We develop confidence sets which provide spatial uncertainty guarantees for the output of a black-box machine learning model designed for image segmentation. To do so we adapt conformal inference to the imaging setting, obtaining thresholds on a calibration dataset based on the distribution of the maximum of the transformed logit scores within and outside of the ground truth masks. We prove that these confidence sets, when applied to new predictions of the model, are guaranteed to contain the true unknown segmented mask with desired probability. We show that learning appropriate score transformations on a learning dataset before performing calibration is crucial for optimizing performance. We illustrate and validate our approach on a polpys tumor dataset. To do so we obtain the logit scores from a deep neural network trained for polpys segmentation and show that using distance transformed scores to obtain outer confidence sets and the original scores for inner confidence sets enables tight bounds on tumor location whilst controlling the false coverage rate.

翻译：我们开发了一种置信集，为用于图像分割的黑盒机器学习模型的输出提供空间不确定性保证。为此，我们将保形推断方法适配到成像场景中，基于校准数据集中变换后的logit分数在真实标注掩码内部和外部的最大值分布来获取阈值。我们证明，当将这些置信集应用于模型的新预测时，它们能以期望的概率保证包含真实的未知分割掩码。我们表明，在执行校准之前，在学习数据集上学习适当的分数变换对于优化性能至关重要。我们在一个息肉肿瘤数据集上演示并验证了我们的方法。为此，我们从一个为息肉分割训练的深度神经网络中获取logit分数，并证明使用距离变换分数来获取外部置信集，以及使用原始分数来获取内部置信集，能够在控制错误覆盖率的同时，对肿瘤位置提供紧密的边界。