Group 1 - The research team from Donghua University, Shanghai Jiao Tong University, and the Chinese Academy of Sciences has proposed two geometry-based homography decomposition methods that significantly reduce the computational load of solving homographies from four points by over 95% compared to conventional sparse linear equation methods [3][4]. - The paper titled "Fast and Interpretable 2D Homography Decomposition: Similarity-Kernel-Similarity and Affine-Core-Affine Transformations" has been accepted by the IEEE T-PAMI journal [5][4]. - The proposed methods are expected to be applicable in various visual applications, including QR code scanning, projective geometry, computer vision, and graphics problems [3]. Group 2 - The traditional Direct Linear Transformation (DLT) method constructs a sparse linear equation system for homography solving, which typically requires around 2000 floating-point operations [7]. - Improved methods have been developed, reducing the computational load to approximately 1800 operations for SVD decomposition and 220 operations for a customized Gaussian elimination method [7]. - The new methods, SKS and ACA, achieve a significant reduction in floating-point operations, with ACA requiring only 29 operations for specific cases like square templates [18][22]. Group 3 - The SKS transformation decomposes the homography matrix into multiple sub-transformations, leveraging the hierarchical nature of geometric transformations [9][10]. - The ACA transformation similarly computes affine transformations from three corresponding points, resulting in an efficient homography matrix decomposition [15]. - The average time for a single four-point homography calculation using the ACA method is reported to be only 17 nanoseconds, achieving acceleration factors of 29 times and 43 times compared to previous methods [22]. Group 4 - The methods can be integrated into various visual processing applications, replacing traditional homography algorithms, particularly in QR code scanning, which is estimated to reach billions of scans daily in China [24]. - The research team is also exploring further applications in deep learning for estimating geometric parameters, P3P pose estimation based on planar homography, and N-dimensional homography matrix decomposition [25].