Locating Overlapping Flexible Shapes Using Geometrical Constraints

In an earlier paper [1] we have proposed a shape representation called the CLD (Chord Length Distribution) which possesses many of the often-quoted desirable properties of a shape representation. It also captures shape variability and complements an object location method using belief updating which integrates low-level evidence and shape constraints. Promising results on synthetic and real rigid objects were given. This paper describes a development to the original definition which makes the location method robust with respect to clutter. We give experimental results which demonstrate the performance of the revised scheme on a class of flexible shapes, both singly and overlapping. We are currently engaged in a research project [see acknowledgements] concerned with automated 2-D inspection of complex (industrial) assemblies. In common with many machine vision applications we seek to exploit object shape and other geometrical constraints to assist in locating objects in scenes and evaluating interpretations with respect to expected appearance. To this end we need suitable representations for shape (intra-object) and inter-object relationships together with location and verification schemes capable of exploiting such representations. Ideally we seek a scheme capable of addressing both shape and inter-object relationships in a uniform manner. We have argued [1] that a shape representation not only needs to satisfy often-quoted [2,3] properties of being easily computable, unique, and exhibiting proportional behaviour, but must also describe expected variability and invariance within a class of shapes and be capable of describing a wide range of shape classes. We have proposed such a representation called a Chord Length Distribution (CLD) and an associated object location scheme which exploits and integrates geometrical (shape) constraints with low-level (edge) evidence in a principled way, originally based on ideas derived from probabilistic reasoning using networks [4]. Unlike many reported methods of applying shape models [5,6,7,8] our approach does not work by matching image primitives to related model elements. Rather, it seeks to label each point in an ordinate space with a likelihood of correspondence to the