Tests of isotropy for rough textures of trended images

In this paper, we propose a statistical methodology to test whether the texture of an image is isotropic or not. This methodology is based on the well-known quadratic variations defined as averages of square image increments. Specific to our approach, these variations are computed in different directions using grid-preserving image rotations. We study asymptotically these variations in a framework of intrinsic random fields allowing us to take into account the presence of polynomial trends in images. We establish a convergence result linking variation and scale logarithms through an asymptotic Gaussian linear model. This model involves direction-dependent intercepts which are equal when textures are isotropic. Hence, we test the texture isotropy using Fisher tests that check the validity of the assumption of the intercept equality. These tests are validated using 6000 realizations of anisotropic fractional Brownian fields simulated on a grid of size 100×100. Results show that more than 70% of anisotropic cases can be detected with less than 1% of misclassified isotropic cases.