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Implement Dice Loss

Loss Functions

Medium

Compute Dice loss for two equally shaped prediction and target masks. First calculate the smoothed Dice coefficient:

\operatorname{Dice}(P,Y) = \frac{2\sum_i P_iY_i + \varepsilon}{\sum_i P_i + \sum_i Y_i + \varepsilon}

Then calculate the loss:

L_{\mathrm{Dice}} = 1 - \operatorname{Dice}(P,Y)

Here, $P_i$ and $Y_i$ are corresponding mask values and $\varepsilon$ is eps. Sum across every dimension and return the loss as a Python float.

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Examples

Input: p = [0.9, 0.7, 0.1, 0.0], y = [1, 1, 0, 0], eps = 1e-8

Output: 0.135135

Explanation: The soft intersection is 1.6, producing a Dice coefficient of approximately 0.864865.

Input: p = [1.0, 1.0, 0.0, 0.0], y = [1, 1, 0, 0], eps = 1e-8

Output: 0.0

Input: p = [1.0, 1.0], y = [0, 0], eps = 1e-8

Output: 1.0

Hint 1

Use np.sum(p * y) for the soft intersection.

Hint 2

Compute the coefficient before returning 1.0 - coefficient.

Requirements

Sum the intersection and both masks across every dimension
Add eps to the numerator and denominator
Return Dice loss as a Python float

Constraints

p and y are nonempty numeric lists with the same shape
Prediction values are between 0 and 1
Target values are 0 or 1
eps is positive
Use NumPy only

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