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We propose an Euler transformation that transforms a given $d$-dimensional cell complex $K$ for $d=2,3$ into a new $d$-complex $\hat{K}$ in which every vertex is part of a uniform even number of edges. Hence every vertex in the graph…
Automatic tumor segmentation is a crucial step in medical image analysis for computer-aided diagnosis. Although the existing methods based on convolutional neural networks (CNNs) have achieved the state-of-the-art performance, many…
Dual-energy computed tomography (DECT) is an advanced CT scanning technique enabling material characterization not possible with conventional CT scans. It allows the reconstruction of energy decay curves at each 3D image voxel, representing…
Cellular Electron Cryo-Tomography (CECT) is a powerful imaging technique for the 3D visualization of cellular structure and organization at submolecular resolution. It enables analyzing the native structures of macromolecular complexes and…
We present a unified group-theoretical derivation of the Continuous Wavelet Transform (CWT) on the circle $\mathbb S^1$ and the real line $\mathbb{R}$, following the general formalism of Coherent States (CS) associated to unitary square…
Semantic segmentation of brain tumors is a fundamental medical image analysis task involving multiple MRI imaging modalities that can assist clinicians in diagnosing the patient and successively studying the progression of the malignant…
Real-world graphs naturally exhibit hierarchical or cyclical structures that are unfit for the typical Euclidean space. While there exist graph neural networks that leverage hyperbolic or spherical spaces to learn representations that embed…
Breast cancer is one of the common cancers that endanger the health of women globally. Accurate target lesion segmentation is essential for early clinical intervention and postoperative follow-up. Recently, many convolutional neural…
Recently, the use of circle representation has emerged as a method to improve the identification of spherical objects (such as glomeruli, cells, and nuclei) in medical imaging studies. In traditional bounding box-based object detection,…
Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being…
The Euler characteristic (EC) is a powerful topological descriptor that can be used to quantify the shape of data objects that are represented as fields/manifolds. Fast methods for computing the EC are required to enable processing of…
We consider a topological integral transform of Bessel (concentric isospectral sets) type and Fourier (hyperplane isospectral sets) type, using the Euler characteristic as a measure. These transforms convert constructible $\zed$-valued…
Brain tumor segmentation is an active research area due to the difficulty in delineating highly complex shaped and textured tumors as well as the failure of the commonly used U-Net architectures. The combination of different neural…
In this work, a general definition of convolution between two arbitrary Ultradistributions of Exponential type (UET) is given. The product of two arbitrary UET is defined via the convolution of its corresponding Fourier Transforms. Some…
Electrical Impedance Tomography (EIT) is a powerful imaging technique with diverse applications, e.g., medical diagnosis, industrial monitoring, and environmental studies. The EIT inverse problem is about inferring the internal conductivity…
The elliptic genus (EG) of a compact complex manifold was introduced as a holomorphic Euler characteristic of some formal power series with vector bundle coefficients. EG is an automorphic form in two variables only if the manifold is a…
Quantifying the dynamics of tumor burden reveals useful information about cancer evolution concerning treatment effects and drug resistance, which play a crucial role in advancing model-informed drug developments (MIDD) towards personalized…
We present a largely self contained account on the K-theory of a weighted smooth projective curve over an algebraically closed field. In particular, we discuss the weighted version of divisor theory, Euler form, and Riemann-Roch theorem.…
Despite recent strides made by AI in image processing, the issue of mixed exposure, pivotal in many real-world scenarios like surveillance and photography, remains inadequately addressed. Traditional image enhancement techniques and current…
How can prior knowledge on the transformation invariances of a domain be incorporated into the architecture of a neural network? We propose Equivariant Transformers (ETs), a family of differentiable image-to-image mappings that improve the…