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Convolutional Neural Networks (CNNs) have exhibited their great power in a variety of vision tasks. However, the lack of transform-invariant property limits their further applications in complicated real-world scenarios. In this work, we…

Convolutional neural network (CNN) architectures utilize downsampling layers, which restrict the subsequent layers to learn spatially invariant features while reducing computational costs. However, such a downsampling operation makes it…

Texture classification is an important and challenging problem in many image processing applications. While convolutional neural networks (CNNs) achieved significant successes for image classification, texture classification remains a…

Standard convolutions are prevalent in image processing and deep learning, but their fixed kernels limits adaptability. Several deformation strategies of the reference kernel grid have been proposed. Yet, they lack a unified theoretical…

In view of the huge success of convolution neural networks (CNN) for image classification and object recognition, there have been attempts to generalize the method to general graph-structured data. One major direction is based on spectral…

Deep learning systems extensively use convolution operations to process input data. Though convolution is clearly defined for structured data such as 2D images or 3D volumes, this is not true for other data types such as sparse point…

Deep learning on non-Euclidean domains is important for analyzing complex geometric data that lacks common coordinate systems and familiar Euclidean properties. A central challenge in this field is to define convolution on domains, which…

This work addresses a fundamental challenge in applying deep learning to power systems: developing neural network models that transfer across significant system changes, including networks with entirely different topologies and…

The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks. Inspired by recent interest in geometric deep learning, which aims to generalize convolutional…

Point clouds are unstructured and unordered data, as opposed to images. Thus, most machine learning approach developed for image cannot be directly transferred to point clouds. In this paper, we propose a generalization of discrete…

Convolutional neural networks (CNN) have led to many state-of-the-art results spanning through various fields. However, a clear and profound theoretical understanding of the forward pass, the core algorithm of CNN, is still lacking. In…

In convolutional neural networks (CNNs), padding plays a pivotal role in preserving spatial dimensions throughout the layers. Traditional padding techniques do not explicitly distinguish between the actual image content and the padded…

For video and volumetric data understanding, 3D convolution layers are widely used in deep learning, however, at the cost of increasing computation and training time. Recent works seek to replace the 3D convolution layer with convolution…

Convolutional Neural Networks have revolutionized vision applications. There are image domains and representations, however, that cannot be handled by standard CNNs (e.g., spherical images, superpixels). Such data are usually processed…

Convolutional neural networks (CNNs) have achieved state-of-the-art results on many visual recognition tasks. However, current CNN models still exhibit a poor ability to be invariant to spatial transformations of images. Intuitively, with…

Recently, various convolutions based on continuous or discrete kernels for point cloud processing have been widely studied, and achieve impressive performance in many applications, such as shape classification, scene segmentation and so on.…

Convolutional neural networks (CNNs) have been used in many machine learning fields. In practical applications, the computational cost of convolutional neural networks is often high with the deepening of the network and the growth of data…

In this paper, we propose a novel formulation to extend CNNs to two-dimensional (2D) manifolds using orthogonal basis functions, called Zernike polynomials. In many areas, geometric features play a key role in understanding scientific…

Convolutional neural networks (CNNs) are being applied to an increasing number of problems and fields due to their superior performance in classification and regression tasks. Since two of the key operations that CNNs implement are…

Surface meshes are widely used shape representations and capture finer geometry data than point clouds or volumetric grids, but are challenging to apply CNNs directly due to their non-Euclidean structure. We use parallel frames on surface…