Shape Database 2

Precision Recall Graph

Precision (purity of retrieval)

... measures how much percent of the returned objects are really wanted (from the same class)

Recall (completeness of retrieval)

... measures how much percent of the desired objects (from the same class) are returned

Precision vs. Recall

Example: Asking for 10 objects, we obtain 6 correct results (from the same class) and 4 wrong results. The desired class has 8 elements, so 2 wanted object did not show up! We have a precision of 60 percent (6 out of 10) and a recall of 75 percent (6 out of 8). It becomes clear that the higher the recall, the lower the precision (if we want to obtain all of the interesting results, we get quite a few wrong ones mixed in).

Our method performs really well on this database (almost perfect).
The following graph shows the Precision P for a given Recall R (so P(R)) :

PR Graph

Minimum: 0.99829 and Integral: 0.999947

In the above experiment all humans (David, Michael, Victoria) were considered to be in the same class. This makes sense since these humans are very similar to each other and very different from the other animals. Nevertheless, if each human gets its own class we obtain quite a few unwanted humans before we get all the humans from one class:

PR Graph

Minimum: 0.921847 and Integral: 0.983301

Technical Note:

These results use the 10 smallest Eigenvalues of the cubic FEM Laplace-Beltrami-Operator with Dirichlet boundary condition (software to compute these can be found here: Shape-DNA). All results are surface area normalized, the dissimilarity is computed by taking the Euclidean distance of the 10 dimensional vectors representing the shapes. We did not check if a different number of Eigenvalues or a different distance metric improves the results. Note, however, that too few Eigenvalues will not contain enough information and too many include too much noise. Therefore 10-15 is usually a good number.