures morphological characteristics via a lossless morphological descriptor, based on both the residual and the transformation. Since there are infinitely many [transformation, residual] pairs that reconstruct a given anatomy, which collectively form a nonlinear manifold embedded in a high-dimensional space, we treat them as members of an Anatomical Equivalence Class (AEC). A unique and optimal representation, according to a certain criterion, of each individual anatomy is then selected from the corresponding AEC, by solving an optimization problem. This process effectively determines the optimal template and transformation parameters for each individual anatomy, and removes respective confounding variation in the data. Based on statistical tests on synthetic 2D images and real 3D brain scans with simulated atrophy, we show that this approach provides significant improvement over descriptors based solely on a transformation, in addition to being nearly independent of the choice of the template.
现有的计算解剖学方法假定，应用于感兴趣解剖结构的完美共形微分同胚能够捕捉其相对于模板的形态特征。然而，生物变异性使得这项任务极其困难，在许多情况下甚至可能根本无法完成。因此，未被变换反映的信息在后续分析中永久丢失。我们证实，这些残余信息对于表征细微的形态变化非常重要，并且是对变换的补充。残余量又取决于变换参数，比如正则化程度以及模板。因此，我们提出一种方法，基于残余和变换，通过无损形态描述符来测量形态特征。由于存在无穷多个重构给定解剖结构的[变换，残余]对，它们共同构成嵌入高维空间的非线性流形，我们将它们视为解剖等价类（AEC）的成员。然后，通过解决一个优化问题，从相应的AEC中为每个个体解剖结构选择根据特定标准的唯一最优表示。这个过程有效地为每个个体解剖结构确定最优模板和变换参数，并消除数据中各自的混杂变异。基于对合成二维图像和具有模拟萎缩的真实三维脑部扫描的统计测试，我们表明，除了几乎与模板选择无关之外，这种方法相对于仅基于变换的描述符有显著改进。
