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Supervised learning method requires a large volume of annotated datasets. Collecting such datasets is time-consuming and expensive. Until now, very few annotated COVID-19 imaging datasets are available. Although self-supervised learning…

Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…

Supervised training a deep neural network aims to "teach" the network to mimic human visual perception that is represented by image-and-label pairs in the training data. Superpixelized (SP) images are visually perceivable to humans, but a…

Object-level SLAM introduces semantic meaningful and compact object landmarks that help both indoor robot applications and outdoor autonomous driving tasks. However, the back end of object-level SLAM suffers from singularity problems…

Decoding approaches are widely used in neuroscience and machine learning to compare stimulus representations across neural systems, such as different brain regions, organisms, and deep learning models. Popular methods include decoding…

Most models of generative AI for images assume that images are inherently low-dimensional objects embedded within a high-dimensional space. Additionally, it is often implicitly assumed that thematic image datasets form smooth or piecewise…

While classical data analysis has addressed observations that are real numbers or elements of a real vector space, at present many statistical problems of high interest in the sciences address the analysis of data that consist of more…

Graph-based medical image segmentation represents anatomical structures using boundary graphs, providing fixed-topology landmarks and inherent population-level correspondences. However, their clinical adoption has been hindered by a major…

In this paper, we develop a new classification method for manifold-valued data in the framework of probabilistic learning vector quantization. In many classification scenarios, the data can be naturally represented by symmetric positive…

Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. The quality of the embeddings is usually determined by how well the geometry…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

Accurate analysis of histopathological images is critical for disease diagnosis and treatment planning. Whole-slide images (WSIs), which digitize tissue specimens at gigapixel resolution, are fundamental to this process but require…

Scribble-supervised medical image segmentation tackles the limitation of sparse masks. Conventional approaches alternate between: labeling pseudo-masks and optimizing network parameters. However, such iterative two-stage paradigm is…

Statistical shape modeling (SSM) is an essential tool for analyzing variations in anatomical morphology. In a typical SSM pipeline, 3D anatomical images, gone through segmentation and rigid registration, are represented using…

Symbolic regression aims to discover human-interpretable equations that explain observational data. However, existing approaches rely heavily on discrete structure search (e.g., genetic programming), which often leads to high computational…

Obtaining high-resolution (HR) segmentations from coarse annotations is a pervasive challenge in computer vision. Applications include inferring pixel-level segmentations from token-level labels in vision transformers, upsampling coarse…

Accurate registration of brain MRI scans is fundamental for cross-subject analysis in neuroscientific studies. This involves aligning both the cortical surface of the brain and the interior volume. Traditional methods treat volumetric and…

Riemannian neural networks, which extend deep learning techniques to Riemannian spaces, have gained significant attention in machine learning. To better classify the manifold-valued features, researchers have started extending Euclidean…

Statistical shape analysis is a very useful tool in a wide range of medical and biological applications. However, it typically relies on the ability to produce a relatively small number of features that can capture the relevant variability…

We introduce a parameterization method called Neural Bayes which allows computing statistical quantities that are in general difficult to compute and opens avenues for formulating new objectives for unsupervised representation learning.…