  We propose a new loss formulation to further advance the multiclass
segmentation of cluttered cells under weakly supervised conditions.
  We improve the separation of touching and immediate cells, obtaining sharp
segmentation boundaries with high adequacy, when we add Youden's $J$ statistic
regularization term to the cross entropy loss. This regularization
intrinsically supports class imbalance thus eliminating the necessity of
explicitly using weights to balance training. Simulations demonstrate this
capability and show how the regularization leads to better results by helping
advancing the optimization when cross entropy stalls.
  We build upon our previous work on multiclass segmentation by adding yet
another training class representing gaps between adjacent cells.
  This addition helps the classifier identify narrow gaps as background and no
longer as touching regions.
  We present results of our methods for 2D and 3D images, from bright field to
confocal stacks containing different types of cells, and we show that they
accurately segment individual cells after training with a limited number of
annotated images, some of which are poorly annotated.
