"Picture" refers to an image captured/replicated by camera, painting, drawing, etc. "Photo" refers an image captured by camera "Image" refers to the general shape and appearance of any object, person, etc. captured or replicated by such means Examples: 1. He painted a picture of a house. 2. He referred to a photo of an actual house. 3. You can see the image of a house in both the photo and the painting. Source: American English (self)

"Photo" is taken by camera. We often say "picture" when it was painted. Image is more likely to "scheme", "avatar", I guess