Related papers: The Mean Shape under the Relative Curvature Condit…
We consider the problem of establishing dense correspondences within a set of related shapes of strongly varying geometry. For such input, traditional shape matching approaches often produce unsatisfactory results. We propose an ensemble…
This study introduces the Spatial Health and Population Estimator (SHAPE), a spatial microsimulation framework that applies hierarchical iterative proportional fitting (IPF) to estimate two health risk behaviors and eleven health outcomes…
We carry out the first main step towards the construction of new examples of complete embedded self-similar surfaces under mean curvature flow. An approximate solution is obtained by taking two known examples of self-similar surfaces and…
Given a computer model of a physical object, it is often quite difficult to visualize and quantify any global effects on the shape representation caused by local uncertainty and local errors in the data. This problem is further amplified…
A pseudo-outcrop visualization is demonstrated for borehole and full-diameter rock core images to augment the ubiquitous unwrapped cylinder view and thereby to assist non-specialist interpreters. The pseudo-outcrop visualization is…
This paper proposes an original Riemmanian geometry for low-rank structured elliptical models, i.e., when samples are elliptically distributed with a covariance matrix that has a low-rank plus identity structure. The considered geometry is…
Accurate characterization of hippocampal substructure is crucial for detecting subtle structural changes and identifying early neurodegenerative biomarkers. However, high inter-subject variability and complex folding pattern of human…
Perception research provides strong evidence in favor of part based representation of shapes in human visual system. Despite considerable differences among different theories in terms of how part boundaries are found, there is substantial…
Conformal Prediction (CP) is a principled framework for quantifying uncertainty in blackbox learning models, by constructing prediction sets with finite-sample coverage guarantees. Traditional approaches rely on scalar nonconformity scores,…
The construction of confidence regions for parameter vectors is a difficult problem in the nonparametric setting, particularly when the sample size is not large. The bootstrap has shown promise in solving this problem, but empirical…
We introduce and begin to explore the mean and median of finite sets of shapes represented as integral currents. The median can be computed efficiently in practice, and we focus most of our theoretical and computational attention on…
The Reeb space, which generalizes the notion of a Reeb graph, is one of the few tools in topological data analysis and visualization suitable for the study of multivariate scientific datasets. First introduced by Edelsbrunner et al., it…
Although transformer-based models have been dominating the field of deep learning, various studies of their embedding space have shown that they suffer from "representation degeneration problem": embeddings tend to be distributed in a…
Modern deep learning reconstruction algorithms generate impressively realistic scans from sparse inputs, but can often produce significant inaccuracies. This makes it difficult to provide statistically guaranteed claims about the true state…
Reshaping accurate and realistic 3D human bodies from anthropometric parameters (e.g., height, chest size, etc.) poses a fundamental challenge for person identification, online shopping and virtual reality. Existing approaches for creating…
In this thesis we develop a functional analytic framework for shape optimization with elliptic partial differential equation (PDE) constraints in classical function spaces (H\"older spaces). This approach is motivated by shape optimization…
How can one analyze detailed 3D biological objects, such as neurons and botanical trees, that exhibit complex geometrical and topological variation? In this paper, we develop a novel mathematical framework for representing, comparing, and…
Grasping objects of different shapes and sizes - a foundational, effortless skill for humans - remains a challenging task in robotics. Although model-based approaches can predict stable grasp configurations for known object models, they…
Ordinal embedding aims at finding a low dimensional representation of objects from a set of constraints of the form "item $j$ is closer to item $i$ than item $k$". Typically, each object is mapped onto a point vector in a low dimensional…
We present RibPull, a methodology that utilizes implicit occupancy fields to bridge computational geometry and medical imaging. Implicit 3D representations use continuous functions that handle sparse and noisy data more effectively than…