Hi,
I found a submission on File Exchange Face, Age and Emotion Detection that essentially use pretrained network capabilities and does the emotion detection. If you have queries regarding running the codes you may directly post a comment on the File exchange submission. From the title I think facial emotion recognition can be done by the above however in the description you mentioned to detect eyes, nose, mouth, eyebrows and their shapes. For this I think some object detection workflow should come into picture for detecting specific features and location of them,.
If the end goal is to classify a face, I suggest looking face recognition. Otherwise If you want location of the face features then going for an object detector network would be the best bet however you will be needing training data for it.
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