One way is to Blur and then Binarize with fixed threshold 0.5:
EdgeDetect[Binarize[Blur[FillingTransform[Closing[img, 1]], 5], .5]] 
In some cases applying Blur twice can give better result:
EdgeDetect[Binarize[Blur[Blur[FillingTransform[Closing[img, 1]], 3], 4], .5]]