Related papers: Rao distances and Conformal Mapping

Lipman et al. [ACM Transactions on Graphics 29 (3) (2010), 1--11] introduced the concept of biharmonic distance to measure the distances between pairs of points on a 3D surface. Biharmonic distance has some advantages over resistance…

Capturing the 3D geometry of transparent objects is a challenging task, ill-suited for general-purpose scanning and reconstruction techniques, since these cannot handle specular light transport phenomena. Existing state-of-the-art methods,…

Mapping is crucial for spatial reasoning, planning and robot navigation. Existing approaches range from metric, which require precise geometry-based optimization, to purely topological, where image-as-node based graphs lack explicit…

There is rising interest in differentiable rendering, which allows explicitly modeling geometric priors and constraints in optimization pipelines using first-order methods such as backpropagation. Incorporating such domain knowledge can…

The method for approximation of planar curve by circular arcs with length preservation, proposed by I.Kh. Sabitov and A.V. Slovesnov, is analyzed. We extend the applicability of the method, and consider some corollaries, not related to the…

With the advancement of computer technology, there is a surge of interest in effective mapping methods for objects in higher-dimensional spaces. To establish a one-to-one correspondence between objects, higher-dimensional quasi-conformal…

Lidar based 3D object detection and classification tasks are essential for automated driving(AD). A Lidar sensor can provide the 3D point coud data reconstruction of the surrounding environment. But the detection in 3D point cloud still…

Rotary Position Embedding (RoPE) is widely adopted in large language models, but when applied to vision-language models (VLMs) it couples text and image position indices and can introduce spurious cross-modal relative-position bias. We…

In this paper, we consider holomorphic mappings between real hypersurfaces in different dimensional complex spaces. We give a number of conditions that imply that such mappings are transversal to the target hypersurface at most points.

The past decade has witnessed the rapid development of feature representation learning and distance metric learning, whereas the two steps are often discussed separately. To explore their interaction, this work proposes an end-to-end…

Past research relates design creativity to 'divergent thinking,' i.e., how well the concept space is explored during the early phase of design. Researchers have argued that generating several concepts would increase the chances of producing…

Metric embeddings traditionally study how to map $n$ items to a target metric space such that distance lengths are not heavily distorted; but what if we only care to preserve the relative order of the distances (and not their length)? In…

In this short technical report, we define on the sample space R^D a distance between data points which depends on their correlation. We also derive an expression for the center of mass of a set of points with respect to this distance.

Modular forms are highly self-symmetric functions studied in number theory, with connections to several areas of mathematics. But they are rarely visualized. We discuss ongoing work to compute and visualize modular forms as 3D surfaces and…

Immersive technologies are capable of transporting people to distant or inaccessible environments that they might not otherwise visit. Practitioners and researchers alike are discovering new ways to replicate and enhance existing tourism…

A key principle in assessing textual similarity is measuring the degree of semantic overlap between two texts by considering the word alignment. Such alignment-based approaches are intuitive and interpretable; however, they are empirically…

Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…

A single Panorama can be drawn perspectively without distortions in arbitrary viewing directions and field-of-views when the camera position is at the origin. This is a key advantage in VR and virtual tour applications because it enables…

We present a joint 3D pose and focal length estimation approach for object categories in the wild. In contrast to previous methods that predict 3D poses independently of the focal length or assume a constant focal length, we explicitly…

This article describes a multi-modal method using simulated Lidar data via ray tracing and image pixel loss with differentiable rendering to optimize an object's position with respect to an observer or some referential objects in a computer…