Related papers: Decomposition-Based Intrinsic Modeling of Shape-Co…

Multivariate functional data can be intrinsically multivariate like movement trajectories in 2D or complementary like precipitation, temperature, and wind speeds over time at a given weather station. We propose a multivariate functional…

A central challenge in analyzing multivariate interactions within complex systems is to decompose how multiple inputs jointly determine an output. Existing approaches generally operate on observed probability distributions and can conflate…

Samples of dynamic or time-varying networks and other random object data such as time-varying probability distributions are increasingly encountered in modern data analysis. Common methods for time-varying data such as functional data…

Intrinsic image decomposition is an important and long-standing computer vision problem. Given an input image, recovering the physical scene properties is ill-posed. Several physically motivated priors have been used to restrict the…

We propose a new 2D shape decomposition method based on the short-cut rule. The short-cut rule originates from cognition research, and states that the human visual system prefers to partition an object into parts using the shortest possible…

The continuous integration of experimental data into coherent models of the brain is an increasing challenge of modern neuroscience. Such models provide a bridge between structure and activity, and identify the mechanisms giving rise to…

The basic problem of shape complementarity analysis appears fundamental to applications as diverse as mechanical design, assembly automation, robot motion planning, micro- and nano-fabrication, protein-ligand binding, and rational drug…

We introduce a new framework to analyze shape descriptors that capture the geometric features of an ensemble of point clouds. At the core of our approach is the point of view that the data arises as sampled recordings from a metric…

In many real-world applications, functional data exhibit considerable variability in both amplitude and phase. This is especially true in biomechanical data such as the knee flexion angle dataset motivating our work, where timing…

Modern geometric measure theory, developed largely to solve the Plateau problem, has generated a great deal of technical machinery which is unfortunately regarded as inaccessible by outsiders. Some of its tools (e.g., flat norm distance and…

In cluster analysis, a common first step is to scale the data aiming to better partition them into clusters. Even though many different techniques have throughout many years been introduced to this end, it is probably fair to say that the…

It is a standard assumption that datasets in high dimension have an internal structure which means that they in fact lie on, or near, subsets of a lower dimension. In many instances it is important to understand the real dimension of the…

Object-oriented data analysis is a fascinating and evolving field in modern statistical science, with the potential to make significant contributions to biomedical applications. This statistical framework facilitates the development of new…

Fine-grained action detection is an important task with numerous applications in robotics and human-computer interaction. Existing methods typically utilize a two-stage approach including extraction of local spatio-temporal features…

Recently, state-of-the-art results have been achieved in semantic segmentation using fully convolutional networks (FCNs). Most of these networks employ encoder-decoder style architecture similar to U-Net and are trained with images and the…

Clinical assessments for neuromuscular disorders, such as Spinal Muscular Atrophy (SMA) and Duchenne Muscular Dystrophy (DMD), continue to rely on subjective measures to monitor treatment response and disease progression. We introduce a…

Functional ANOVA offers a principled framework for interpretability by decomposing a model's prediction into main effects and higher-order interactions. For independent features, this decomposition is well-defined, strongly linked with SHAP…

We initiate a systematic study of intrinsic dimensional versions of classical functional inequalities which capture refined properties of the underlying objects. We focus on model spaces: Euclidean space, Hamming cube, and manifolds of…

The Transformer structures have been widely used in computer vision and have recently made an impact in the area of medical image registration. However, the use of Transformer in most registration networks is straightforward. These networks…

This paper addresses the fundamental task of estimating covariance matrix functions for high-dimensional functional data/functional time series. We consider two functional factor structures encompassing either functional factors with scalar…