SED - editing file names (End of line problem?)

For lists in sed, to say what to replace, is this correct: [$ .]

I am hoping that this would recognise that either a "." is present, or that the substitution happens at the end of the line.

For files with extensions [picture.jpg], my script works perfectly.

My problem is, files without extentions, i.e. [picture]. The script gives the following message for these cases: "picture and picture are identical".

Please provide us with the actual sed script