Optimal Surface Fusion

This paper presents a general method for combining stereo surfaces using a Kalman filter. A measure of error in surface representation is suggested, and the work shows how a set of surfaces may be combined to give a single surface which minimises this measure. The analysis shows how a stochastic surface may be generated using stereo, and how errors in surface-to-surface registration may be modeled. The cases of multiple, mutually-occluding surfaces and unknown three-dimensional camera motion are considered. Performance is analysed using semi-artificial data. The results are important to multi-sensor fusion and automatic model generation. The problem of estimating a single optimal surface from noisy measurements occurs in many vision and robotics applications [1, 2, 3, 4]. Here it is considered in the context of building a description of a complex object or environment using stereo reconstruction from many viewpoints [5]. A definition is offered of the optimal surface to represent a set of measured surfaces, and the paper shows how it may be found using the Kalman filter framework. Models of errors in stereo surface reconstruction derived from [6] and [7], and of surfaceto-surface registration [8] are presented. Finally performance is analysed using artificial and real data. Other authors have used Kalman filtering to incrementally combine visual measurements [1, 9}. This paper differs from previous work by representing uncertainty in surface location rather than features such as corners [9] and lines [1] and so relates most closely to [7]. However their work is extended to allow unknown three-dimensional camera motion and model multiple mutuallyoccluding surfaces. The results presented are of general interest to active vision, sensor fusion and automatic model generation. 1 PROBLEM FORMULATION Consider N surfaces, S\...SN. We want to find the best representation of these surfaces by a single surface So defined by a regular grid of spline control points relative to an origin O (figure 1). We define the error in surface fit as follows — BMVC 1991 doi:10.5244/C.5.21