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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…

In this paper, we address a manifold constrained nonsmooth optimization problem involving the composition of a weakly convex function and a smooth mapping under the availability of a parametrization of the manifold. To find a stationary…

Thin surfaces, such as the leaves of a plant, pose a significant challenge for implicit surface reconstruction techniques, which typically assume a closed, orientable surface. We show that by approximately interpolating a point cloud of the…

Point clouds are a basic data type that is increasingly of interest as 3D content becomes more ubiquitous. Applications using point clouds include virtual, augmented, and mixed reality and autonomous driving. We propose a more efficient…

Surface reconstruction from an unorganized point cloud is an important problem due to its widespread applications. White noise, possibly clustered outliers, and noisy perturbation may be generated when a point cloud is sampled from a…

We propose the use of a Transformer to accurately predict normals from point clouds with noise and density variations. Previous learning-based methods utilize PointNet variants to explicitly extract multi-scale features at different input…

Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms in that it does not make a low rank assumption. This makes MMF especially well suited to modeling certain types of graphs with complex…

We propose an unsupervised image fusion architecture for multiple application scenarios based on the combination of multi-scale discrete wavelet transform through regional energy and deep learning. To our best knowledge, this is the first…

Wavelet (Besov) priors are a promising way of reconstructing indirectly measured fields in a regularized manner. We demonstrate how wavelets can be used as a localized basis for reconstructing permeability fields with sharp interfaces from…

In this work, we study the perception problem for sampled surfaces (possibly with boundary) using tools from computational topology, specifically, how to identify their underlying topology starting from point-cloud samples in space, such as…

Wavelets are waveform functions that describe transient and unstable variations, such as noises. In this work, we study the advantages of discrete and continuous wavelet transforms (DWT and CWT) of microlensing data to denoise them and…

The optimization of deep neural networks can be more challenging than traditional convex optimization problems due to the highly non-convex nature of the loss function, e.g. it can involve pathological landscapes such as saddle-surfaces…

Convolution on 3D point clouds that generalized from 2D grid-like domains is widely researched yet far from perfect. The standard convolution characterises feature correspondences indistinguishably among 3D points, presenting an intrinsic…

Diffusion models have emerged as potential tools to tackle the challenge of sparse-view CT reconstruction, displaying superior performance compared to conventional methods. Nevertheless, these prevailing diffusion models predominantly focus…

Recently, it has been proven [R. Soc. Open Sci. 1 (2014) 140124] that the continuous wavelet transform with non-admissible kernels (approximate wavelets) allows for an existence of the exact inverse transform. Here we consider the…

Exploiting convolutional neural networks for point cloud processing is quite challenging, due to the inherent irregular distribution and discrete shape representation of point clouds. To address these problems, many handcrafted convolution…

We propose a general scheme for solving convex and non-convex optimization problems on manifolds. The central idea is that, by adding a multiple of the squared retraction distance to the objective function in question, we "convexify" the…

Image Fusion, a technique which combines complimentary information from different images of the same scene so that the fused image is more suitable for segmentation, feature extraction, object recognition and Human Visual System. In this…

(Bi)orthogonal (multi)wavelets on the real line have been extensively studied and employed in applications with success. A lot of problems in applications are defined on bounded intervals or domains. Therefore, it is important in both…

This paper presents a learning-based, lossless compression method for static point cloud geometry, based on context-adaptive arithmetic coding. Unlike most existing methods working in the octree domain, our encoder operates in a hybrid…