Associations among Image Assessments as Cost Functions in Linear Decomposition: MSE, SSIM, and Correlation Coefficient
Abstract
The traditional methods of image assessment, such as mean squared error (MSE), signaltonoise ratio (SNR), and Peak signaltonoise ratio (PSNR), are all based on the absolute error of images. Pearson's innerproduct correlation coefficient (PCC) is also usually used to measure the similarity between images. Structural similarity (SSIM) index is another important measurement which has been shown to be more effective in the human vision system (HVS). Although there are many essential differences among these image assessments, some important associations among them as cost functions in linear decomposition are discussed in this paper. Firstly, the selected bases from a basis set for a target vector are the same in the linear decomposition schemes with different cost functions MSE, SSIM, and PCC. Moreover, for a target vector, the ratio of the corresponding affine parameters in the MSEbased linear decomposition scheme and the SSIMbased scheme is a constant, which is just the value of PCC between the target vector and its estimated vector.
 Publication:

arXiv eprints
 Pub Date:
 August 2017
 arXiv:
 arXiv:1708.01541
 Bibcode:
 2017arXiv170801541W
 Keywords:

 Computer Science  Computer Vision and Pattern Recognition
 EPrint:
 11 pages, 0 figures