Spatial Inference with Constraints

We present an approach for solving constraint nets occurring in spatial inference using methods of Machine Learning. In contrast to qualitative spatial reasoning we use a metric description. Relations between pairs of objects are represented by parameterised homogeneous transformation matrices and numerical (nonlinear) constraints on the parameters. For drawing inferences we have to multiply the matrices and to propagate the constraints. The resulting constraint net consists of equations and inequalities containing trigonometric functions, which can be solved analytically only in rare cases. So we employ decision tree learning for learning and solving the constraints. We also use the decision trees for giving additional constraints for inferring a spatial relation from a set of other relations.