Zhou Luping, Hartley Richard, Wang Lei, Lieby Paulette, Barnes Nick
RSISE, Australian National University, Canberra, ACT 0200, Australia.
IEEE Trans Med Imaging. 2009 Jun;28(6):937-50. doi: 10.1109/TMI.2009.2012556. Epub 2009 Jan 19.
Identifying the shape difference between two groups of anatomical objects is important for medical image analysis and computer-aided diagnosis. A method called "discriminative direction" in the literature has been proposed to solve this problem. In that method, the shape difference between groups is identified by deforming a shape along the discriminative direction. This paper conducts a thorough study about inferring this discriminative direction in an efficient and accurate way. First, finding the discriminative direction is reformulated as a preimage problem in kernel-based learning. This provides a complementary but conceptually simpler solution than the previous method. More importantly, we find that a shape deforming along the original discriminative direction cannot faithfully maintain its anatomical correctness. This unnecessarily introduces spurious shape differences and leads to inaccurate analysis. To overcome this problem, this paper further proposes a regularized discriminative direction by requiring a shape to conform to its underlying distribution when it deforms. Two different approaches are developed to impose the regularization, one from the perspective of probability distributions and the other from a geometric point of view, and their relationship is discussed. After verifying their superior performance through controlled experiments, we apply the proposed methods to detecting and localizing the hippocampal shape difference between sexes. We get results consistent with other independent research, providing a more compact representation of the shape difference compared with the established discriminative direction method.
识别两组解剖对象之间的形状差异对于医学图像分析和计算机辅助诊断至关重要。文献中提出了一种名为“判别方向”的方法来解决这个问题。在该方法中，通过沿判别方向对形状进行变形来识别组间的形状差异。本文对以高效且准确的方式推断此判别方向进行了深入研究。首先，将寻找判别方向重新表述为基于核学习中的原像问题。这提供了一种与先前方法互补但概念上更简单的解决方案。更重要的是，我们发现沿原始判别方向变形的形状不能如实地保持其解剖学正确性。这不必要地引入了虚假的形状差异并导致分析不准确。为克服此问题，本文通过要求形状在变形时符合其潜在分布，进一步提出了一种正则化判别方向。开发了两种不同的方法来施加正则化，一种从概率分布的角度，另一种从几何角度，并讨论了它们之间的关系。通过对照实验验证了它们的优越性能后，我们将所提出的方法应用于检测和定位两性之间海马体形状差异。我们得到的结果与其他独立研究一致，与已确立的判别方向方法相比，提供了更紧凑的形状差异表示。
