How to fit implicit function to data

I have these data points

data=[0   1
    0.355257 0.726061
    0.749002 0.382696
    1        0
    2.401699 -0.9817
    3.049682 -1.49588
    4.105308 -2.51708
    3.419108 -2.79514
    1.784289 -2.188
    0.763907 -1.56124
    0        -1];

I have to fit this implicit function to the data

f = @(x,y) abs(x)^a + abs(y)^b +c*x*y-1

where a,b,c are the three positive parameters to be estimated.

any hints?