arXiv subjects

Issam-Ali Moindjié

Publications and source records attributed to Issam-Ali Moindjié.

4 recordsLinked to original sources

arXiv2026

Multivariate Planar Curves: A Statistical Framework for Shape Analysis in Images

Recent developments in computer vision have made segmented images widely available across many domains, such as medicine, where segmented radiographs play an important role in diagnosis. As prediction problems are common in image analysis, this work explores the use of the object contours highlighted by such images as predictors in a supervised classification context. To this end, we develop a new statistical learning framework that accounts for the joint shape of the multiple objects contained in an image. We introduce a formalism that extends the study of a single random planar curve to the joint analysis of several planar curves, referred to as a multivariate planar curve. Modeling the contours jointly, rather than separately, preserves the inter-component information, such as their relative position, scale, and orientation, which is often essential to the analysis. Based on this model, we propose a joint alignment procedure and we extend core inferential tools to multivariate shapes: shape dissimilarity, Fréchet mean estimation, and tangent-space representation. These tangent coordinates are then used as predictors in standard functional classification models. A simulation study shows accurate recovery of deformation parameters over increasing noise levels. Then, through a cardiomegaly detection problem on segmented chest X-rays, we show that jointly modeling the contours is robust to misalignment and improves classification accuracy over both a contour-wise univariate analysis and a naive approach based on the raw curves.

stat.ME↗

arXiv2026

A Functional Data Framework For Analyzing Shapes and Textures in Images

Images represent objects characterized by contours and textures. From a statistical perspective these features can be defined as observations of continuous random functions. However, most existing approaches rely on pixel-based discretizations which lead to high-dimensional representations and heavy computational costs. In this note, we introduce an alternative more frugal representation. This representation assumes that the object has a star-shaped domain interior. Under this condition, we explore the analysis of images from a functional data analysis perspective. The proposed framework is illustrated on a real data supervised image classification problem.

stat.ME↗

arXiv2026

A Functional Approach to Curve Alignment and Shape Analysis

In many image analysis problems, the contours of objects carry important statistical information about shape. Such contours are typically affected by deformation variables including scaling, translation, rotation, and reparametrization. Previous studies in statistical shape analysis have mainly focused on analyzing contours and shapes through discrete observations. While this approach might offer computational advantages, it overlooks the continuous nature of these objects and their underlying geometric structure. It also ignores potential dependencies between the deformation variables and their effect on the shape, which may result in a loss of statistical information and reduced interpretability. In this paper, we introduce a novel framework for analyzing shapes within the context of Functional Data Analysis (FDA). Basis expansion techniques are employed to derive analytic solutions for the estimation of deformation variables, namely scaling, translation, rotation, and reparametrization, thereby achieving curve alignment. A generative model for random contours is then developed using principal component analysis techniques. Numerical experiments on simulated data and the \textit{MPEG-7} database demonstrate that our method successfully identifies deformation parameters and captures the underlying distribution of random contours in settings where traditional FDA methods fail.

stat.ME↗

arXiv2024

Fusion regression methods with repeated functional data

Linear regression and classification methods with repeated functional data are considered. For each statistical unit in the sample, a real-valued parameter is observed over time under different conditions related by some neighborhood structure (spatial, group, etc.). Two regression methods based on fusion penalties are proposed to consider the dependence induced by this structure. These methods aim to obtain parsimonious coefficient regression functions, by determining if close conditions are associated with common regression coefficient functions. The first method is a generalization to functional data of the variable fusion methodology based on the 1-nearest neighbor. The second one relies on the group fusion lasso penalty which assumes some grouping structure of conditions and allows for homogeneity among the regression coefficient functions within groups. Numerical simulations and an application of electroencephalography data are presented.

stat.ME↗