Related papers: M\"obius Convolutions for Spherical CNNs
Convolution kernels are the basic structural component of convolutional neural networks (CNNs). In the last years there has been a growing interest in fisheye cameras for many applications. However, the radially symmetric projection model…
Image registration is a fundamental task that aligns anatomical structures between images. While CNNs perform well, they lack rotation equivariance - a rotated input does not produce a correspondingly rotated output. This hinders…
Deep learning-based image registration methods have shown state-of-the-art performance and rapid inference speeds. Despite these advances, many existing approaches fall short in capturing spatially varying information in non-local regions…
Convolutional Neural Networks (CNNs) are a popular deep learning architecture widely applied in different domains, in particular in classifying over images, for which the concept of convolution with a filter comes naturally. Unfortunately,…
The M\"obius polynomial is an invariant of ranked posets, closely related to the M\"obius function. In this paper, we study the M\"obius polynomial of face posets of convex polytopes. We present formulas for computing the M\"obius…
The convolutional layers of standard convolutional neural networks (CNNs) are equivariant to translation. However, the convolution and fully-connected layers are not equivariant or invariant to other affine geometric transformations.…
Vision transformers have become popular as a possible substitute to convolutional neural networks (CNNs) for a variety of computer vision applications. These transformers, with their ability to focus on global relationships in images, offer…
For many years, it has been shown how much exploiting equivariances can be beneficial when solving image analysis tasks. For example, the superiority of convolutional neural networks (CNNs) compared to dense networks mainly comes from an…
We propose a framework for rotation and translation covariant deep learning using $SE(2)$ group convolutions. The group product of the special Euclidean motion group $SE(2)$ describes how a concatenation of two roto-translations results in…
Learning depth from spherical panoramas is becoming a popular research topic because a panorama has a full field-of-view of the environment and provides a relatively complete description of a scene. However, applying well-studied CNNs for…
Finding semantic correspondences is a challenging problem. With the breakthrough of CNNs stronger features are available for tasks like classification but not specifically for the requirements of semantic matching. In the following we…
The study of astronomical phenomena through ground-based observations is always challenged by the distorting effects of Earth's atmosphere. Traditional methods of post-facto image correction, essential for correcting these distortions,…
We use the method of equivariant moving frames to revisit the problem of normal forms and equivalence of nondegenerate real hypersurfaces M \subset C^2 under the pseudo-group action of holomorphic transformations. The moving frame…
Convolution is spatially-symmetric, i.e., the visual features are independent of its position in the image, which limits its ability to utilize contextual cues for visual recognition. This paper addresses this issue by introducing a…
The weight-sharing mechanism of convolutional kernels ensures translation-equivariance of convolution neural networks (CNNs). Recently, rotation-equivariance has been investigated. However, research on scale-equivariance or simultaneous…
Transformationally invariant processors constructed by transformed input vectors or operators have been suggested and applied to many applications. In this study, transformationally identical processing based on combining results of all…
From early image processing to modern computational imaging, successful models and algorithms have relied on a fundamental property of natural signals: symmetry. Here symmetry refers to the invariance property of signal sets to…
Let $\mathbb{M}(\mathbb{S}^{n+1})$ denote the M\"{o}bius transformation group of the $(n+1)$-dimensional sphere $\mathbb{S}^{n+1}$. A hypersurface $x:M^n\to \mathbb{S}^{n+1}$ is called a M\"{o}bius homogeneous hypersurface if there exists a…
Optical metasurfaces have enabled high-speed, low-power image processing within a compact footprint. However, reconfigurable imaging in such flat devices remains a critical challenge for fully harnessing their potential in practical…
Dynamic MR images possess various transformation symmetries,including the rotation symmetry of local features within the image and along the temporal dimension. Utilizing these symmetries as prior knowledge can facilitate dynamic MR imaging…