Performance comparison of laplacian-based features

Three feature sets based on the eigenvalues of the Laplacian operator with different boundary conditions were generated and their computational complexity and effectiveness in a pattern recognition application were compared. The first feature set is based on the eigenvalues of the Laplacian operator with Dirichlet boundary condition, the second feature set uses Neumann boundary condition, and the third set uses Stekloff boundary condition. All feature sets are rotation, translation, and size invariant. The effectiveness of these features is demonstrated by using them in the classification of 5 types of binary hand-drawn shapes. The classification was done using 4 to 20 features fed to a simple feed-forward neural network. Even though the Dirichlet and Neumann feature sets were computationally more complex than the Stekloff features, they were more tolerant of input variations and clearly outperformed the Stekloff feature sets in the pattern classification application. The correct classification rates of the Stekloff feature sets ranged from 34.0% to 61.0% while those of the Dirichlet and Neumann feature sets were 60.0%-95.5% and 87.5-95.5%, respectively.