Related papers: Ellipsoid fitting with the Cayley transform

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Data heterogeneity is an inherent challenge that hinders the performance of federated learning (FL). Recent studies have identified the biased classifiers of local models as the key bottleneck. Previous attempts have used classifier…

Clustered federated learning (CFL) addresses the performance challenges posed by data heterogeneity in federated learning (FL) by organizing edge devices with similar data distributions into clusters, enabling collaborative model training…

Federated Learning (FL) enables collaborative model training across distributed devices while preserving data privacy. Nonetheless, the heterogeneity of edge devices often leads to inconsistent performance of the globally trained models,…

We study a popular algorithm for fitting polynomial curves to scattered data based on the least squares with gradient weights. We show that sometimes this algorithm admits a substantial reduction of complexity, and, furthermore, find…

Elliptic Fourier analysis (EFA) is a powerful tool for shape analysis, which is often employed in geometric morphometrics. However, the normalization of elliptic Fourier descriptors has persistently posed challenges in obtaining unique…

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Given a set of 2-dimensional (2-D) scattering points, which are usually obtained from the edge detection process, the aim of ellipse fitting is to construct an elliptic equation that best fits the collected observations. However, some of…

Inverse ellipsometry, i.e., reconstructing optical constants and film thickness from the measured phase difference $\Delta$ and amplitude ratio $\Psi$, is a fundamentally ill-posed problem. Traditional solutions rely on slow, expert-driven…

We introduce the notion of multiscale covariance tensor fields (CTF) associated with Euclidean random variables as a gateway to the shape of their distributions. Multiscale CTFs quantify variation of the data about every point in the data…

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Fitting a body to a 3D clothed human point cloud is a common yet challenging task. Traditional optimization-based approaches use multi-stage pipelines that are sensitive to pose initialization, while recent learning-based methods often…

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Deep convolutional Neural Networks (CNN) are the state-of-the-art performers for object detection task. It is well known that object detection requires more computation and memory than image classification. Thus the consolidation of a…

Multi-dimensional distributions of discrete data that resemble ellipsoids arise in numerous areas of science, statistics, and computational geometry. We describe a complete algebraic algorithm to determine the quadratic form specifying the…

Top-down methods dominate the field of 3D human pose and shape estimation, because they are decoupled from human detection and allow researchers to focus on the core problem. However, cropping, their first step, discards the location…

Ellipse fitting, an essential component in pupil or iris tracking based video oculography, is performed on previously segmented eye parts generated using various computer vision techniques. Several factors, such as occlusions due to eyelid…

Clustering high-dimensional data is especially challenging when cluster distributions are heavy tailed and only approximately elliptical. Existing high-dimensional methods are largely built for Gaussian or other light-tailed models, whereas…

Modern datasets often contain high-dimensional features exhibiting complex dependencies. To effectively analyze such data, dimensionality reduction methods rely on estimating the dataset's intrinsic dimension (id) as a measure of its…