Why normalize images by subtracting dataset's image mean, instead of the current image mean in deep learning? There are some variations on how to normalize the images but most seem to use these two methods:


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*Subtract the mean per channel calculated over all images (e.g.  VGG_ILSVRC_16_layers)

*Subtract by pixel/channel calculated over all images (e.g. CNN_S, also see Caffe's reference network)


The natural approach would in my mind to normalize each image. An image taken in broad daylight will cause more neurons to fire than a night-time image and while it may inform us of the time we usually care about more interesting features present in the edges etc. 
Pierre Sermanet refers in 3.3.3 that local contrast normalization that would be per-image based but I haven't come across this in any of the examples/tutorials that I've seen. I've also seen an interesting Quora question and Xiu-Shen Wei's post but they don't seem to support the two above approaches. 
What exactly am I missing? Is this a color normalization issue or is there a paper that actually explain why so many use this approach?
 A: Per-image normalization is common and is even the only in-built function currently in Tensorflow (primarily due to being very easy to implement).  It is used for the exact reason you mentioned (day VS night for the same image).  However, if you imagine a more ideal scenario where lighting was controlled, then the relative differences between each image would be of great value in the algorithm, and we wouldn't want to wipe that out with per-image normalization (and would want to do normalization in the context of the entire training data set).
A: There are two aspects to this topic:

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*Normalization to keep all data in the same scale --> the outcome is going to be similar when normalizing both on a per-image basis or across the entire image data set

*Preservation of relative information --> this is where doing normalization on a per-image or per-set basis makes a big difference

For example if you want to learn a CNN to recognize night scenes vs. daytime scenes and you normalize on a per-image basis, the network will fail miserably because all the images will be scaled equally.
Another pitfall of per-image normalization is that you may be artificially gaining up image sensor shot noise (e.g. for very dark scenes) and this will throw off the CNN in confusing such noise as useful information.
Last word of caution on normalization: if it is done incorrectly it can lead to unrecoverable loss of information, for example image clipping (generating values that are below the valid range of the image datatype) or saturation (above the valid range). This is a classic mistake when operating with uint8 variables to represent images and values either go below 0 or exceed 255 due to normalization / pre-processing operations. Once this happens, image information is lost and it cannot be recovered, so the CNN will fail to learn any useful information from those image pixels.
A: This is called preprocessing of data before using it. You can process in many ways but there is one condition that you should process each data with same function X_preproc = f(X) and this f(.) should not depend on data itself, so if you use the current image mean to process this current image then your f(X) will actually be really f(X, image) and you don't want that.
The image contrast normalization you were talking about is for a different purpose. Image contrast normalization will help in feature.
But f(.) above will help on optimization by keeping all the features numerically equal to each other (of-course approximately)
A: Subtracting the dataset mean serves to "center" the data. Additionally, you ideally would like to divide by the sttdev of that feature or pixel as well if you want to normalize each feature value to a z-score. 
The reason we do both of those things is because in the process of training our network, we're going to be multiplying (weights) and adding to (biases) these initial inputs in order to cause activations that we then backpropogate with the gradients to train the model. 
We'd like in this process for each feature to have a similar range so that our gradients don't go out of control (and that we only need one global learning rate multiplier). 
Another way you can think about it is deep learning networks traditionally share many parameters - if you didn't scale your inputs in a way that resulted in similarly-ranged feature values (ie: over the whole dataset by subtracting mean) sharing wouldn't happen very easily because to one part of the image weight w is a lot and to another it's too small.
You will see in some CNN models that per-image whitening is used, which is more along the lines of your thinking.  
A: Prior to batch normalization, mean subtraction per channel was used to center the data around zero mean for each channel (R, G, B). This typically helps the network to learn faster since gradients act uniformly for each channel. I suspect if you use batch normalization, the per channel mean subtraction pre-processing step is not really necessary since you are normalizing per mini-batch anyway. 
