A Dual-Metric Framework for Image Filtering Performance Assessment Via Eigenvalue Variance and Restoration Error Analysis

Abstract Image filtering is a fundamental operation in computer vision and image processing, yet its evaluation remains challenging due to the conflicting requirements of noise suppression and structural preservation. Traditional performance measures often emphasize either statistical consistency or fidelity to reference images, but rarely provide a holistic perspective. In this paper, we introduce a dual-metric framework for image filtering performance assessment, combining eigenvalue variance with restoration error analysis. Eigenvalue variance serves as a structural descriptor, capturing variations in local image matrices that indicate texture retention and edge clarity. Restoration error complements this by quantifying fidelity to the original image, thereby reflecting the degree of noise suppression. By integrating these two complementary measures, the framework delivers a balanced evaluation that accounts for both perceptual quality and quantitative accuracy. Experimental studies across a range of filtering techniques including linear, nonlinear, and adaptive methods demonstrate that the dual-metric approach effectively differentiates filters and reveals inherent trade-offs. This comprehensive methodology offers a reliable foundation for filter selection and optimization in diverse image processing applications.