Rotation matrix factorization Impact on the quality of images rotation


Kingsley Nathaniel and Innocent Saffin

Most efficient algorithms for rotating 2D images are based on the succession of three translations, following the lines, then the columns and the lines of the image again (LCL). These translations result from the decomposition of the rotation matrix into a product of an upper triangular matrix, a lower triangular matrix and an upper triangular matrix (ULU). We have shown in this paper that the decomposition of the rotation matrix is not unique and have separated it into a product of a lower triangular matrix, an upper triangular matrix and a lower triangular matrix (LUL). This new decomposition led to a new algorithm based on a succession of three translations following the columns, then the lines and the columns of the images again (CLC). Statistical analysis of experimental results showed that the computational complexity of images rotation does not depend significantly (p>0.05) on the factorization ULU or LUL, whereas the precision depends on it significantly (p<0.05). Each of the two algorithms of rotation is more precise for certain images and for certain angles. The method can be generalized in a case of 3D image rotation using the Euler angles.

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