First of all, the picture isn't really going to help in determining if your girl is beautiful or not. That being said, it doesn't matter what we think. You think she's beautiful, and that's all that really matters. Your question was actually about why she isn't taking your compliments, and that is another matter entirely.
She's got something eating at her self esteem. It may have nothing to do with her body directly. She probably appreciates your compliments more than she's letting on, so if you truly feel this way, by all means, continue with the compliments. No matter what we may say, we female critters love compliments.
On the flip side of anorexic being viewed as perfection, there's the other part : it's still okay to treat fat people poorly in our current society. Your friend may see this and be bothered by it enough to fear getting treated poorly because of weight.
Before anyone throws tomatoes at me, honestly think about it. When's the last time you heard a fat joke and laughed? When's the last time you saw a fat person and was disgusted? Does it bother you if you're disgusted by someone overweight? It's subtle, but the message is there... fat people are disgusting and it's okay to shun them. Give it a hard thought before you disagree. If it isn't so, then why are men and women alike afraid of becomming fat? I'm not saying it's right. I'm simply saying that right or wrong, that's how things are currently.
You've got your work cut out for you if you're seeking to change your friend's belief. Only she can change her belief. Convincing her isn't really an option. Are you okay with that until she finds the confidence to accept herself? Confidence doesn't come easliy for everyone, and that's the real root of this issue. When she finds something she is confident about, she'll come around.
Until then, just love her. Tell her reasons you love her body and tell her the reasons you love her that don't involve her body. Whatever she's talented in, encourage it. If you see her taking on characteristics of bulemia or anorexia, by all means intervene because both of these conditions can turn deadly but don't expect her to appreciate you for it. She's one lucky lady that you care enough to honestly try to get the female perspective.
That's my 2 cents. Feel free to dispense change.