Algorithm Certainty Analysis of Spatial Data for Terrain Model

TL;DR

This paper introduces a novel algorithm to generate a certainty score for terrain models derived from spatial data, addressing shadow zone limitations in terrain surveying techniques.

Contribution

It develops a method to produce a continuous terrain model with an associated certainty measure, using advanced mathematical tools like Riemann surfaces and probability distributions.

Findings

Generated certainty scores for terrain mapping.

Mapped shadow zones with continuous spatial coordinates.

Applied probabilistic normalization to discrete data.

Abstract

The terrain survey techniques of photogrammetry, LIDAR, Sonar or seismic studies are subject to limitation of shadow zones. It is not possible to capture the terrain pattern and requires interpolation and extrapolation for conformal mapping of spatial coordinates for generation of terrain model. The discrete data is mapped through a function set whose domain returns the analytic test in Riemann map. The algorithm adopted in analysis for such mapping does not have a certainty score or probability of degree of correctness conforming to the physical landscape of shadow zones. The aim of the paper is to establish a generator of certainty degree of the mapping along with a continuous terrain model generator. The confirmed mapping of terrain presents a continuous spatial coordinate set which form the boundary of the shadow zone with discrete spatial coordinates. The discrete set is normalized in Gaussian distribution through a Poisson distribution transition. The continuous data set is represented by Laurentian series in which the function will be analytic and can be mapped to Riemann surface with singularities within the annulus and outside the annulus of approximate space sub set (Euclidean space).The singularities will be discarded through Picard's theorem and analytic test at poles with Cauchy's residual theorem is done. The resulting set of spatial coordinates will restructure within Riemann number sphere which will be mapped on the plane as stereographic projection. The Gaussian distribution which forms the basis of analysis will provide with the tool for generating the probability of certainty of every terrain model idealised to conform to the physical landscape.