End punctuation for captions is ultimately a house style issue. I would certainly expect a caption containing more than one complete sentence to have end punctuation. But sentence fragments are subject to idiosyncratic handling.
At the magazine where I work, for example, we would leave unpunctuated a fragmentary caption consisting solely of a manufacturer name + product name:
Samsung Galaxy S4
but we would punctuate even a slightly longer fragmentary caption that conveys additional information:
Samsung's Android 4.2.2–based Galaxy S4.
Other publishers draw the punctuate/don't punctuate line between full sentences and fragments; and still others provide end punctuation for all captions.
The Chicago Manual of Style, 15th Edition (2003) provides sensible general guidelines on end punctuation:
12.32 ...No punctuation is needed after a caption consisting solely of an incomplete sentence. If one or more full sentences follow it, each (including the opening phrase) has closing punctuation. In a work in which most captions consist of full sentences, even incomplete ones may be followed by a period for consistency.
Words Into Type, Third Edition (1974) has a lengthier discussion of captions, starting with the point that "technically caption refers to the title or headline for a figure or illustration, and legend refers to an explanatory or descriptive statement about the figure or illustration." It then gives this rule:
No period is used after a caption unless it is run in on the same line with a legend. The period may be omitted from the end of a short legend that resembles a caption. If a legend consists of two or more sentences, however, it must have sentence-style punctuation.
According to this discussion, "Little Diane necklace" is the caption in your longer example, and everything else is the legend. The punctuation you provide matches the style that Words Into Type recommends for a caption with a run-in legend, except that WIT would have you use some additional formatting to distinguish the caption from the legend. For example, you might use headline style for the three-word caption ("Little Diane Necklace"); or you might run those three words in bold or in large-and-small capital letters, and the legend in sentence-case regular roman.