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We investigate different approaches to machine learning of line bundle cohomology on complex surfaces as well as on Calabi-Yau three-folds. Standard function learning based on simple fully connected networks with logistic sigmoids is…

Lower bounds on the generation of smooth bi-cubic surfaces imply that geometrically smooth ($G^1$) constructions need to satisfy conditions on the connectivity and layout. In particular, quadrilateral meshes of arbitrary topology can not in…

This paper proposes a novel algorithm for semisupervised learning. This algorithm learns graph cuts that maximize the margin with respect to the labels induced by the harmonic function solution. We motivate the approach, compare it to…

The robustness of image segmentation has been an important research topic in the past few years as segmentation models have reached production-level accuracy. However, like classification models, segmentation models can be vulnerable to…

A good object segmentation should contain clear contours and complete regions. However, mask-based segmentation can not handle contour features well on a coarse prediction grid, thus causing problems of blurry edges. While contour-based…

This paper proposes a simple technique of curve and surface construction with B-splines. Given a control polygon or a control mesh together with node ordinates corresponding to all control points, a rational curve or surface is obtained by…

Boundary representation (B-rep) is the industry standard for computer-aided design (CAD). While deep learning shows promise in processing B-rep models, existing methods suffer from a representation gap: continuous approaches offer…

Supervised machine learning provides state-of-the-art solutions to a wide range of computer vision problems. However, the need for copious labelled training data limits the capabilities of these algorithms in scenarios where such input is…

Poles and building edges are frequently observable objects on urban roads, conveying reliable hints for various computer vision tasks. To repetitively extract them as features and perform association between discrete LiDAR frames for…

The scarcity of labeled data often impedes the application of deep learning to the segmentation of medical images. Semi-supervised learning seeks to overcome this limitation by exploiting unlabeled examples in the learning process. In this…

Subgraph GNNs enhance message-passing GNNs expressivity by representing graphs as sets of subgraphs, demonstrating impressive performance across various tasks. However, their scalability is hindered by the need to process large numbers of…

Consider a sequence of closed, orientable surfaces of fixed genus $g$ in a Riemannian manifold $M$ with uniform upper bounds on mean curvature and area. We show that on passing to a subsequence and choosing appropriate parametrisations, the…

Many recent efforts have been devoted to designing sophisticated deep learning structures, obtaining revolutionary results on benchmark datasets. The success of these deep learning methods mostly relies on an enormous volume of labeled…

In this paper we propose a high-order accurate scheme for image segmentation based on the level-set method. In this approach, the curve evolution is described as the 0-level set of a representation function but we modify the velocity that…

Deep co-training has recently been proposed as an effective approach for image segmentation when annotated data is scarce. In this paper, we improve existing approaches for semi-supervised segmentation with a self-paced and self-consistent…

Multimodal learning aims to leverage information from diverse data modalities to achieve more comprehensive performance. However, conventional multimodal models often suffer from modality imbalance, where one or a few modalities dominate…

We develop Self2Seg, a self-supervised method for the joint segmentation and denoising of a single image. To this end, we combine the advantages of variational segmentation with self-supervised deep learning. One major benefit of our method…

This paper outlines a methodology for constructing a geometrically smooth interpolatory curve in $\mathbb{R}^d$ applicable to oriented and flattenable points with $d\ge 2$. The construction involves four essential components: local…

Lightweight and effective models are essential for devices with limited resources, such as intelligent vehicles. Structured pruning offers a promising approach to model compression and efficiency enhancement. However, existing methods often…

In this paper, we present a surface remeshing method with high approximation quality based on Principal Component Analysis. Given a triangular mesh and a user assigned polygon/vertex budget, traditional methods usually require the extra…