Dynamic Reconstruction of Linear Images Using Visual Data

Splines have been investigated in 1970s as a basic tool of applied mathematics (de Boor, 1978), (Schumaker, 1981). The dynamic splines based on linear control theory were first used in trajectory planning by Crouch and collaborators (Crouch and Jackson, 1991). For statistical applications, an important result was made by Wahba (Wahba, 1990). Further, in a series of papers (Agwu and Martin, 1998), (Egerstedt and Martin, 2001), (Martin and Egerstedt, 2001), (Sun and Martin, 2000), Martin and his collaborators have studied some of the basic properties of smoothing splines from the view point of optimal control. Based on these papers, it is possible to reconstruct noisy distance data using visual information. We will use this data to reconstruct unknown boundaries using smoothing splines. For purpose of this paper our data was collected using a laser range finder. This results in less noisy data, then would have been obtained using strictly visual information.