Error-Driven Refinement of Multi-scale Gaussian Maps

The accuracy of Grid-based maps can be enhanced by putting a Gaussian in every cell of the map. However, this solution works poorly for coarse discretizations in multi-scale maps. This paper proposes a method to overcome the problem by allowing several Gaussians per cell at coarse scales. We introduce a multi-scale approach to compute an error measure for each scale with respect to the finer one. This measure constitutes the basis of an incremental refinement algorithm where the error is used to select the cells in which the number of Gaussians should be increased. As a result, the accuracy of the map can be selectively enhanced by making efficient use of computational resources. Moreover, the error measure can also be applied to compress a map by deleting the finer scale clusters when the error in the coarse ones is low.

The approach is based on a recent clustering algorithm that models input data as Gaussians rather than points, as is the case for conventional algorithms. In addition to mapping, this clustering paradigm makes it possible to perform map merging and to represent feature hierarchies under a sound theoretical framework. Our approach has been validated with both real and simulated 3-D data.