| Surfaces of revolution (SoRs) describe many man-made objects and exhibit several interesting and useful mathematical properties. This thesis explores these relationships from within a Euclidean-based framework and derives minimal problems and algebraic forms for the tasks of single-view and multi-view SoR shape reconstruction, pose recovery, and perceptual grouping. The assumption of a camera with calibrated intrinsic parameters allows projective space to be upgraded to Euclidean space, where image metrology is more readily performed. Specifically, the pose, shape and perspective projection of SoRs are intimately related; knowledge of any two of these three aspects constrains the estimation of the remaining parameters. Four metrology tasks are considered in this dissertation, the first three of which assume known SoR contours. If the SoR shape is known, the absolute pose is recovered from a single view using a one-point minimal correspondence problem (MCP). Both shape and absolute pose are recovered from two extrinsically calibrated views by triangulating the SoR's 3D central axis using estimates of its 2D projection in each view. This two-view triangulation procedure is generalized without the extrinsic calibration in a structure-from-motion (SfM) manner to a two-point MCP to recover the SoR shape and pose---modulo scale. The last metrology task assumes unknown SoR contours. If the SoR pose in n views are known, the SoR geometry permits all views to be mapped into a common shape space. This enables a simultaneous n-view perceptual grouping and shape recovery algorithm. This algorithm is first demonstrated on noise-corrupted SoR views and then applied to a stereoscopic parallax cue that allows the reconstruction of optically challenging SoRs. These methods are validated on real and synthetic datasets. |
