Related papers: Combining high-order metric interpolation and geom…

Object pose estimation is a prominent task in computer vision. The object pose gives the orientation and translation of the object in real-world space, which allows various applications such as manipulation, augmented reality, etc. Various…

This paper introduces a new mathematical formulation and numerical approach for the computation of distances and geodesics between immersed planar curves. Our approach combines the general simplifying transform for first-order elastic…

We propose the first general framework to automatically correct different types of geometric distortion in a single input image. Our proposed method employs convolutional neural networks (CNNs) trained by using a large synthetic distortion…

We propose SharpDepth, a novel approach to monocular metric depth estimation that combines the metric accuracy of discriminative depth estimation methods (e.g., Metric3D, UniDepth) with the fine-grained boundary sharpness typically achieved…

This paper presents strong worst-case iteration and operation complexity guarantees for Riemannian adaptive regularized Newton methods, a unified framework encompassing both Riemannian adaptive regularization (RAR) methods and Riemannian…

A number of key scientific computing applications that are based upon tensor-product grid constructions, such as numerical weather prediction (NWP) and combustion simulations, require property-preserving interpolation. Essentially…

Orientation learning plays a pivotal role in many tasks. However, the rotation group SO(3) is a Riemannian manifold. As a result, the distortion caused by non-Euclidean geometric nature introduces difficulties to the incorporation of local…

Mask-guided matting networks have achieved significant improvements and have shown great potential in practical applications in recent years. However, simply learning matting representation from synthetic and lack-of-real-world-diversity…

We propose a deep learning strategy to estimate the mean curvature of two-dimensional implicit interfaces in the level-set method. Our approach is based on fitting feed-forward neural networks to synthetic data sets constructed from…

High-order implicit shock tracking (fitting) is a class of high-order, optimization-based numerical methods to approximate solutions of conservation laws with non-smooth features by aligning elements of the computational mesh with…

We investigate the use of regularized Newton methods with adaptive norms for optimizing neural networks. This approach can be seen as a second-order counterpart of adaptive gradient methods, which we here show to be interpretable as…

Metric embeddings are a widely used method in algorithm design, where generally a ``complex'' metric is embedded into a simpler, lower-dimensional one. Historically, the theoretical computer science community has focused on bi-Lipschitz…

Interpolation methodologies have been widely used within the domain of indoor positioning systems. However, existing indoor positioning interpolation algorithms exhibit several inherent limitations, including reliance on complex…

Neural implicit representations have emerged as a powerful paradigm for 3D reconstruction. However, despite their success, existing methods fail to capture fine geometric details and thin structures, especially in scenarios where only…

Neural implicit surfaces have become an important technique for multi-view 3D reconstruction but their accuracy remains limited. In this paper, we argue that this comes from the difficulty to learn and render high frequency textures with…

Metric learning aims to embed one metric space into another to benefit tasks like classification and clustering. Although a greatly distorted metric space has a high degree of freedom to fit training data, it is prone to overfitting and…

Recent techniques have been successful in reconstructing surfaces as level sets of learned functions (such as signed distance fields) parameterized by deep neural networks. Many of these methods, however, learn only closed surfaces and are…

In this paper, we suggest two ways of calculating interpolation models for unconstrained smooth nonlinear optimization when Hessian-vector products are available. The main idea is to interpolate the objective function using a quadratic on a…

Neural surrogates for stiff differential-algebraic equations (DAEs) face two barriers: soft-constraint methods leave algebraic residuals that stiffness amplifies into errors, and hard-constraint methods require trajectory data from stiff…

Encoding 3D points is one of the primary steps in learning-based implicit scene representation. Using features that gather information from neighbors with multi-resolution grids has proven to be the best geometric encoder for this task.…