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Surgery for brain cancer is a major problem in neurosurgery. The diffuse infiltration into the surrounding normal brain by these tumors makes their accurate identification by the naked eye difficult. Since surgery is the common treatment…
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…
Recently, many methods to interpret and visualize deep neural network predictions have been proposed and significant progress has been made. However, a more class-discriminative and visually pleasing explanation is required. Thus, this…
We introduce Riemannian Integrated Gradients (RIG); an extension of Integrated Gradients (IG) to Riemannian manifolds. We demonstrate that RIG restricts to IG when the Riemannian manifold is Euclidean space. We show that feature attribution…
There has been a growing adoption of computer vision tools and technologies in architectural design workflows over the past decade. Notable use cases include point cloud generation, visual content analysis, and spatial awareness for robotic…
In the domain of image-set based classification, a considerable advance has been made by representing original image sets as covariance matrices which typical lie in a Riemannian manifold. Specifically, it is a Symmetric Positive Definite…
Symmetric Positive Definite (SPD) matrix learning methods have become popular in many image and video processing tasks, thanks to their ability to learn appropriate statistical representations while respecting Riemannian geometry of…
The brain computer interface (BCI) is a nonstimulatory direct and occasionally bidirectional communication link between the brain and a computer or an external device. Classically, EEG-based BCI algorithms have relied on models such as…
The classification of shapes is of great interest in diverse areas ranging from medical imaging to computer vision and beyond. While many statistical frameworks have been developed for the classification problem, most are strongly tied to…
Segmentation of very large images is a common problem in microscopy, medical imaging or remote sensing. The problem is usually addressed by sliding window inference, which can theoretically lead to seamlessly stitched predictions. However,…
Generating realistic brain connectivity matrices is key to analyzing population heterogeneity in brain organization, understanding disease, and augmenting data in challenging classification problems. Functional connectivity matrices lie in…
A major hurdle to clinical translation of brain-machine interfaces (BMIs) is that current decoders, which are trained from a small quantity of recent data, become ineffective when neural recording conditions subsequently change. We tested…
In this work, we investigate Riemannian geometry based dimensionality reduction methods that respect the underlying manifold structure of the data. In particular, we focus on Principal Geodesic Analysis (PGA) as a nonlinear generalization…
Restricted Boltzmann Machines (RBMs) and models derived from them have been successfully used as basic building blocks in deep artificial neural networks for automatic features extraction, unsupervised weights initialization, but also as…
The cognitive framework of conceptual spaces bridges the gap between symbolic and subsymbolic AI by proposing an intermediate conceptual layer where knowledge is represented geometrically. There are two main approaches for obtaining the…
Recent work has demonstrated that complex visual stimuli can be decoded from human brain activity using deep generative models, offering new ways to probe how the brain represents real-world scenes. However, many existing approaches first…
Diffusion-weighted magnetic resonance imaging (dMRI) is widely used to assess the brain white matter. One of the most common computations in dMRI involves cross-subject tract-specific analysis, whereby dMRI-derived biomarkers are compared…
Recently, advanced technologies have unlimited potential in solving various problems with a large amount of data. However, these technologies have yet to show competitive performance in brain-computer interfaces (BCIs) which deal with brain…
Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these problems by equipping the constraint set with a Riemannian…
Linear models are widely used in computational neuroimaging to identify biomarkers associated with brain pathologies. However, interpreting the learned weights remains challenging, as they do not always yield clinically meaningful insights.…