1. Acknowledgments
Thanks grass Gone with the Wind Spirit sky (QQ 2550688560) understand the formula given guidance and information provided!
2. repetitious presentation (skippable)
The evaluation result of image processing is image processing very important part, so I think it is necessary to clarify the source of mathematical formulas used in the evaluation model. Because I never studied digital image processing and related courses, so there is no source of their own to figure out the formula, the network blog mostly just realized this formula, do not understand the origin of the formula of the description (feel should be the formula too simple, no need to explain QAQ). But I never had as a digital image processing is white, indicating comprehension or necessary.
3. personal understanding
First posted formula:
MSE here do not explain, most blog has mentioned that it is the mean square error, this is not difficult to understand. Key is the last PSNR of this formula. Look at the ratio of the number of brackets. Where $ \ frac {(2 ^ n - 1) ^ 2} {MSE} $, look at the (2 n- -1), where represents the value corresponding to the maximum pixel value of an image, i.e. amplitude. Here the overall formula is in fact seeking to noise ratio. SNR is defined as follows (from FIG Baidu Encyclopedia)
The output signal power is simply
The ratio of the noise power, but the image signal to noise ratio in the entry item, as shown below:
Wherein " maximum local variance signal variance that is a minimum value of noise variance, to obtain their ratio " describes the ratio of the meanings indicated above. This sentence of the second half, " then into several dB " is just the number corresponding to the source of the formula. DB is calculated as shown below (images from Baidu Encyclopedia)
After the above-mentioned legends are floating grass I got the spiritual sky pointing, data query summarizing. I do not know here to represent the ratio of signal-to-noise ratio is not know what to say and do not know the point of view expressed in decibels operands convert what I think it is necessary to guide the floating grass doubt and spiritual sky listed.
- Why use logarithms?
- 为什么在比值中要取最大值？
对于取最大值这里，结合 草飘灵sky 的回答，我个人理解的是：如果抛开名称上的“峰值”以及百度百科上的定义，我认为这里用最大值可能是为了比较明显的表现出图像处理的结果。
以上就是我对 PSNR 公式的理解，再次感谢 草飘灵sky ！