Chapter 7 - Analyzing Errors

Abstract

This chapter discusses the types of errors that occur in watermarking systems and how these errors can be modeled and measured. There are three main types of errors: a message error occurs when the decoded message is not the same as the message that was embedded, a false positive occurs when a watermark is detected in an unwatermarked Work, and a false negative occurs when a watermark is not detected in a watermarked Work. When messages are coded as binary strings, message error rates are often expressed as bit error rates (BER), which measure the frequency with which individual bits are incorrectly decoded. Additionally, various different types of false positive and false negative rates might be relevant: random-watermark false positives and negatives occur when a Work is fixed and the watermark is chosen at random. These are easy to analyze because the distribution of watermarks is determined by the design of the system. However, they are not necessarily relevant in most applications. Random-Work false positives and negatives occur when the watermark is fixed and the Work is chosen at random. These are more difficult to analyze because they depend on the distribution of unwatermarked content. Furthermore, two methods for analyzing the performance of normalized correlation detectors were presented: the approximate Gaussian method models the distribution of detection values as a Gaussian distribution. This yields reasonable predictions at low detection thresholds, but overestimates false positive probabilities as the threshold increases toward 1. The spherical method yields exact predictions of false positive probabilities under the assumption that random vectors are drawn from a radially symmetric distribution. It can also be used to predict random watermark false negative probabilities for blind embedders.