We address the problem of grasping unknown objects identified from top-down images with a parallel gripper. When no object 3D model is available, the state-of-the-art grasp generators identify the best candidate locations for planar grasps using the RGBD image. However, while they generate the Cartesian location and orientation of the gripper, the height of the grasp center is often determined by heuristics based on the highest point in the depth map, which leads to unsuccessful grasps when the objects are not thick, or have transparencies or curved shapes. In this paper, we propose to learn a regressor that predicts the best grasp height based from the image. We train this regressor with a dataset that is automatically acquired thanks to the DIGIT optical tactile sensors, which can evaluate grasp success and stability. Using our predictor, the grasping success is improved by 6% for all objects, by 16% on average on difficult objects, and by 40% for objects that are notably very difficult to grasp (e.g., transparent, curved, thin).