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On page 8 of the paper An automatic nuclei segmentationmethod based on deep convolutional neuralnetworks for histopathology images, the authors show performance of their deep model on test sets. They have clearly mentioned two separate columns for F1 score and Average Dice Coefficient (ADC) (This answer does not answer my specific question):

table

Suppose the test set consisted of 4 images then Average Dice Coefficient (ADC) would be the average of Dice coefficient of 4 predictions of the input test images. They have defined F1 and Dice Coefficient as:

formulas

This is where my doubt comes. In binary segmentation (I mean two class segmentation, foreground or background), we get a sigmoid output. It consists of values in range [0,1], while ground truth contains only 1 and 0. Is it like for Dice coefficient, we take the sigmoid map as it is and compute Dice by (2*prediction*ground truth)/(prediction+ground truth) and for F1 we threshold sigmoid map so that it contains only 1 and 0 and then compute precision, recall and F1 by finding TPs, FPs and FNs? Is this the correct thinking or am I wrong?

To clarify my way of understanding here is an example:

example

Example input image, ground truth and prediction, my example above considers 2x2 output and ground truth instead of 256x256 output and ground truth as in image below:

example

Prasanjit Rath
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  • Pardon, I did not quite understand the question, especially "In binary segmentation, we get a sigmoid output". Maybe you use "binary" in a special meaning, not usual "two class segmentation, the class of interest and not the class of interest". However, I might remark that for a 2x2 confusion table Dice coef. and F1 measure are just two words of the same thing, they are synonyms. – ttnphns Feb 05 '21 at 21:00
  • By binary segmentation I mean two class segmentation. The ground truth (target) of input (to model) images consist of 1s (foreground) and 0s (background). The output of model is an image of size same as that of ground truth and input image with values in between 0-1 (because of sigmoid activation), meaning if we choose threshold 0.5 then pixels above that are foreground and below are background. Also, if F1 and Dice are same then why has author given 2 columns with distinct values? So, I meant to ask if there is a difference in way of computing the 2 values. – Prasanjit Rath Feb 06 '21 at 04:39
  • As I said F1 and Dice are synonyms. Sensu stricto, this coefficient is for the 2x2 classification table only, and extensions for nonbinary data usually bear other names. In your results, as you said, they show column "Average" Dice. I wonder what they mean. Try to consult with the documentation or the authors, to get clarity. – ttnphns Feb 06 '21 at 09:15
  • I did not understand your 2x2 tables you've included. The 2x2 table from which the Dice/F1 measure is computed is the frequncy table {TP,TN;FP,FN} or a transpose of it. So it must contain four nonnegative integers, counts – ttnphns Feb 06 '21 at 09:47
  • The 2x2 tables that I have included are not TP,TN,FP, FN tables, it is a 2x2 image output with pixel values taking values in range(0-1). I have added an image where I show input tissue image, ground truth (desired output, consisting of only 1s and 0s), and my predicted output (has values from 0 to 1 due to sigmoid). The 2x2 tables i have included are small sized images (for the purpose of example) – Prasanjit Rath Feb 07 '21 at 05:58

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