Is very easy

http://picasaweb.google.com/data/entry/api/user/<hereYourUserIdOrYourEmail>?alt=json

just has a little problem.

You only can get the picture of your Google+ profile, not directly from your gmail.

UPDATE:

This API is being deprecated and will be turned down in January 2019. Migrate to Google Photos Library API as soon as possible to avoid disruptions to your application.

More Info Here

If you want to retrieve the full quality profile picture without ever having uploaded it to Google+, follow these steps:

1. If you have multiple google accounts, open a private window by pressing CTRL + SHIFT + N for Chrome or CTRL + SHIFT + P for Firefox.
2. Go to any google service such as gmail.com and log into the account you wish to retrieve a profile picture of.
3. Go to https://get.google.com/albumarchive
4. Navigate to Profile photos > profile photos. All the profile pictures of your account can be found here.
5. You can use the triple dot button in the top right corner to either download a single picture, download all pictures or delete individual ones.

This is also where to find your uploaded Google Maps photos, and all Google Hangouts photos. I hope these keywords help future search-wizards having this problem.