On the evaluation of cost functions for parameter optimization of a multiscale shape descriptor

Shape description often relies on parameter adjustment in order to configure a meaningful scale that enables a computer vision task. Instead of manual interaction, which is prohibitive for large datasets, an alternative solution towards supporting multiscale methodology is to apply metaheuristic optimization. Nevertheless, the cost function assigned to the optimization process is an open question that we fully address in this paper. Our investigation describes the influence of the cost function on the performance of an optimized multiscale shape descriptor using three distinct clustering metrics: the Silhouette, Davies-Bouldin and Calinski-Harabasz indices. Thus, we optimize the scale parameters of the Normalized Multiscale Bending Energy descriptor using the Simulated Annealing metaheuristic; both classification and retrieval experiments are conducted using a synthetic shape dataset (Kimia 99), two real plant leaf datasets (ShapeCN and Swedish) and the National Library of Medicine (NLM) pill image dataset (NLM Pills). Using the Bulls-eye ratio and the Accuracy measure, the performance evaluation showed that optimized descriptor with the Calinski-Harabasz cost function underperformed other functions for datasets where there is high level of dissimilarity between classes. Particularly for the NLM Pills, where each class has a well-defined pattern and differences within pill classes are quite small, the Normalized Multiscale Bending Energy descriptor did not benefit from the optimization methodology. We also present a qualitative assessment of the cluster arrangements produced by the Self-Organizing Map (SOM) which reinforced that the three cost functions performed differently within the optimized shape descriptor.