Using Algebraic Geometry to Reconstruct a Darboux Cyclide from a Calibrated Camera Picture

TL;DR

This paper presents a method to recognize Darboux cyclides from a single image by leveraging algebraic geometry and their singularity properties, enabling reconstruction up to Euclidean similarity.

Contribution

It introduces a novel approach using algebraic geometry to identify Darboux cyclides from images based on their singularities and discriminants.

Findings

Successful recognition of Darboux cyclides from single images

Reconstruction up to Euclidean similarity transformations

Utilization of algebraic properties for surface recognition

Abstract

The task of recognizing an algebraic surface from a single apparent contour can be reduced to the recovering of a homogeneous equation in four variables from its discriminant. In this paper, we use the fact that Darboux cyclides have a singularity along the absolute conic in order to recognize them up to Euclidean similarity transformations.