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Despite being vastly ignored in the literature, coping with topological noise is an issue of increasing importance, especially as a consequence of the increasing number and diversity of 3D polygonal models that are captured by devices of…

Surface parameterizations are widely applied in computer graphics, medical imaging and transformation optics. In this paper, we rigorously derive the gradient vector and Hessian matrix of the discrete conformal energy for spherical…

Flattening curved, wrinkled, and rotated document images captured by portable photographing devices, termed document image dewarping, has become an increasingly important task with the rise of digital economy and online working. Although…

This paper addresses the problem of document image dewarping, which aims at eliminating the geometric distortion in document images for document digitization. Instead of designing a better neural network to approximate the optical flow…

Triangulated meshes have become ubiquitous discrete-surface representations. In this paper we address the problem of how to maintain the manifold properties of a surface while it undergoes strong deformations that may cause topological…

Kernel density estimation is a key component of a wide variety of algorithms in machine learning, Bayesian inference, stochastic dynamics and signal processing. However, the unsupervised density estimation technique requires tuning a…

Depth estimation is an essential component in understanding the 3D geometry of a scene, with numerous applications in urban and indoor settings. These scenes are characterized by a prevalence of human made structures, which in most of the…

Document dewarping aims to rectify deformations in photographic document images, thus improving text readability, which has attracted much attention and made great progress, but it is still challenging to preserve document structures. Given…

We extend a well-known theorem by Jones and Makarov [JM] on the singularity of boundary distortion of planar conformal mappings. We use a different technique to recover the previous result and, moreover, generalize the result for…

We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…

We present a novel Eigenentropy-optimized neighboorhood densification strategy EntON in 3D Gaussian Splatting (3DGS) for geometrically accurate and high-quality rendered 3D reconstruction. While standard 3DGS produces Gaussians whose…

This paper addresses the limitations of existing 3D Gaussian Splatting (3DGS) methods, particularly their reliance on adaptive density control, which can lead to floating artifacts and inefficient resource usage. We propose a novel densify…

In the classical context of robotic mapping and localization, map matching is typically defined as the task of finding a rigid transformation (i.e., 3DOF rotation/translation on the 2D moving plane) that aligns the query and reference maps…

In this paper, we introduce a definition of discrete conformality for triangulated surfaces with flat cone metrics and describe an algorithm for solving the problem of prescribing curvature, that is to deform the metric discrete conformally…

3D Gaussian Splatting (3DGS) has recently attracted wide attentions in various areas such as 3D navigation, Virtual Reality (VR) and 3D simulation, due to its photorealistic and efficient rendering performance. High-quality reconstrution of…

Although shape correspondence is a central problem in geometry processing, most methods for this task apply only to two-dimensional surfaces. The neglected task of volumetric correspondence--a natural extension relevant to shapes extracted…

The parameterization of open and closed anatomical surfaces is of fundamental importance in many biomedical applications. Spherical harmonics, a set of basis functions defined on the unit sphere, are widely used for anatomical shape…

With advances in technology, there has been growing interest in developing effective mapping methods for 3-dimensional objects in recent years. Volumetric parameterization for 3D solid manifolds plays an important role in processing 3D…

We introduce a linear dimensionality reduction technique preserving topological features via persistent homology. The method is designed to find linear projection $L$ which preserves the persistent diagram of a point cloud $\mathbb{X}$ via…

Geometric rectification of images of distorted documents finds wide applications in document digitization and Optical Character Recognition (OCR). Although smoothly curved deformations have been widely investigated by many works, the most…