“by”, “from” and “of” – What is the difference

I asked myself: “When to use which word?”. I think I understand the difference. Let me try to explain with the help of a example:

• This is a picture by Peter
  Peter created this picture
• This is a picture of Peter
  Peter is on this picture
  
• This is a picture from Peter
  Peter gave it to me

I hope the explanation is right.

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