Related papers: Banana: Banach Fixed-Point Network for Pointcloud …

Fine-grained image recognition is a challenging computer vision problem, due to the small inter-class variations caused by highly similar subordinate categories, and the large intra-class variations in poses, scales and rotations. In this…

Let $\Omega$ be a nonempty closed and convex subset of a uniformly smooth and uniformly convex real Banach space $\mathcal{X}$ with dual space $\mathcal{X}^*$. This article presents a hybrid algorithm for finding a common element of the set…

Interactive 3D point cloud segmentation enables efficient annotation of complex 3D scenes through user-guided prompts. However, current approaches are typically restricted in scope to a single domain (indoor or outdoor), and to a single…

In this paper, the convergence of alternating minimization is established for non-smooth convex optimization in Banach spaces, and novel rates of convergence are provided. As objective function a composition of a smooth and a non-smooth…

Motivated by the vast success of deep convolutional networks, there is a great interest in generalizing convolutions to non-Euclidean manifolds. A major complication in comparison to flat spaces is that it is unclear in which alignment a…

We present a novel rotation invariant architecture operating directly on point cloud data. We demonstrate how rotation invariance can be injected into a recently proposed point-based PCNN architecture, at all layers of the network,…

Recently, Ogita and Aishima proposed an efficient eigendecomposition refinement algorithm for the symmetric eigenproblem. Their basic algorithm involves division by the difference of two approximate eigenvalues, and can become unstable when…

This paper proposes EyeNet, a novel semantic segmentation network for point clouds that addresses the critical yet often overlooked parameter of coverage area size. Inspired by human peripheral vision, EyeNet overcomes the limitations of…

The explicit incorporation of task-specific inductive biases through symmetry has emerged as a general design precept in the development of high-performance machine learning models. For example, group equivariant neural networks have…

We show that deep ensembles become equivariant for all inputs and at all training times by simply using data augmentation. Crucially, equivariance holds off-manifold and for any architecture in the infinite width limit. The equivariance is…

We present a novel lightweight convolutional neural network for point cloud analysis. In contrast to many current CNNs which increase receptive field by downsampling point cloud, our method directly operates on the entire point sets without…

Many machine learning tasks involve learning functions that are known to be invariant or equivariant to certain symmetries of the input data. However, it is often challenging to design neural network architectures that respect these…

In spite of the recent progresses on classifying 3D point cloud with deep CNNs, large geometric transformations like rotation and translation remain challenging problem and harm the final classification performance. To address this…

In this paper, using sunny generalized nonexpansive retraction, we propose new extragradient and linesearch algorithms for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a…

Convolutional Neural Networks (CNNs) have performed extremely well on data represented by regularly arranged grids such as images. However, directly leveraging the classic convolution kernels or parameter sharing mechanisms on sparse 3D…

Conventional point cloud semantic segmentation methods usually employ an encoder-decoder architecture, where mid-level features are locally aggregated to extract geometric information. However, the over-reliance on these class-agnostic…

Invariant and equivariant networks have been successfully used for learning images, sets, point clouds, and graphs. A basic challenge in developing such networks is finding the maximal collection of invariant and equivariant linear layers.…

In this paper, we present a comprehensive point cloud semantic segmentation network that aggregates both local and global multi-scale information. First, we propose an Angle Correlation Point Convolution (ACPConv) module to effectively…

We prove an extension of a celebrated equivariant bifurcation result of J. Smoller and A. Wasserman, in an abstract framework for geometric variational problems. With this purpose, we prove a slice theorem for continuous affine actions of a…

The goal of point cloud assembly is to reconstruct a complete 3D shape by aligning multiple point cloud pieces. This work presents a novel equivariant solver for assembly tasks based on flow matching models. We first theoretically show that…