A theoretical framework is introduced for the perception of specular surface geometry. When an observer moves in three-dimensional space, real scene features, such as surface markings, remain stationary with respect to the surfaces they belong to. In contrast, a virtual feature, which is the specular reflection of a real feature, travels on the surface. Based on the notion of caustics, a novel feature classification algorithm is developed that distinguishes real and virtual features from their image trajectories that result from observer motion. Next, using support functions of curves, a closedform relation is derived between the image trajectory of a virtual feature and the geometry of the specular surface it travels on. It is shown that in the 2D case where camera motion and the surface profile are coplanar, the profile is uniquely recovered by tracking just two unknown virtual features. Finally, these results are generalized to the case of arbitrary 3D surface profiles that are trav...

A technique is presented to compute the reflected illumination from curved mirror surfaces onto other surfaces. In accordance with Fermat's principle, this is equivalent to finding extremal paths from the light source to the visible surface via the mirrors. Once pathways of illumination are found, irradiance is computed from the Gaussian curvature of the geometrical wavefront. Techniques from optics, differential geometry and interval analysis are applied to solve these problems. CR Categories and Subject Descriptions: I.3.3 [ Computer Graphics ]: Picture/Image Generation; I.3.7 [ Computer Graphics ]: Three-Dimensional Graphics and Realism General Terms: Algorithms Additional Keywords and Phrases: Caustics, Differential Geometry, Geometrical Optics, Global Illumination, Interval Arithmetic, Ray Tracing, Wavefronts 1. Introduction Ray tracing provides a straightforward means for synthesizing realistic images on the computer. A scene is first modeled, usually by a collection of implici...

2. Ray theory for the scalar wave equation and scalar Helmhlotz equation. 2.1 The ray theory ansatz, amplitude and phase, slowness