Persons who want to understand when their eyes may be misleading them
A readable, yet rigorous discussion of the relationship between signal, contrast, and noise
Contrast and noise. (A) The graph depict the signal intensity and noise of the line through the inset grey squares and demonstrates the problem with background in the context of contrast. Contrast in an image is the perceived ability to distinguish between the background and the signal of interest. If both were noiseless, this would not be too difficult even if the signal was nearly identical to the background. However, camera noise and photon shot noise create an overlap in the signal and background regions with similar intensity, making it difficult to separate signal from background.
(B) Because of Fn the noise in imagestaken with an EM-CCD is greater than those from an ORCA-Flash4.0. Thus, when background is high, separation of signal from background in an EM-CCD image will be more difficult.
CNR also describes how we perceive the quality of the image. A good rule of thumb is that a pixel with a CNR of 2 can be detected by eye. On the low side, a pixel with a CNR of 1 can be just barely detected. However, this is a CNR for a single pixel of signal relative to background. Images with a CNR < 1 can show structures at reduced spatial or temporal resolution. When pixels of much lower CNR are grouped together, there is an effect called spatial pixel averaging.
When we look at images our brain performs complex functions including integrating large areas of similar signal, looking for patterns, symmetries and edges. For this reason, if we have a collection of adjacent pixels even with a very poor CNR (< 1), we may still be able to detect them visually.
Mathematically, visibility is improved by the square root of the number of pixels averaged.2 In a quantitative imaging experiment, measurements are made by well-defined algorithms, not by eye. But we can only view images in any publication or presentation with our eyes and therefore we must be aware of the spatial averaging or integration that is happening automatically in our brain.
Along with this automatic visual processing, images that are displayed are subject to many variables intrinsic to the display format (e.g., quality of the monitor, intensity scaling of the image data, printing technique, etc.) that can affect the perceived contrast. For these reasons, determinations of the quality of an image from a given camera should never be assessed exclusively by eye or on image files that have been subject to lossy compression, such as jpeg.
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