There has been considerable interest recently in employing simple observer behaviors that either make the recovery of scene properties easier (e.g., fixation), or combine simple behaviors in order to perform complex tasks such as navigation and obstacle avoidance. Our work focuses on the ability of an active observer to control the point of observation to perform tasks involving the exploration of an object. The developed behaviors that are provably-correct, make simple motion decisions that are based on the observed local geometry of the scene, and require minimal processing of each image.
We first consider the task of recovering the local shape of the surface at a selected point. Our approach is based on the general observation that some positions provide more information about an object than others. The existence of such special viewpoints can be exploited only if the observer is mobile and has an efficient and deterministic strategy for reaching them. We show that the local shape-recovery task can be achieved using a simple and qualitative strategy for smoothly controlling the point of observation until the viewing direction is "aligned" with a principal direction at the selected point. Second, we consider the task of deriving a global description of an object. We formulate global surface reconstruction as the qualitative task of smoothly controlling the point of observation so that the visible rim "slides" over a maximal, connected, reconstructible region. We show that this task can be provably achieved for arbitrary smooth surfaces by attempting to maintain a well-defined geometric relationship between the point of observation and the viewed surface.
Our approach suggests that the ability to smoothly control the point of observation can lead to provably-correct behaviors for achieving both local and global tasks (e.g., scene exploration, 3D navigation) while also simplifying per-frame computations.