I\'m actually working on a contour detection for head side. As pictures are taken in front of a white wall, I decided to run a snake (active contour model algorithm) on the
A typical snake or active contour algorithm converges during a trade-off between 3 kind of cost functions: edge strength/distance (data term), spacing and smoothness (prior terms). Immediately, you may notice a connection to your "nose-problem" - the nose has high curvature. Your snake also have troubles getting into concave regions since this certainly increases its curvature compared to a convex hull.
SOLUTIONS:
A. Since your snake performance isn't better than one of a convex hull, as one of the remedies I would proceed with a simpler convex hull algorithm and then rerun it on its inverted residuals. It will get a nose right and then concavities will turn into convexities in the residuals. Or you can use convexity defect function of openCV instead of working with convexHull.
B. Another fix can be to reduce snake curvature parameter to allow it to curve around the nose sharply. Since you have little noise and you can actually clean it up a bit I see no problem of enforcing some constraints instead of making "softer" trade-offs. Perhaps a head silhouette prior model can help here too.
Below I tried to write my own snake algorithm using various distance transforms and weights of a distance parameter. The conclusion - the parameter matters more than distance metrics and does have some effect (a left picture uses smaller parameter than the right and thus cuts the nose more). The distance from contour (red) is shown with grey, snake is green.
C. Since your background is almost solid color, invest a bit into cleaning some residual noise (use morphological operations or connected components) and just findContrours() of the clean silhouette. I implemented this last solution below: a first image has noise deleted and the second is just a contour function from openCV.
