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We introduce a new spatial data structure for high dimensional data called the \emph{approximate principal direction tree} (APD tree) that adapts to the intrinsic dimension of the data. Our algorithm ensures vector-quantization accuracy…

Similarity plays a fundamental role in many areas, including data mining, machine learning, statistics and various applied domains. Inspired by the success of ensemble methods and the flexibility of trees, we propose to learn a similarity…

The kernel method is an essential tool for the study of generating series of walks in the quarter plane. This method involves equating to zero a certain polynomial, the kernel polynomial, and using properties of the curve, the kernel curve,…

Feature descriptors of point clouds are used in several applications, such as registration and part segmentation of 3D point clouds. Learning discriminative representations of local geometric features is unquestionably the most important…

This work derives closed-form expressions computing the expectation of co-presence and of number of co-occurrences of nodes on paths sampled from a network according to general path weights (a bag of paths). The underlying idea is that two…

Diffusion maps are a commonly used kernel-based method for manifold learning, which can reveal intrinsic structures in data and embed them in low dimensions. However, as with most kernel methods, its implementation requires a heavy…

While balancing covariates between groups is central for observational causal inference, selecting which features to balance remains a challenging problem. Kernel balancing is a promising approach that first estimates a kernel that captures…

Some lung diseases are related to bronchial airway structures and morphology. Although airway segmentation from chest CT volumes is an important task in the computer-aided diagnosis and surgery assistance systems for the chest, complete 3-D…

The cerebrovascular tree is a complex anatomical structure that plays a crucial role in the brain irrigation. A precise identification of the bifurcations in the vascular network is essential for understanding various cerebral pathologies.…

Accurate coronary artery segmentation from coronary computed tomography angiography is essential for quantitative coronary analysis and clinical decision support. Nevertheless, reliable segmentation remains challenging because of small…

We present a unified statistical approach to modeling disconnected 3D anatomical structures extracted from medical images. Due to image acquisition and preprocessing noises, it is expected the imaging data is noisy. The surface coordinates…

Respiratory diseases impose a significant burden on global health, with current diagnostic and management practices primarily reliant on specialist clinical testing. This work aims to develop machine learning-based algorithms to facilitate…

Decision forests are widely used for classification and regression tasks. A lesser known property of tree-based methods is that one can construct a proximity matrix from the tree(s), and these proximity matrices are induced kernels. While…

Purpose: to optimize a pipeline of clinical data gathering and CT images processing implemented during the COVID-19 pandemic crisis and to develop artificial intelligence model for different of viral pneumonia. Methods: 1028 chest CT image…

Rooted, weighted continuum random trees are used to describe limits of sequences of random discrete trees. Formally, they are random quadruples $(\mathcal{T},d,r,p)$, where $(\mathcal{T},d)$ is a tree-like metric space, $r\in\mathcal{T}$ is…

Segmentation is often an essential intermediate step in image analysis. A volume segmentation characterizes the underlying volume image in terms of geometric information--segments, faces between segments, curves in which several faces…

This work addresses the problem of non-rigid registration of 3D scans, which is at the core of shape modeling techniques. Firstly, we propose a new kernel based on geodesic distances for the Gaussian Process Morphable Models (GPMMs)…

We propose a framework for 2D shape analysis using positive definite kernels defined on Kendall's shape manifold. Different representations of 2D shapes are known to generate different nonlinear spaces. Due to the nonlinearity of these…

Coronary Artery Disease (CAD) diagnostic to be a major global cause of death, necessitating innovative solutions. Addressing the critical importance of early CAD detection and its impact on the mortality rate, we propose the potential of…

Much information about a graph can be obtained by studying its spanning trees. On the other hand, a graph can be regarded as a 1-dimensional cell complex, raising the question of developing a theory of trees in higher dimension. As observed…