Related papers: A Functional Approach to Curve Alignment and Shape…
This article introduces a full mathematical and numerical framework for treating functional shapes (or fshapes) following the landmarks of shape spaces and shape analysis. Functional shapes can be described as signal functions supported on…
In a world increasingly awash with data, the need to extract meaningful insights from data has never been more crucial. Functional Data Analysis (FDA) goes beyond traditional data points, treating data as dynamic, continuous functions,…
In many phenomena, data are collected on a large scale and of different frequencies. In this context, functional data analysis (FDA) has become an important statistical methodology for analyzing and modeling such data. The approach of FDA…
Statistical shape modeling aims at capturing shape variations of an anatomical structure that occur within a given population. Shape models are employed in many tasks, such as shape reconstruction and image segmentation, but also shape…
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…
Diffusion models have become a leading framework in generative modeling, yet their theoretical understanding -- especially for high-dimensional data concentrated on low-dimensional structures -- remains incomplete. This paper investigates…
Reconstructing the missing parts of a curve has been the subject of much computational research, with applications in image inpainting, object synthesis, etc. Different approaches for solving that problem are typically based on processes…
Functional data analysis almost always involves smoothing discrete observations into curves, because they are never observed in continuous time and rarely without error. Although smoothing parameters affect the subsequent inference,…
The methodological contribution in this paper is motivated by biomechanical studies where data characterizing human movement are waveform curves representing joint measures such as flexion angles, velocity, acceleration, and so on. In many…
The present work shows a novel fractal dimension method for shape analysis. The proposed technique extracts descriptors from the shape by applying a multiscale approach to the calculus of the fractal dimension of that shape. The fractal…
The analysis of curves has been routinely dealt with using tools from functional data analysis. However its extension to multi-dimensional curves poses a new challenge due to its inherent geometric features that are difficult to capture…
Topological methods can provide a way of proposing new metrics and methods of scrutinising data, that otherwise may be overlooked. In this work, a method of quantifying the shape of data, via a topic called topological data analysis will be…
This paper explores the application of functional data analysis (FDA) as a means to study the dynamics of software evolution in the open source context. Several challenges in analyzing the data from software projects are discussed, an…
For the shape control of deformable free-form surfaces, simulation plays a crucial role in establishing the mapping between the actuation parameters and the deformed shapes. The differentiation of this forward kinematic mapping is usually…
The study of shapes is one of the most fundamental problems in life sciences. Although numerous methods have been developed for the morphometry of planar biological shapes over the past several decades, most of them focus solely on either…
There is growing interest in using the close connection between differential geometry and statistics to model smooth manifold-valued data. In particular, much work has been done recently to generalize principal component analysis (PCA), the…
Approximation theory plays an important role in image processing, especially image deconvolution and decomposition. For piecewise smooth images, there are many methods that have been developed over the past thirty years. The goal of this…
Functional Data Analysis (FDA) is an extension of traditional data analysis to functional data, for example spectra, temporal series, spatio-temporal images, gesture recognition data, etc. Functional data are rarely known in practice;…
Representing 3D shape deformations by linear models in high-dimensional space has many applications in computer vision and medical imaging, such as shape-based interpolation or segmentation. Commonly, using Principal Components Analysis a…
Functional data analysis (FDA) involves the analysis of data whose ideal units of observation are functions defined on some continuous domain, and the observed data consist of a sample of functions taken from some population, sampled on a…