Measure of image sharpness using eigenvalues

This paper deals with the design and implementation of a novel image sharpness metric based on the statistical approach. This sharpness metric is derived by modelling the image sharpness problem as a generalized eigenvalues problem. This problem is solved using Rayleigh quotient optimization where relevant statistical information of an image is extracted and then represented through a series of eigenvalues. The novelty of this paper comes from the application of eigenvalues in image sharpness metric formulation to provide robust assessment with the presence of various blur and noisy conditions. Firstly, the input image is normalized by its energy to minimize the effects caused by image contrast. Secondly, the covariance matrix is computed from this normalized image before it is diagonalized using Singular Values Decomposition (SVD) to obtain a series of eigenvalues. Finally, the image sharpness of the normalized image is determined by the trace of the first several eigenvalues. The performance of the proposed metric is gauged by comparing with several objective image sharpness metrics. Experimental results using synthetic and real images with known and unknown distortion conditions show the robustness and feasibility of the proposed metric in providing relative image sharpness. In particular, the proposed metric provides wider working range and more precise prediction consistency under all tested deformation conditions although it is slightly expensive in terms of computation than other metrics.