Related papers: Convolutional Networks for Spherical Signals
We discuss how the kernel convolution approach can be used to accurately approximate the spatial covariance model on a sphere using spherical distances between points. A detailed derivation of the required formulas is provided. The proposed…
Pixelizations of Platonic solids such as the cube and icosahedron have been widely used to represent spherical data, from climate records to Cosmic Microwave Background maps. Platonic solids have well-known global symmetries. Once we…
Exploiting data invariances is crucial for efficient learning in both artificial and biological neural circuits. Understanding how neural networks can discover appropriate representations capable of harnessing the underlying symmetries of…
This paper demonstrates spherical convolutional neural networks (S-CNN) offer distinct advantages over conventional fully-connected networks (FCN) at estimating scalar parameters of tissue microstructure from diffusion MRI (dMRI). Such…
Convolutions encode equivariance symmetries into neural networks leading to better generalisation performance. However, symmetries provide fixed hard constraints on the functions a network can represent, need to be specified in advance, and…
Due to the current lack of large-scale datasets at the million-scale level, tasks involving panoramic images predominantly rely on existing two-dimensional pre-trained image benchmark models as backbone networks. However, these networks are…
The translation equivariance of convolutions can make convolutional neural networks translation equivariant or invariant. Equivariance to other transformations (e.g. rotations, affine transformations, scalings) may also be desirable as soon…
We demonstrate the use of machine learning through convolutional neural networks to solve inverse design problems of optical resonator engineering. The neural network finds a harmonic modulation of a spherical mirror to generate a resonator…
We study inverse problems consisting on determining medium properties using the responses to probing waves from the machine learning point of view. Based on the understanding of propagation of waves and their nonlinear interactions, we…
Convolutional neural network (CNN) has achieved impressive success in computer vision during the past few decades. The image convolution operation helps CNNs to get good performance on image-related tasks. However, the image convolution has…
Modern deep neural networks require a tremendous amount of data to train, often needing hundreds or thousands of labeled examples to learn an effective representation. For these networks to work with less data, more structure must be built…
Partial differential equation (PDE) models and their associated variational energy formulations are often rotationally invariant by design. This ensures that a rotation of the input results in a corresponding rotation of the output, which…
Convolutional neural networks revolutionized computer vision and natrual language processing. Their efficiency, as compared to fully connected neural networks, has its origin in the architecture, where convolutions reflect the translation…
Performance of neural networks can be significantly improved by encoding known invariance for particular tasks. Many image classification tasks, such as those related to cellular imaging, exhibit invariance to rotation. We present a novel…
In this work, we propose "tangent images," a spherical image representation that facilitates transferable and scalable $360^\circ$ computer vision. Inspired by techniques in cartography and computer graphics, we render a spherical image to…
Convolutional neural networks (CNNs) have achieved remarkable performance in various fields, particularly in the domain of computer vision. However, why this architecture works well remains to be a mystery. In this work we move a small step…
In this paper we challenge the common assumption that convolutional layers in modern CNNs are translation invariant. We show that CNNs can and will exploit the absolute spatial location by learning filters that respond exclusively to…
The widespread success of convolutional neural networks may largely be attributed to their intrinsic property of translation equivariance. However, convolutions are not equivariant to variations in scale and fail to generalize to objects of…
Steerable convolutional neural networks (SCNNs) enhance task performance by modelling geometric symmetries through equivariance constraints on weights. Yet, unknown or varying symmetries can lead to overconstrained weights and decreased…
Spatial transformer networks (STNs) were designed to enable convolutional neural networks (CNNs) to learn invariance to image transformations. STNs were originally proposed to transform CNN feature maps as well as input images. This enables…