We address the problem of verifying neural networks against geometric transformations of the input image, including rotation, scaling, shearing, and translation. The proposed method computes provably sound piecewise linear constraints for the pixel values by using sampling and linear approximations in combination with branch-and-bound Lipschitz optimisation. The method obtains provably tighter over-approximations of the perturbation region than the present state-of-the-art. We report results from experiments on a comprehensive set of verification benchmarks on MNIST and CIFAR10. We show that our proposed implementation resolves up to 32% more verification cases than present approaches.