Physical distortions (such as thorn-offs and scratches) are commonly seen in historical documents. Their presence disturbs downstream processes such as optical character recognition (OCR) and layout analysis, which leads to reduced productivity in automatic document information retrieval. A proper characterization of such physical noise is an important step in the development of historical document denoising methods. In this paper, we tackle noise characterization with Bayesian labeling, where noise and text pixels are characterized in terms of likelihood densities. We employ in particular two different significance measures, which are formulated using pointwise and cone-of-influence (COI) approximation of local Lipschitz regularity in the wavelet domain. We evaluate the effectiveness of the proposed noise characterization using a binary noise versus text classification model, where we show that a naive binary classifier using average point ratio (APR) or average cone ratio (ACR) distribution densities leads to effective classification of noise and text pixels with encouraging overall success rates. This encourages future work on the development of Bayesian frameworks for the recognition of physical distortions in historical documents.