Fig. 1. We are not only able to find the best matching part P of the target object T for a given query part Q but also to modify P to composed of only the features of P that are similar to Q. The algorithm introduced in Section 4 automatically computed the result shown.

Fig. 2. Illustration of the computation of partial similarity ps(Q, A), where A is part P from Fig. 1. We see a few simplified versions of A. The global minimum is obtained for

Fig. 3. The plot of the values of the similarity measure The global minimum is obtained for k=15, which is for polyline (shown in Fig. 2).

Fig. 4. Some shapes used in part B of MPEG-7 core experiment CE-Shape-1. Shapes in each row belong to the same class, i.e. we see in the first row four different shapes (out of 20) of class ‘bone’.

Fig. 5. Top: the 21 most similar shapes retrieved from the MPEG-7 shape database for the query part Q (shown on top). Bottom: the subparts of the top shapes that are similar to Q.

Fig. 6. Our small test database composed of 27 objects grouped into 9 classes (shown in rows).

Fig. 7. The set of 18 query parts grouped into 9 classes corresponding to the 9 classes in the database in Fig. 6.

Fig. 8. The best six published retrieval rates in percents on the MPEG-7 shape-1 part B dataset.

Fig. 9. Correspondence of visual parts as computed by our global shape similarity measure. Corresponding arcs are labeled with the same numbers.

Fig. 10. Our global shape similarity measure is able to compute an intuitive correspondence of visual parts.

Fig. 11. (a),(b): Two shapes from the MPEG-7 database as extracted from their images with resolutions of 100×100, 40×40, and 10×10 pixel each. (c) Relative similarity of matching the shape depicted in (a) against the shapes in (a) and (b). Each column represents the relative similarity for a query at the resolutions 100×100, 90×90,…, down to 10×10 pixel. Black columns denote the results of global similarity measure s, gray columns the results of opsss. The higher the columns, the more reliable the retrieval. (d) The same as (c), but for retrieval of shape (b).

Fig. 12. (a) Two exemplary polylines as could be obtained when sensing an object with a laser range finder. As the upper polyline is free of noise, tire lower one suffers from distortions in the same magnitude as the shape features present. The grid shown denotes 1 cm distances. (b) Applying the opsss to compare the two polylines, differing shape features are removed prior to computing shape similarity (dashed lines). The cost for removal is low, as the removed vertices are judged likely to be caused by noise.