Related papers: Hypersurface Curvatures of Geological Features

The idea of curvature analysis has been widely used in subsurface structure interpretation from three-dimensional (3D) seismic data (e.g., fault/fracture detection and geomorphology delineation) by measuring the lateral changes in the…

Feature curves are largely adopted to highlight shape features, such as sharp lines, or to divide surfaces into meaningful segments, like convex or concave regions. Extracting these curves is not sufficient to convey prominent and…

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…

To analyze seismic wave propagation in geological structures, it is possible to consider various numerical approaches: the finite difference method, the spectral element method, the boundary element method, the finite element method, the…

We consider a system consisting of a geometric evolution equation for a hypersurface and a parabolic equation on this evolving hypersurface. More precisely, we discuss mean curvature flow scaled with a term that depends on a quantity…

Conventional field parameters for surface measurement use all data points, while feature characterization focuses on subsets extracted by watershed segmentation. This approach enables the extraction of specific features that are potentially…

We explore the use of multiresolution analysis techniques as texture attributes for seismic image characterization, especially in representing subsurface structures in large migrated seismic data. Namely, we explore the Gaussian pyramid,…

Integral invariants obtained from Principal Component Analysis on a small kernel domain of a submanifold encode important geometric information classically defined in differential-geometric terms. We generalize to hypersurfaces in any…

In this paper, we explore how to computationally characterize subsurface geological structures presented in seismic volumes using texture attributes. For this purpose, we conduct a comparative study of typical texture attributes presented…

Accurate surround-view depth estimation provides a competitive alternative to laser-based sensors and is essential for 3D scene understanding in autonomous driving. While empirical studies have proposed various approaches that primarily…

In this work, we provide a local classification of certain special classes of surfaces determined by the prescription of the radial mean curvature in terms of the height and angle functions. Moreover, we introduce a special class of…

Curving beams are a promising new method for bypassing obstacles in future millimeter-wave to sub-terahertz (sub-THz) networks but lack a general predictive model for their reflections from arbitrary surfaces. We show that, unfortunately,…

The analysis of curves has been routinely dealt with using tools from functional data analysis. However its extension to multi-dimensional curves poses a new challenge due to its inherent geometric features that are difficult to capture…

On some specified convex supporting sets of spheres, we find a generalized longitude function whose level sets are totally geodesic. Given an arbitrary (weakly) harmonic map into spheres, the composition of the generalized longitude…

We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…

We give a relationship that yields an effective geometric way of evaluating mean curvature of surfaces. The approach is reminiscent of the Gauss's contour based evaluation of intrinsic curvature. The presented formula may have a number of…

Geometric data analysis and learning has emerged as a distinct and rapidly developing research area, increasingly recognized for its effectiveness across diverse applications. At the heart of this field lies curvature, a powerful and…

This paper focuses on the denoising and enhancing of 3-D reflection seismic data. We propose a pre-processing step based on a non linear diffusion filtering leading to a better detection of seismic faults. The non linear diffusion…

In this paper, we examine several typical texture attributes developed in the image processing community in recent years with respect to their capability of characterizing a migrated seismic volume. These attributes are generated in either…

Accurately rendering scenes with reflective surfaces remains a significant challenge in novel view synthesis, as existing methods like Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3DGS) often misinterpret reflections as physical…