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Motion segmentation in dynamic scenes is highly challenging, as conventional methods heavily rely on estimating camera poses and point correspondences from inherently noisy motion cues. Existing statistical inference or iterative…

Aerodynamic shape optimization has many industrial applications. Existing methods, however, are so computationally demanding that typical engineering practices are to either simply try a limited number of hand-designed shapes or restrict…

In wireless sensing applications, such as ISAC, one of the first crucial signal processing steps is the detection and estimation targets from a channel estimate. Effective algorithms in this context must be robust across a broad SNR range,…

Semantic segmentation is the task to cluster pixels on an image belonging to the same class. It is widely used in the real-world applications including autonomous driving, medical imaging analysis, industrial inspection, smartphone camera…

The principle of equivariance to symmetry transformations enables a theoretically grounded approach to neural network architecture design. Equivariant networks have shown excellent performance and data efficiency on vision and medical…

This study investigates the application of Riemannian geometry-based methods for brain decoding using invasive electrophysiological recordings. Although previously employed in non-invasive, the utility of Riemannian geometry for invasive…

Deep learning based pipelines for semantic segmentation often ignore structural information available on annotated images used for training. We propose a novel post-processing module enforcing structural knowledge about the objects of…

Computing intrinsic distances on discrete surfaces is at the heart of many minimization problems in geometry processing and beyond. Solving these problems is extremely challenging as it demands the computation of on-surface distances along…

Medical image segmentation is crucial for disease diagnosis and monitoring. Though effective, the current segmentation networks such as UNet struggle with capturing long-range features. More accurate models such as TransUNet, Swin-UNet, and…

In this paper we propose a deep learning approach for segmenting sub-cortical structures of the human brain in Magnetic Resonance (MR) image data. We draw inspiration from a state-of-the-art Fully-Convolutional Neural Network (F-CNN)…

Fully convolutional neural networks (CNNs) have proven to be effective at representing and classifying textural information, thus transforming image intensity into output class masks that achieve semantic image segmentation. In medical…

This paper advocates a novel framework for segmenting a dataset in a Riemannian manifold $M$ into clusters lying around low-dimensional submanifolds of $M$. Important examples of $M$, for which the proposed clustering algorithm is…

Recent works have demonstrated promising performances of neural networks on hyperbolic spaces and symmetric positive definite (SPD) manifolds. These spaces belong to a family of Riemannian manifolds referred to as symmetric spaces of…

Computing geodesics for Riemannian manifolds is a difficult task that often relies on numerical approximations. However, these approximations tend to be either numerically unstable, have slow convergence, or scale poorly with manifold…

Deep Neural Networks (DNNs) are widely used for decision making in a myriad of critical applications, ranging from medical to societal and even judicial. Given the importance of these decisions, it is crucial for us to be able to interpret…

Image segmentation is a complex mathematical problem, especially for images that contain intensity inhomogeneity and tightly packed objects with missing boundaries in between. For instance, Magnetic Resonance (MR) muscle images often…

Convolutional neural networks (CNNs) have been applied to various automatic image segmentation tasks in medical image analysis, including brain MRI segmentation. Generative adversarial networks have recently gained popularity because of…

With the rise of the Internet of Things, strategies for effectively processing big data are essential for discovering meaningul insights. The time series datasets produced by groups of interconnected devices contain valuable underlying…

Group equivariant convolutional neural networks (G-CNNs) have been successfully applied in geometric deep learning. Typically, G-CNNs have the advantage over CNNs that they do not waste network capacity on training symmetries that should…

We first introduce a class of divergence measures between power spectral density matrices. These are derived by comparing the suitability of different models in the context of optimal prediction. Distances between "infinitesimally close"…