Shape analysis is increasingly becoming important to study changes in brain structures in relation to clinical neurological outcomes. This is a challenging task due to the high dimensionality of shape representations and the often limited number of available shapes. Current techniques counter the poor ratio between dimensions and sample size by using regularization in shape space, but do not take into account the spatial relations within the shapes. This can lead to models that are biologically implausible and difficult to interpret. We propose to use $P$-spline based regression, which combines a generalized linear model (GLM) with the coefficients described as $B$-splines and a penalty term that constrains the regression coefficients to be spatially smooth. Owing to the GLM, this method can naturally predict both continuous and discrete outcomes and can include non-spatial covariates without penalization. We evaluated our method on hippocampus shapes extracted from magnetic resonance (MR) images of 510 non-demented, elderly people. We related the hippocampal shape to age, memory score, and sex. The proposed method retained the good performance of current techniques, such as ridge regression, but produced smoother coefficient fields that are easier to interpret.

中文翻译：

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使用基于P样条的形状回归对海马进行空间正则化形状分析

形状分析对于研究与临床神经系统结果相关的大脑结构变化变得越来越重要。由于形状表示的高维性和可用形状的数量通常有限，因此这是一项具有挑战性的任务。当前的技术通过使用形状空间中的正则化来解决尺寸与样本大小之间的不良比率，但是没有考虑形状内的空间关系。这可能导致模型在生物学上难以置信且难以解释。我们建议使用基于$ P $ -spline的回归，该回归将广义线性模型（GLM）与描述为$ B $ -splines的系数和将回归系数约束为空间平滑的惩罚项相结合。由于GLM，这种方法自然可以预测连续和离散的结果，并且可以包含非空间协变量而不会受到惩罚。我们评估了从510名无痴呆的老年人的磁共振（MR）图像中提取的海马形状的方法。我们将海马体的形状与年龄，记忆力得分和性别相关联。所提出的方法保留了当前技术的良好性能，例如岭回归，但产生了更平滑的系数场，更易于解释。