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We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
Highly accurate geometric precision and dense image features characterize True Digital Orthophoto Maps (TDOMs), which are in great demand for applications such as urban planning, infrastructure management, and environmental monitoring.…
We present a method for computing the topological entropy of one-dimensional maps. As an approximation scheme, the algorithm converges rapidly and provides both upper and lower bounds.
We present a fine-tuning method to improve the appearance of 3D geometries reconstructed from single images. We leverage advances in monocular depth estimation to obtain disparity maps and present a novel approach to transforming 2D…
Given a toric degeneration (a degeneration to a toric variety), over the complex numbers, we construct a surjective continuous map from a general fiber to the special fiber of the degeneration in the classical topology. The construction is…
Construction of spline surfaces from given boundary curves is one of the classical problems in computer aided geometric design, which regains much attention in isogeometric analysis in recent years and is called domain parameterization.…
The second part of the paper is devoted to enumeration of $r$-regular toroidal maps up to all homeomorphisms of the torus (unsensed maps). We describe in detail the periodic orientation reversing homeomorphisms of the torus which turn out…
In this investigation we focus on the problem of mapping the ground reflectivity with multiple laser scanners mounted on mobile robots/vehicles. The problem originates because regions of the ground become populated with a varying number of…
This paper describes an interdisciplinary approach to geometry modeling of geospatial boundaries. The objective is to extract surfaces from irregular spatial patterns using differential geometry and obtain coherent directional predictions…
Currently, state-of-the-art exploration methods maintain high-resolution map representations in order to optimize exploration goals in each step that maximizes information gain. However, during exploring, those "optimal" selections could…
We address the challenge of incorporating document-level metadata into topic modeling to improve topic mixture estimation. To overcome the computational complexity and lack of theoretical guarantees in existing Bayesian methods, we extend…
Volumetric parameterization problem refers to parameterization of both the interior and boundary of a 3D model. It is a much harder problem compared to surface parameterization where a parametric representation is worked out only for the…
Surveillance and surveying are two important applications of empirical research. A major part of terrain modelling is supported by photographic surveys which are used for capturing expansive natural surfaces using a wide range of sensors --…
Homogeneous diffusion inpainting can reconstruct missing image areas with high quality from a sparse subset of known pixels, provided that their location as well as their gray or color values are well optimized. This property is exploited…
Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, e.g., scalar functions, Euclidean curves, or surfaces, etc. For objects that differ in more complex ways, the…
Our goal is to provide a novel method of representing 2D shapes, where each shape will be assigned a unique fingerprint - a computable approximation to a conformal map of the given shape to a canonical shape in 2D or 3D space (see page 22…
We introduce several possible generalizations of tomography for quadratic surfaces. We analyze different types of elliptic, hyperbolic and hybrid tomograms. In all cases it is possible to consistently define the inverse tomographic map. We…
Topology is a powerful tool for categorizing magnetization textures by defining a topological index in both two-dimensional (2D) systems, such as thin films or curved surfaces, and in 3D bulk systems. In the emerging field of 3D…
Object counting and localization are key steps for quantitative analysis in large-scale microscopy applications. This procedure becomes challenging when target objects are overlapping, are densely clustered, and/or present fuzzy boundaries.…
Map-to-map matching is a critical task for aligning spatial data across heterogeneous sources, yet it remains challenging due to the lack of ground truth correspondences, sparse node features, and scalability demands. In this paper, we…