Using Expectation-Maximization for exposing image forgeries by revealing inconsistencies in shadow geometry

Abstract

In this study, a new approach and mathematical framework are proposed for exposing image forgeries by detecting inconsistencies in the geometry of cast shadows. The main difficulty in detecting shadow inconsistencies is the precise establishment of correspondences between object points and their corresponding shadow points. To counter the problem, a mathematical framework is proposed to formulate the geometric transformation between the object points and their corresponding shadow points. We assume a rough correspondence between the object and shadow points and use Expectation-Maximization (EM) algorithm to simultaneously calculate the transformation parameters and categorize rough correspondences as inliers or outliers. To enhance the efficiency of the proposed algorithm, we extend the proposed algorithm to handle the ambiguity in initial correspondence by using the one-to-many correspondence strategy. Experimental results on the provided database comprising forged and authentic images showed the accuracy of 84% and 98% for one-to-one and one-to-many correspondence strategies, respectively.