Frame-Based Facial Expression Recognition Using Geometrical Features

Table 1

The mean (𝜇) and standard deviation (𝜎) of the facial point (𝑃_𝑠) position for the six basic facial expressions, plus neutral expression (based on CK+ database). 𝜎 is square root of the average sum of the squared standard deviations in 𝑥- and 𝑦-coordinates. Each point is positioned inside a detected face of normalized size of 1∗1, where the upper left corner is the origin.

Facial point	Happiness	Surprise	Anger	Disgust	Fear	Sadness	Neutral
𝑝rec
𝜇	0.395, 0.417	0.397, 0.420	0.389, 0.402	0.392, 0.407	0.401, 0.419	0.398, 0.418	0.392, 0.410
𝜎	0.010	0.012	0.014	0.013	0.012	0.012	0.012
𝑝lec
𝜇	0.603, 0.416	0.592, 0.418	0.603, 0.400	0.603, 0.404	0.597, 0.415	0.598, 0.415	0.600, 0.407
𝜎	0.012	0.011	0.016	0.015	0.011	0.012	0.012
𝑝reb
𝜇	0.275, 0.281	0.268, 0.242	0.281, 0.283	0.278, 0.289	0.284, 0.271	0.282, 0.278	0.275, 0.273
𝜎	0.019	0.024	0.016	0.019	0.024	0.017	0.019
𝑝leb
𝜇	0.713, 0.278	0.711, 0.236	0.707, 0.276	0.704, 0.284	0.704, 0.268	0.704, 0.271	0.705, 0.265
𝜎	0.018	0.023	0.017	0.020	0.023	0.021	0.018
𝑝rm
𝜇	0.305, 0.732	0.371, 0.848	0.352, 0.779	0.354, 0.764	0.318, 0.798	0.346, 0.807	0.353, 0.788
𝜎	0.019	0.026	0.023	0.021	0.027	0.025	0.021
𝑝lm
𝜇	0.702, 0.728	0.628, 0.844	0.648, 0.775	0.653, 0.758	0.691, 0.794	0.660, 0.805	0.652, 0.782
𝜎	0.022	0.028	0.025	0.021	0.027	0.023	0.021
𝑝upm
𝜇	0.502, 0.716	0.498, 0.742	0.498, 0.746	0.503, 0.715	0.501, 0.734	0.502, 0.743	0.502, 0.743
𝜎	0.014	0.018	0.017	0.017	0.017	0.018	0.016
𝑝lom
𝜇	0.505, 0.859	0.502, 1.002	0.499, 0.808	0.504, 0.823	0.504, 0.875	0.502, 0.831	0.504, 0.839
𝜎	0.023	0.044	0.025	0.025	0.026	0.023	0.023