Rolf Lakämper

Shape descriptors for non-rigid shapes with a single closed contour

The Core Experiment CE-Shape-1 for shape descriptors performed for the MPEG-7 standard gave a unique opportunity to compare various shape descriptors for non-rigid shapes with a single closed contour. There are two main differences with respect to other comparison results reported in the literature: (1) For each shape descriptor the experiments were carried out by an institute that is in favor of this descriptor. This implies that the parameters for each system were optimally determined and the implementations were thoroughly rested. (2) It was possible to compare the performance of shape descriptors based on totally different mathematical approaches. A more theoretical comparison of these descriptors seems to be extremely hard. In this paper we report on the MPEG-7 Core Experiment CE-Shape.

Shape similarity measure based on correspondence of visual parts

A cognitively motivated similarity measure is presented and its properties are analyzed with respect to retrieval of similar objects in image databases of silhouettes of 2D objects. To reduce influence of digitization noise, as well as segmentation errors, the shapes are simplified by a novel process of digital curve evolution. To compute our similarity measure, we first establish the best possible correspondence of visual parts (without explicitly computing the visual parts). Then, the similarity between corresponding parts is computed and aggregated. We applied our similarity measure to shape matching of object contours in various image databases and compared it to well-known approaches in the literature. The experimental results justify that our shape matching procedure gives an intuitive shape correspondence and is stable with respect to noise distortions.

Convexity Rule for Shape Decomposition Based on Discrete Contour Evolution

We concentrate here on decomposition of 2D objects into meaningfulparts of visual form, orvisual parts. It is a simple observation that convex parts of objects determine visual parts. However, the problem is that many significant visual parts are not convex, since a visual part may have concavities. We solve this problem by identifying convex parts at different stages of a proposed contour evolution method in which significant visual parts will become convex object parts at higher stages of the evolution. We obtain a novel rule for decomposition of 2D objects into visual parts, called the hierarchical convexity rule, which states that visual parts are enclosed by maximal convex (with respect to the object) boundary arcs at different stages of the contour evolution. This rule determines not only parts of boundary curves but directly the visual parts of objects. Moreover, the stages of the evolution hierarchy induce a hierarchical structure of the visual parts. The more advanced the stage of contour evolution, the more significant is the shape contribution of the obtained visual parts.

Application of planar shape comparison to object retrieval in image databases

A similarity measure for silhouettes of 2D objects is presented, and its properties are analyzed with respect to retrieval of similar objects in image databases. To reduce influence of digitization noise as well as segmentation errors the shapes are simplified by a new process of digital curve evolution. To compute our similarity measure, we first establish the best possible correspondence of visual parts (without explicitly computing the visual parts). Then the similarity between corresponding parts is computed and summed. Experimental results show that our shape matching procedure gives an intuitive shape correspondence and is stable with respect to noise distortions.

Polygon Evolution by Vertex Deletion

We propose a simple approach to evolution of polygonal curves that is specially designed to fit discrete nature of curves in digital images. It leads to simplification of shape complexity with no blurring (i.e., shape rounding) effects and no dislocation of relevant features. Moreover, in our approach the problem to determine the size of discrete steps for numerical implementations does not occur, since our evolution method leads in a natural way to a finite number of discrete evolution steps which are just the iterations of a basic procedure of vertex deletion.

Shape Similarity and Visual Parts

Human perception of shape is based on visual parts of objects to a point that a single, significant visual part is sufficient to recognize the whole object. For example, if you see a hand in the door, you expect a human behind the door. Therefore, a cognitively motivated shape similarity measure for recognition applications should be based on visual parts. This cognitive assumption leads to two related problems of scale selection and subpart selection. To find a given query part Q as part of an object C, Q needs to have a correct size with regards to C (scale selection). Assuming that the correct size is selected, the part Q must be compared to all possible subparts of C (subpart selection). For global, contour-based similarity measures, scaling the whole contour curves of both objects to the same length usually solves the problem of scale selection. Although this is not an optimal solution, it works if the whole contour curves are ‘sufficiently’ similar. Subpart selection problem does not occur in the implementation of global similarity measures.

Contour-Based Shape Similarity

A similarity measure for silhouettes of 2D objects is presented, and its properties are analyzed with respect to retrieval of similar objects in an image database. Our measure profits from a novel approach to subdivision of objects into parts of visual form. To compute our similarity measure, we first establish the best possible correspondence of visual parts, which is based on a correspondence of convex boundary arcs. Then the similarity between corresponding arcs is computed and aggregated. We applied our similarity measure to shape matching of object contours in various image databases and compared it to well-known approaches in the literature. The experimental results justify that our shape matching procedure gives an intuitive shape correspondence and is stable with respect to noise distortions.

Shape-Based Robot Mapping

We present a novel geometric model for robot mapping suited for robots equipped with a laser range finder. The geometric representation is based on shape. Cyclic ordered sets of polygonal lines are the underlying data structures. Specially adapted shape matching techniques originating from computer vision are applied to match range scan against the partially constructed map. Shape matching respects for a wider context than conventional scan matching approaches, allowing to disregard pose estimations. The described shape based approach is an improvement of the underlying geometric models of todays SLAM implementations. Moreover, using our object-centered approach allows for compact representations that are well-suited to bridge the gap from metric information needed in robot motion and path planning to more abstract, i.e. topological or qualitative spatial knowledge desired in complex navigational tasks or communication.

Discrete Approach to Curve Evolution

We propose a simple approach to evolution of digital planar curves that is specially designed to fit discrete nature of curves in digital images. The obtained curve evolution method by digital linearization has many advantages in comparison to curve evolutions in scale-space theories that are usually guided by diffusion equations. We will show that it leads to simplification of shape complexity, analog to evolutions guided by diffusion equations, but with no blurring (i.e., shape rounding) effects and no dislocation of relevant features. Moreover, in our approach the problem to determine the size of discrete steps for numerical implementations does not occur, since our evolution method leads in a natural way to a finite number of discrete evolution steps which are just the iterations of a basic procedure of digital linearization.

Shape Decomposition and Shape Similarity Measure

We propose a simple and natural rule for decomposition of 2D objects into parts of visual form. The hierarchical convexity rule states that visual parts axe enclosed by maximal convex boundary arcs (with respect to the object) at various levels of curve evolution. The proposed rule is based on a novel curve evolution method by digital linearization in which a significant visual part will become a convex part at some level of the evolution. The hierarchical convexity rule determines not only parts of boundary curves but directly the visual parts of objects, and the evolution hierarchy induces a hierarchical structure of the obtained visual parts.