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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:

Dice⁡(P,Y)=2∑iPiYi+ε∑iPi+∑iYi+ε\operatorname{Dice}(P,Y) = \frac{2\sum_i P_iY_i + \varepsilon}{\sum_i P_i + \sum_i Y_i + \varepsilon}Dice(P,Y)=∑i​Pi​+∑i​Yi​+ε2∑i​Pi​Yi​+ε​

Then calculate the loss:

LDice=1−Dice⁡(P,Y)L_{\mathrm{Dice}} = 1 - \operatorname{Dice}(P,Y)LDice​=1−Dice(P,Y)

Here, PiP_iPi​ and YiY_iYi​ are corresponding mask values and ε\varepsilonε 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
Try Similar Problems
Binary Focal LossFocal LossCross Entropy LossIou Bounding BoxContrastive Loss

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Case 1
Case 2
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Accepts: array

Accepts: array

Accepts: number

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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:

Dice⁡(P,Y)=2∑iPiYi+ε∑iPi+∑iYi+ε\operatorname{Dice}(P,Y) = \frac{2\sum_i P_iY_i + \varepsilon}{\sum_i P_i + \sum_i Y_i + \varepsilon}Dice(P,Y)=∑i​Pi​+∑i​Yi​+ε2∑i​Pi​Yi​+ε​

Then calculate the loss:

LDice=1−Dice⁡(P,Y)L_{\mathrm{Dice}} = 1 - \operatorname{Dice}(P,Y)LDice​=1−Dice(P,Y)

Here, PiP_iPi​ and YiY_iYi​ are corresponding mask values and ε\varepsilonε is eps. Sum across every dimension and return the loss as a Python float.

Loading visualization...

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
Try Similar Problems
Binary Focal LossFocal LossCross Entropy LossIou Bounding BoxContrastive Loss

Sign in to take notes on this problem

Case 1
Case 2
Case 3

Accepts: array

Accepts: array

Accepts: number

You must run your code first.