Jaccard and Dice Scores

Two overlap scores for binary masks, the standard metrics for segmentation.

Jaccard (IoU) = |A and B| / |A or B|
Dice (F1)     = 2 * |A and B| / (|A| + |B|)

y_true and y_pred are arrays of the same shape containing 0 and 1, and may be multidimensional (a 2-D image mask, for instance). Flatten them and treat every element as one pixel.

Both range over [0, 1] and agree at 0 and 1, but Dice is always the more generous of the two in between, since it counts the intersection twice. Dice on binary masks is exactly the F1 score with pixels as samples.

If both masks are empty, define both scores as 1.0: the prediction of "nothing here" was correct.

Return (jaccard, dice).

Function signature

def jaccard_dice(y_true, y_pred):

Example

Input

y_true = np.array([1, 1, 0, 0])
y_pred = np.array([1, 0, 1, 0])
jaccard_dice(y_true, y_pred)

Output

(0.3333333333333333, 0.5)

Reasoning

Only the first pixel is in both masks, so the intersection is 1. The union is 3, so Jaccard is 1/3. Each mask has two pixels, so Dice is 2 * 1 / (2 + 2) = 0.5.

Constraints and notes

• Flatten the masks. They can have any shape.
• If both masks are empty, both scores are 1.0.