This paper mainly studies the Laplacian-energy-like invariants of the modified hexagonal lattice, modified Union Jack lattice, and honeycomb lattice. By utilizing the tensor product of matrices and the diagonalization of block circulant matrices, we derive closed-form formulas expressing the Laplacian-energy-like invariants of these lattices. In addition, we obtain explicit asymptotic values of...

This paper presents the performance evaluation of eight focus measure operators namely Image CURV (Curvature), GRAE (Gradient Energy), HISE (Histogram Entropy), LAPM (Modified Laplacian), LAPV (Variance of Laplacian), LAPD (Diagonal Laplacian), LAP3 (Laplacian in 3D Window) and WAVS (Sum of Wavelet Coefficients). Statistical matrics such as MSE (Mean Squared Error), PNSR (Peak Signal to Noise R...