We propose new metrics to measure the performance of a deep learning model applied to seismic interpretation tasks such as fault and horizon extraction. Faults and horizons are thin geologic boundaries (1 pixel thick on the image) for which a small prediction error could lead to inappropriately large variations in common metrics (precision, recall, and intersection over union). Through two examples, we show how classical metrics could fail to indicate the true quality of fault or horizon extraction. Measuring the accuracy of reconstruction of thin objects or boundaries requires introducing a tolerance distance between ground truth and prediction images to manage the uncertainties inherent in their delineation. We therefore adapt our metrics by introducing a tolerance function and illustrate their ability to manage uncertainties in seismic interpretation. We compare classical and new metrics through different examples and demonstrate the robustness of our metrics. Finally, we show on a 3D West African data set how our metrics are used to tune an optimal deep learning model.