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Backward compatibility for high dynamic range image and video compression forms one of the essential requirements in the transition phase from low dynamic range (LDR) displays to high dynamic range (HDR) displays. In a recent work , an optimized solution for tone mapping and inverse tone mapping of HDR images is achieved in terms of mean square error (MSE) of the logarithm of luminance values of HDR image pixels for backward-compatible compression. A disadvantage of this approach was to use non uniform luminance values according to Human perception for minimization, which causes quite non-natural over-illumination in the produced LDR images. In this paper, we propose to use perceptually uniform luminance values as an alternative for the optimization of tone mapping curve. The results indicate that the proposed approach gives better performance (0.5-1 dB gains) in terms of Perceptually Uniform Peak Signal to Noise Ratio (PU-PSNR) and produces more realistic LDR images.