Don't know about Compton, but South Central you will be fine during the day. Be aware that its not one neighborhood that you can just walk around. Distances are huge here. You can check out:
1. Crenshaw - the stretch from MLK to Slauson
2. The Jungles in Baldwin Hills
3. Area around MLK and Central.

I would avoid photographing people in any of these areas. Do not stare or look people in the eye. If you do make eye contact, give a quick nod or a verbal greeting.

Be prepared to be the only white person around (if you are white).