This paper presents a framework to automatically measure the intensity of naturally occurring facial actions. Naturalistic expressions are non-posed spontaneous actions. The Facial Action Coding System (FACS) is the gold standard technique for describing facial expressions, which are parsed as comprehensive, nonoverlapping Action Units (Aus). AUs have intensities ranging from absent to maximal on a six-point metric (i.e., 0 to 5). Despite the efforts in recognizing the presence of non-posed action units, measuring their intensity has not been studied comprehensively. In this paper, we develop a framework to measure the intensity of AU12 (Lip Corner Puller) and AU6 (Cheek Raising) in videos captured from infant-mother live faceto-face communications. The AU12 and AU6 are the most challenging case of infant's expressions (e.g., low facial texture in infant's face). One of the problems in facial image analysis is the large dimensionality of the visual data. Our approach for solving this problem is to utilize the spectral regression technique to project high dimensionality facial images into a low dimensionality space. Represented facial images in the low dimensional space are utilized to train Support Vector Machine classifiers to predict the intensity of action units. Analysis of 18 minutes of captured video of non-posed facial expressions of several infants and mothers shows significant agreement between a human FACS coder and our approach, which makes it an efficient approach for automated measurement of the intensity of non-posed facial action units.