@
Paul - That's utterly amazing, Paul! You must have used the brand new "replace children" mode of the content aware fill filter. But, be careful -- I understand that for some strange reason, many parents throughout the world have started to campaign against its use.
@OP - In all seriousness though, to address the OP's question, there are two methods that are most often recommended. The first method is to use the "shadows / highlight tool", and the second method is to select the (dark) subject, and then use ordinary methods (eg, "levels", "curves", "exposure" adjustment layers, etc.) to brighten just the subject and then either leave the background completely alone, or try to repair the completely blown highlights in the background.
Both methods can help salvage important photos when the degree of underexposure of the subjects is moderate and the photo was taken with a fairly high quality camera and lens.
Unfortunately, there is no method that will produce high quality results when the degree of underexposure is severe, as it is in the example link provided by the OP, and/or the picture was taken with a low quality camera and a bad or dirty lens.
The problem is that the image being seen by the sensor or film simply has too large a dynamic range (ie, ratio of brightest to darkest light levels). Under such conditions, the slightest stray reflection either in the lens or the camera body can bounce back onto the sensor/film and cause either oddly shaped patterns of light to appear in the image (traditional "lens flare" -- Google it), or a softness and loss of contrast in the dark areas of the image ("veiling flare" -- Google it). Another problem is that even if the lens and camera design is perfect, both digital sensors and film behave terribly in parts of the image that are severely underexposed. They tend to produce noisy / grainy / mottled images with poor color, poor contrast, and poor everything-else-you-can-think-of.
The bottom line is that there simply are fundamental limitations because of the physics of light and light sensors that just can't be circumvented by post-processing, no matter how adroit. The example image is one of them (see below). In such cases, the best option is often to either (a) replace the subjects in this picture with images of them taken from properly exposed pix (as Paul jokingly did using other kids); or, (b) draw/paint in the subjects by hand, and turn the photo into a painting / drawing.
To illustrate these problems, I attempted to brighten up the subjects in the example image provided using only conventional means. Here is the original:
And, here is about as good as one can get without going to extraordinary lengths:
If this photo was tremendously important and/or irreplaceable (eg, last photo ever taken before one of them was hit by a car, or maybe they just egged your car and you want to identify them to the police, LOL), the poor quality of the "fixed" version might be acceptable. However, I think that most people would feel the quality is unacceptable and would likely throw it in the trash bin. Then, then next time they went to the beach, they would remember to turn on the fill flash in such a situation, and the resulting photo would vastly better.
HTH,
Tom M
