Automatic image inspector inspects the quality of printed circuit boards using image-processing technology. In this study, we change an automatic inspection problem into a problem for detecting the signal singularities. Based on the wavelet theory that the wavelet transform can focus on localized signal structures with a zooming procedure, a novel singularity detection and measurement algorithm is proposed. Singularity positions are detected with the local wavelet transform modulus maximum (WTMM) line, and the Lipschitz exponent is estimated at each singularity from the decay of the wavelet transform amplitude along the WTMM line. According to the theoretical analysis and computer simulation results, the proposed algorithm is shown to be successful for solving the automatic inspection problem and calculating the Lipschitz exponents of signals. These Lipschitz exponents successfully characterize singular behavior of signals at singularities.