Enhanced algorithm based on Chio-like Method for Non-Square Determinant Calculations for application in CBVR

In this paper, we propose an enhanced algorithm based on the Chio-like method for calculating non-square determinants, optimized for content-based video retrieval (CBVR) systems. The algorithm accelerates the computation of determinant kernels used for similarity score generation, which is critical for efficient video indexing and retrieval. While the classical Chio-like method reduces the determinant order by one at each step, our improved approach reduces the order by four, providing notable computational benefits. Although the asymptotic time complexity remains the same, considering the fact that the resulting determinant is decreased by four orders compared to one and two orders, respectively, from existing Chio-like methods, the proposed method demonstrates clear practical performance improvements. The computer implementation of the proposed algorithm in MATLAB shows an average execution time reduction of approximately 24.5% compared to the standard Chio-like method and 3.2% compared to its modified version. These enhancements make the method well-suited for large-scale or real-time CBVR applications, where fast and accurate similarity evaluation is essential.