Computing Valid P-Values for Image Segmentation by Selective Inference

Image segmentation is one of the most fundamental tasks of computer vision. In many practical applications, it is essential to properly evaluate the reliability of individual segmentation results. In this study, we propose a novel framework for determining the statistical significance of segmentation results in the form of p-values. Specifically, we utilize a statistical hypothesis test for determining the difference between the object region and the background region. This problem is challenging because the difference can be deceptively large (called segmentation bias) due to the adaptation of the segmentation algorithm to the data. To overcome this difficulty, we introduce a statistical approach called selective inference, and develop a framework for computing valid p-values in which segmentation bias is properly accounted for. Although the proposed framework is potentially applicable to various segmentation algorithms, here we focus on graph-cut-and threshold-based segmentation algorithms, and develop two specific methods for computing valid p-values for the segmentation results obtained by these algorithms. We prove the theoretical validity of these two methods and demonstrate their practicality by applying them to the segmentation of medical images.