How to find the lower eyelid in an image? I have an image of 480x360 px that contains eye portion only i.e., sclera iris, pupil, eyebrows  etc. Now I have to find the lower eyelid in the image. 

What I've done till now is that cut the image in 2 parts upper and lower half. Now apply edge detector (Canny) on lower part and then parabola fitting on the resultant image. 

I am getting ok results but eyelid is not parabola so sometimes  the parabola goes into the sclera region also.

I am thinking to doing curve fitting but a better idea looks like funding a curved line in the edge map. 

Can you help in finding the curved line in the edge map ?
There is a section in this paper¹ that deals with eyelid contour approximation. It should help you out.

¹ Pernek, Ákos and Hajder, Levente (2014) Precise 3D Pose Estimation of Human Faces. In: VISAPP 2014. Proceedings of the 9th International Conference on Computer Vision Theory and Applications. Vol. 3. SciTePress, Lisszabon, pp. 618-625. ISBN 978-989-758-005-5