Absolute Pose and Structure from Motion for Surfaces of Revolution: Minimal Problems Using Apparent Contours

The class of objects that can be represented by surfaces of revolution (SoRs) is highly prevalent in human work and living spaces. Due to their prevalence and convenient geometric properties, SoRs have been employed over the past thirty years for single-view camera calibration and pose estimation, and have been studied in terms of SoR object reconstruction and recognition. Such treatment has provided techniques for the automatic identification and classification of important SoR structures, such as apparent contours, cross sections, bitangent points, creases, and inflections. The presence of these structures are crucial to most SoR-based image metrology algorithms. This paper develops single-view and two-view pose recovery and reconstruction formulations that only require apparent contours, and no other SoR features.The primary objective of this paper is to present and experimentallyvalidate the minimal problems pertaining toSoR metrology from apparent contours. For a single view with a known reference model, this includes absolute pose recovery. For many views and no reference model this is extended to structure from motion (SfM). Assuming apparent contours as input that have been identified and segmented with reasonable accuracy, the minimal problems aredemonstrated to produce accurate SoR pose and shape results when used as part of a RANSAC-based hypothesis generation and evaluation pipeline.