Recent developments in computer vision have enabled the availability of segmented images across various domains, such as medicine, where segmented radiography images play an important role in diagnosis-making. As prediction problems are common in medical image analysis, this work explores the use of segmented images (through the associated contours they highlight) as predictors in a supervised classification context. Consequently, we develop a new approach for image analysis that takes into account the shape of objects within images. For this aim, we introduce a new formalism that extends the study of single random planar curves to the joint analysis of multiple planar curves-referred to here as multivariate planar curves. In this framework, we propose a solution to the alignment issue in statistical shape analysis. The obtained multivariate shape variables are then used in functional classification methods through tangent projections. Detection of cardiomegaly in segmented X-rays and numerical experiments on synthetic data demonstrate the appeal and robustness of the proposed method.

The shape $\tilde{\mathbf{X}}$ of a random planar curve $\mathbf{X}$ is what remains after removing deformation effects such as scaling, rotation, translation, and parametrization. Previous studies in statistical shape analysis have focused on analyzing $\tilde{\bf X}$ through discrete observations of the curve ${\bf X}$. While this approach has some computational advantages, it overlooks the continuous nature of both ${\bf X}$ and its shape $\tilde{\bf X}$. It also ignores potential dependencies among the deformation variables and their effect on $\tilde{ \bf X}$, which may result in information loss and reduced interpretability. In this paper, we introduce a novel framework for analyzing $\bf X$ in the context of Functional Data Analysis (FDA). Basis expansion techniques are employed to derive analytic solutions for estimating the deformation variables such as rotation and reparametrization, thereby achieving shape alignment. The generative model of $\bf X$ is then investigated using a joint-principal component analysis approach. Numerical experiments on simulated data and the \textit{MPEG-7} database demonstrate that our new approach successfully identifies the deformation parameters and captures the underlying distribution of planar curves in situations where traditional FDA methods fail to do so.