We present a Gaussian Mixture Model (GMM) fitting method for estimating the unknown neutral face shape for frontal facial expression recognition using geometrical features. Subtracting the estimated neutral face, which is related to the identity-specific component of the shape leaves us with the component related to the variations resulting from facial expressions. Experimental results on the Extended Cohn-Kanade (CK+) database show that subtracting the estimated neutral face shape gives better emotion recognition rates as compared to classifying the geometrical facial features directly, when the person-specific neutral face shape is not available. We also experimentally evaluate two different geometric facial feature extraction methods for emotion recognition. The average emotion recognition rates achieved with the proposed neutral shape estimation method and coordinate based features is 88%, which is higher than the baseline results presented in the literature, although we do not use the person-specific neutral shapes (94% if we use), and any appearance based features.