Keep the file names lower case, with hyphens between the words:
this-is-my-picture.png
The rationale is as follows:
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Having everything in lower case add security in all situations where you are to type the file name (referring to the file from a different source file, HTML++) as you always know the case of all the words.
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Lower case file names are easier on the eyes. When looking at files for hours on end, having them in lower case easens the strain on the eyes as:
MiXEDCaseWordsAreConfusing_and_can_STRAIN-youreyes.doc
In stead, consider this file name:
mixed-case-words-are-confusing-and-can-strain-your-eyes.doc
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Lower case is faster to type as you don't have to press shift or caps lock to get upper case letters.
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Hyphens are easier to type than underscores as you don't have to press another key to get the character.