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Convolutional neural networks (CNNs) are usually used as a backbone to design methods in biomedical image segmentation. However, the limitation of receptive field and large number of parameters limit the performance of these methods. In…
Understanding the structure of the brain, and how it changes with time and disease, is a core goal of structural neuroimaging. Contemporary approaches to structural brain analysis are dominated by voxel-wise, mass-univariate methods such as…
Convolutional neural networks (CNNs) are one of the most successful computer vision systems to solve object recognition. Furthermore, CNNs have major applications in understanding the nature of visual representations in the human brain. Yet…
Based on the continuous interpretation of deep learning cast as an optimal control problem, this paper investigates the benefits of employing B-spline basis functions to parameterize neural network controls across the layers. Rather than…
In this paper we study an emerging class of neural networks based on the morphological operators of dilation and erosion. We explore these networks mathematically from a tropical geometry perspective as well as mathematical morphology. Our…
Convolutional neural networks (CNNs) have massively impacted visual recognition in 2D images, and are now ubiquitous in state-of-the-art approaches. CNNs do not easily extend, however, to data that are not represented by regular grids, such…
Graph Neural Networks (GNNs) extend the success of neural networks to graph-structured data by accounting for their intrinsic geometry. While extensive research has been done on developing GNN models with superior performance according to a…
In many normative theories of synaptic plasticity, weight updates implicitly depend on the chosen parametrization of the weights. This problem relates, for example, to neuronal morphology: synapses which are functionally equivalent in terms…
This paper describes how realistic neuromorphic networks can have their connectivity properties fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the…
Precise identification of spinal nerve rootlets is relevant to delineate spinal levels for the study of functional activity in the spinal cord. The goal of this study was to develop an automatic method for the semantic segmentation of…
We use graphical methods to probe neural nets that classify images. Plots of t-SNE outputs at successive layers in a network reveal increasingly organized arrangement of the data points. They can also reveal how a network can diminish or…
One of the critical steps in improving accurate single neuron reconstruction from three-dimensional (3D) optical microscope images is the neuronal structure segmentation. However, they are always hard to segment due to the lack in quality.…
We investigate the computation of minimum-cost spanning trees satisfying prescribed vertex degree constraints: Given a graph $G$ and a constraint function $D$, we ask for a (minimum-cost) spanning tree $T$ such that for each vertex $v$, $T$…
Divergent brain connectivity is thought to underlie the behavioral and cognitive symptoms observed in many neurodevelopmental disorders. Quantifying divergence from neurotypical connectivity patterns offers a promising pathway to inform…
Understanding the common topological characteristics of the human brain network across a population is central to understanding brain functions. The abstraction of human connectome as a graph has been pivotal in gaining insights on the…
We present a novel approach to automatically segment magnetic resonance (MR) images of the human brain into anatomical regions. Our methodology is based on a deep artificial neural network that assigns each voxel in an MR image of the brain…
The coincidence similarity index, based on a combination of the Jaccard and overlap similarity indices, has noticeable properties in comparing and classifying data, including enhanced selectivity and sensitivity, intrinsic normalization,…
This paper presents methods to analyze functional brain networks and signals from graph spectral perspectives. The notion of frequency and filters traditionally defined for signals supported on regular domains such as discrete time and…
Recently, the deep learning community has given growing attention to neural architectures engineered to learn problems in relational domains. Convolutional Neural Networks employ parameter sharing over the image domain, tying the weights of…
We introduce the problem of finding a spanning tree along with a partition of the tree edges into fewest number of feasible sets, where constraints on the edges define feasibility. The motivation comes from wireless networking, where we…