  Although a vast body of literature relates to image segmentation methods that
use deep neural networks (DNNs), less attention has been paid to assessing the
statistical reliability of segmentation results. In this study, we interpret
the segmentation results as hypotheses driven by DNN (called DNN-driven
hypotheses) and propose a method by which to quantify the reliability of these
hypotheses within a statistical hypothesis testing framework. Specifically, we
consider a statistical hypothesis test for the difference between the object
and background regions. This problem is challenging, as the difference would be
falsely large because of the adaptation of the DNN to the data. To overcome
this difficulty, we introduce a conditional selective inference (SI) framework
-- a new statistical inference framework for data-driven hypotheses that has
recently received considerable attention -- to compute exact (non-asymptotic)
valid p-values for the segmentation results. To use the conditional SI
framework for DNN-based segmentation, we develop a new SI algorithm based on
the homotopy method, which enables us to derive the exact (non-asymptotic)
sampling distribution of DNN-driven hypothesis. We conduct experiments on both
synthetic and real-world datasets, through which we offer evidence that our
proposed method can successfully control the false positive rate, has good
performance in terms of computational efficiency, and provides good results
when applied to medical image data.
