Selecting salient points from two or more images for computing correspondences is a fundamental problem in image analysis. Three methods originally proposed by Harris et al., by Noble et al. and by Shi et al. proved to be quite effective and robust and have been widely used by the computer vision community. The goal of this paper is to analyze these point detectors starting from the algebraic and numerical properties of the image auto-correlation matrix. To accomplish this task we will first introduce a "natural" constraint that needs to be satisfied by any point detector based on the auto-correlation matrix. Then, by casting the point detection problem in a mathematical framework based on condition theory, we will show that under certain hypothesis the point detectors are equivalent modulo the choice of a specific matrix norm. The results presented in this paper will provide a novel unifying description for the most commonly used point detection algorithms.