How to create a binary mask of an image

img2 = FillingTransform@
  GeodesicClosing[MorphologicalBinarize[img, {.1, .5}, CornerNeighbors -> False], 10]

A smoothed outline (thanks to Rahul):

Binarize@CurvatureFlowFilter[img2, 3]

This approach uses ImageData to work on the lines, rather than the whole image. After a few manipulations, it detects the first and last white pixel on each line and turn the whole segment to 1 (i.e. white).

img = Import["https://i.stack.imgur.com/Mw1iJ.png"]
edges = EdgeDetect[img, 2]
data = ImageData@edges;
Table[line = data[[j]]; pos = Flatten@Position[line, 1];
  If[Length[pos] > 1, data[[j, pos[[1]] ;; pos[[-1]]]] = 1];
  , {j, Length@data}];
Image@data

With GrowCutComponents[], one can obtain this :

A little bit lifting with Dilation/Erosion will probably improve the result.

How to use GrowCutComponents[] ?

you have to create the 2 masks and evaluate the following :

One can create the masks with Drawing Tools see here