Monocular depth estimation (MDE) with self-supervised training approaches struggles in low-texture areas, where photometric losses may lead to ambiguous depth predictions. To address this, we propose a novel technique that enhances spatial information by applying a distance transform over pre-semantic contours, augmenting discriminative power in low texture regions. Our approach jointly estimates pre-semantic contours, depth and ego-motion. The pre-semantic contours are leveraged to produce new input images, with variance augmented by the distance transform in uniform areas. This approach results in more effective loss functions, enhancing the training process for depth and ego-motion. We demonstrate theoretically that the distance transform is the optimal variance-augmenting technique in this context. Through extensive experiments on KITTI and Cityscapes, our model demonstrates robust performance, surpassing conventional self-supervised methods in MDE.