Sylvia Wiebrock

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We present an approach to spatial reasoning that is based on homogenous coordinate systems and their transformations. In contrast to qualitative approaches, spatial relations are not represented by symbolic expressions only but additionally by parameters with constraints, which are subsets of real numbers. Our work is based on the notion of mental models in(More)
In the spatial domain, the inclusion of an object in a region can be defined by inequations containing trigonometric expressions and several variables. Proving that a relation holds involves constraint solving. To circumvent the computational difficulties arising for these problems, we explore the applicablility of classification learning programs to this(More)
We present an approach to spatial inference which is based on the procedural semantics of spatial relations. In contrast to qualitative reasoning, we do not use discrete symbolic models. Instead, relations between pairs of objects are represented by parameterized homogeneous transformation matrices with numerical constraints. A textual description of a(More)
In this paper we describe how methods of concept (classi cation) learning can be used to solve constraint satisfaction problems in the spatial domain, for example if a set of numerical constraints de nes a complicated region in the physical or feature (parameter) space. In this case it is in general not easy or even not possible to nd explicit boundary(More)
Text understanding in a spatial domain is often seen as the construction of a mental model. In this paper we present the rst prototype of a program that realizes some of the characteristics claimed for spatial reasoning processes in mental models. Our work is based on homogeneous coordinate systems and transformation matrices. This means that a relation(More)
The paper represents first results on solving constraint nets consisting of equations and inequations containing trigonometric functions by methods of Machine Learning. Constraints of this type occur for example in planning movements of a mobile robot on a symbolic level in a workspace where obstacles or other “dangerous regions” have to be avoided. Another(More)
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