We present a procedure using continuous wavelet transforms (CWTs) to extract the phase information from moiré interferograms. The relationship between precise ridge detection of the two-dimensional CWT magnitude map and accurate phase extraction is detailed. A cost function is introduced for the adaptive selection of the ridge, and a computationally inexpensive implementation of the cost function ridge detection algorithm is explored with dynamic programming optimization. The results of the proposed ridge detection algorithm on actual interferograms are illustrated. Moreover, the resulting extracted phase is demonstrated to be smooth and accurate. As a result, the sensitivity of the moiré interferometry method is improved to obtain a pixel-by-pixel in-plane strain distribution map.