Related papers: M\"obius Convolutions for Spherical CNNs

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…

We establish an equivalence between two different quantum quench problems, the joining local quantum quench and the M\"obius quench, in the context of $(1+1)$-dimensional conformal field theory (CFT). Here, in the former, two initially…

Convolution is an equivariant operation, and image position does not affect its result. A recent study shows that the zero-padding employed in convolutional layers of CNNs provides position information to the CNNs. The study further claims…

There is a resurging interest in developing a neural-network-based solution to the supervised machine learning problem. The convolutional neural network (CNN) will be studied in this note. To begin with, we introduce a RECOS transform as a…

In this paper we introduce a novel method for segmentation that can benefit from general semantics of Convolutional Neural Network (CNN). Our segmentation proposes visually and semantically coherent image segments. We use binary encoding of…

The Symmetric group $S_{n}$ manifests itself in large classes of quantum systems as the invariance of certain characteristics of a quantum state with respect to permuting the qubits. The subgroups of $S_{n}$ arise, among many other…

Semantic segmentation of remotely sensed urban scene images is required in a wide range of practical applications, such as land cover mapping, urban change detection, environmental protection, and economic assessment.Driven by rapid…

Like other applications in computer vision, medical image segmentation has been most successfully addressed using deep learning models that rely on the convolution operation as their main building block. Convolutions enjoy important…

We investigate the relationship between quasisymmetric and convergence groups acting on the circle. We show that the M\"obius transformations of the circle form a maximal convergence group. This completes the characterization of the…

Convolutional neural networks (CNNs) show outstanding performance in many image processing problems, such as image recognition, object detection and image segmentation. Semantic segmentation is a very challenging task that requires…

Object Skeletonization is the process of extracting skeletal, line-like representations of shapes. It provides a very useful tool for geometric shape understanding and minimal shape representation. It also has a wide variety of…

In recent years, computer-aided diagnosis has become an increasingly popular topic. Methods based on convolutional neural networks have achieved good performance in medical image segmentation and classification. Due to the limitations of…

Convolutional Neural Networks (CNNs) have become the state-of-the-art in supervised learning vision tasks. Their convolutional filters are of paramount importance for they allow to learn patterns while disregarding their locations in input…

Extending the translation equivariance property of convolutional neural networks to larger symmetry groups has been shown to reduce sample complexity and enable more discriminative feature learning. Further, exploiting additional symmetries…

The escalating energy demands and parallel-processing bottlenecks of electronic neural networks underscore the need for alternative computing paradigms. Optical neural networks, capitalizing on the inherent parallelism and speed of light…

Convolutional layers have long served as the primary workhorse for image classification. Recently, an alternative to convolution was proposed using the Sharpened Cosine Similarity (SCS), which in theory may serve as a better feature…

Convolutional neural networks (CNNs) have made great breakthroughs in 2D computer vision. However, their irregular structure makes it hard to harness the potential of CNNs directly on meshes. A subdivision surface provides a hierarchical…

Spherical equivariant graph neural networks (EGNNs) provide a principled framework for learning on three-dimensional molecular and biomolecular systems, where predictions must respect the rotational symmetries inherent in physics. These…

Convolutional neural network (CNN) based methods have achieved great successes in medical image segmentation, but their capability to learn global representations is still limited due to using small effective receptive fields of convolution…

The majority of medical images, especially those that resemble cells, have similar characteristics. These images, which occur in a variety of shapes, often show abnormalities in the organ or cell region. The convolution operation possesses…