You will have to query the person API and the take the profile image.url data to get the photo. AFAIK there is no default format for that url that contains the userID.
You can get the URL for the profile image using the people.get method of the Google+ API. That does require an extra round trip, but is the most reliable way to get the image.
You technically can also use the URL https://s2.googleusercontent.com/s2/photos/profile/{id}?sz={size} which will then redirect to the final URL. {id} is the Google user ID or one of the old Google Profiles usernames (they still exist for users who had them, but I don't think you can create new ones anymore). {size} is the desired size of the photo in pixels. I'm almost certain this is not a documented, supported feature, so I wouldn't rely on it for anything important as it may go away at anytime without notice. But for quick prototypes or small one-off applications, it may be sufficient.
They redirect to the same image url you get from Google API, an ugly link as
lh6.googleusercontent.com/-x1W2-XNKA-A/AAAAAAAAAAI/AAAAAAAAAAA/ooSNulbLz8U/photo.jpg
The simplest is to directly use like image source:
If you want to show the profile picture for the currently logged in user, you do not even need to know the {user_id}. Simply using https://plus.google.com/s2/photos/profile/me will be enough.
trying to access the /s2/profile/photo url works for most users but not all.
The only full proof method is to use the Google+ API. You don't need user authentication to request public profile data so it's a rather simple method:
Note the + before the username.
If you use user ids instead (the long string of digits), you don't need the +
you will get a very comprehensive JSON representation of the profile data which includes:
"image":{"url": "https://lh4.googleusercontent.com/..... the rest of the picture url...."}
You may notice in the url the portion "s64-c" which means the image size to be 64, I've tried using other values like "s100-c" and they worked. Also if you remove the "s64-c" part and append the "?sz=100" parameter, that will also work as of now. Though this is not very good way of getting the profile picture of a gplus user, but the advantage is it do not require any api key.