# generalizedDice

Generalized Sørensen-Dice similarity coefficient for image segmentation

## Syntax

``similarity = generalizedDice(X,target)``
``similarity = generalizedDice(X,target,'DataFormat',dataFormat)``

## Description

The generalized Dice similarity coefficient measures the overlap between two segmented images. Generalized Dice similarity is based on Sørensen-Dice similarity and controls the contribution that each class makes to the similarity by weighting classes by the inverse size of the expected region. When working with imbalanced data sets, class weighting helps to prevent the more prevalent classes from dominating the similarity score.

example

````similarity = generalizedDice(X,target)` calculates the generalized Sørensen-Dice similarity coefficient between test image `X` and target image `target`.```
````similarity = generalizedDice(X,target,'DataFormat',dataFormat)` also specifies the dimension labels, `dataFormat`, of unformatted image data. You must use this syntax when the input are unformatted `dlarray` (Deep Learning Toolbox) objects.```

## Examples

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```data = load('triangleSegmentationNetwork'); net = data.net;```

Load the triangle image data set using `imageDatastore`.

```dataDir = fullfile(toolboxdir('vision'),'visiondata','triangleImages'); testImageDir = fullfile(dataDir,'testImages'); imds = imageDatastore(testImageDir);```

Load ground truth labels for the triangle data set using `pixelLabelDatastore`.

```labelDir = fullfile(dataDir,'testLabels'); classNames = ["triangle" "background"]; pixelLabelID = [255 0]; pxdsTruth = pixelLabelDatastore(labelDir,classNames,pixelLabelID);```

Read a sample image and the corresponding ground truth labels.

```I = readimage(imds,1); gTruthLabels = readimage(pxdsTruth,1);```

Run semantic segmentation on the image.

`[predictions,scores] = semanticseg(I,net);`

Encode the categorical predictions and targets using the `onehotencode` function.

```featureDim = ndims(predictions) + 1; encodedPredictions = onehotencode(predictions,featureDim); encodedGroundTruthLabels = onehotencode(gTruthLabels,featureDim);```

Ignore any undefined classes in the encoded data.

```encodedPredictions(isnan(encodedPredictions)) = 0; encodedGroundTruthLabels(isnan(encodedGroundTruthLabels)) = 0;```

Compute generalized Dice similarity coefficient between the segmented image and the ground truth.

`gDice = generalizedDice(encodedPredictions,encodedGroundTruthLabels)`
```gDice = 0.4008 ```

Create input data as a formatted `dlarray` object containing 32 observations with unnormalized scores for ten output categories.

```spatial = 10; numCategories = 10; batchSize = 32; X = dlarray(rand(spatial,numCategories,batchSize),'SCB');```

Convert unnormalized scores to probabilities of membership of each of the ten categories.

`X = sigmoid(X);`

Create target values for membership in the second and sixth category.

```targets = zeros(spatial,numCategories,batchSize); targets(:,2,:) = 1; targets(:,6,:) = 1; targets = dlarray(targets,'SCB');```

Compute the generalized Dice similarity coefficient between probability vectors X and targets for multi-label classification.

```Z = generalizedDice(X,targets); whos Z```
``` Name Size Bytes Class Attributes Z 1x1x32 262 dlarray ```

Calculate the generalized Dice loss.

`loss = 1 - mean(Z,'all')`
```loss = 1(S) x 1(C) x 1(B) dlarray 1 ```

## Input Arguments

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Test image to be analyzed, specified as one of these values.

• A numeric array of any dimension. The last dimension must correspond to classes.

• An unformatted `dlarray` (Deep Learning Toolbox) object. You must specify the data format using the `dataFormat` argument.

• A formatted `dlarray` object. The `dlarray` input must contain a channel dimension, `'C'` and can contain a batch dimension, `'B'`.

`dlarray` input requires Deep Learning Toolbox™.

Target image, specified as a numeric array or a `dlarray` (Deep Learning Toolbox) object. The size and format of `target` must match the size and format of the test image, `X`. `dlarray` input requires Deep Learning Toolbox.

Dimension labels for unformatted `dlarray` image input, specified as a string scalar or character vector. Each character in `dataFormat` must be one of these labels:

• `S` — Spatial

• `C` — Channel

• `B` — Batch observations

The format must include one channel label. The format cannot include more than one channel label or batch label. Do not specify the '`dataFormat`' argument when the input images are formatted `dlarray` objects.

Example: `'SSC'` indicates that the array has two spatial dimensions and one channel dimension

Example: `'SSCB'` indicates that the array has two spatial dimensions, one channel dimension, and one batch dimension

## Output Arguments

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Generalized Dice similarity coefficient, returned as a numeric scalar or a `dlarray` (Deep Learning Toolbox) object with values in the range [0, 1]. A `similarity` of 1 means that the segmentations in the two images are a perfect match.

• If the input arrays are numeric images, then `similarity` is a numeric scalar.

• If the input arrays are `dlarray` objects, then `similarity` is a `dlarray` object of the same dimensionality as the input images. The spatial and channel dimensions of `similarity` are singleton dimensions. There is one generalized Dice measurement for each element along the batch dimension.

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### Generalized Dice Similarity

Generalized Dice similarity is based on Sørensen-Dice similarity for measuring overlap between two segmented images.

The generalized Dice similarity function S used by `generalizedDice` for the similarity between one image Y and the corresponding ground truth T is given by:

`$S=\frac{2{\sum }_{k=1}^{K}{w}_{k}{\sum }_{m=1}^{M}{Y}_{km}{T}_{km}}{{\sum }_{k=1}^{K}{w}_{k}{\sum }_{m=1}^{M}{Y}_{km}^{2}+{T}_{km}^{2}}$`

K is the number of classes, M is the number of elements along the first two dimensions of Y, and wk is a class specific weighting factor that controls the contribution each class makes to the score. This weighting helps counter the influence of larger regions on the generalized Dice score. wk is typically the inverse area of the expected region:

`${w}_{k}=\frac{1}{{\left({\sum }_{m=1}^{M}{T}_{km}\right)}^{2}}$`

There are several variations of generalized Dice scores [1], [2]. The `generalizedDice` function uses squared terms to ensure that the derivative is 0 when the two images match [3].

## References

[1] Crum, William R., Oscar Camara, and Derek LG Hill. "Generalized overlap measures for evaluation and validation in medical image analysis." IEEE Transactions on Medical Imaging. 25.11, 2006, pp. 1451–1461.

[2] Sudre, Carole H., et al. "Generalised Dice overlap as a deep learning loss function for highly unbalanced segmentations." Deep Learning in Medical Image Analysis and Multimodal Learning for Clinical Decision Support. Springer, Cham, 2017, pp. 240–248.

[3] Milletari, Fausto, Nassir Navab, and Seyed-Ahmad Ahmadi. "V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation". Fourth International Conference on 3D Vision (3DV). Stanford, CA, 2016: pp. 565–571.

## Version History

Introduced in R2021a