Our method for estimating the mouth elongation is inspired by the method of Hennecke et al. as described in [HPS94]. Inasmuch as the procedure we describe here makes use of gradient operations followed by processing on the gradient vector field, it is closely related to OTC. The main difference is that the direction of the gradient vectors are not removed by an angle doubling step. Thus we retain the abililty to discriminate between ``positive'' and ``negative'' edges, wherein the sign indicates the direction of change from light to dark.
The first step of our procedure is to compute the gradient of the extracted lip image using finite differences. We assume that the lip image has been pre-smoothed with the gauss5 kernel to eliminate noise. Two examples of gradient vector fields resulting from this step are shown in Figure 15.
Figure 14: Examples of extracted lip images (with smoothing).
Figure 15: Gradient vector fields for extracted lip images.
In subsequent steps, we assume that the gradient vector field is represented by an array of complex numbers. The next step is to compute the real part of the correlation of the gradient vector field with a special operator L which is designed to be sensitive to the horizontal gap between the lips near the mouth corners. One choice of L which serves this purpose is the function
which is depicted in Figure 16.
Figure 16: Vector field operator for horizontal lip gap detection.
In our implementation, we sample this function on a grid with x and y ranging over the integer values from -4 to 4. The real part of the correlation of L with the gradient vector field for the two examples in Figure 14 is shown in Figure 17.
Figure 17: Real part of correlation between gradient vector fields and horizontal vector field operator.
The final step is to apply a threshold to the correlation result to obtain a binary blob which lies roughly between the upper and lower lips, between the left and right mouth corners. We have found that a threshold equal to 50% of the correlation maximum is effective for this purpose. Two binary blobs obtained via this method are shown in Figure 18.
Figure 18: Thresholded binary blobs representing mouth elongation.
From such a blob we retain the leftmost and rightmost nonzero values, which may be used to determine the approximate mouth width. A sample sequence of lips together with the thresholded blobs is shown in Figure 19.
Figure 19: Thresholded binary blobs for sample sequence. The extreme left and extreme right nonzero pixels in each thresholded image are used to estimate the mouth elongation.