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## Color-Based Segmentation Using K-Means Clustering

This example shows how to segment colors in an automated fashion using the L*a*b* color space and K-means clustering.

This example requires Statistics and Machine Learning Toolbox™.

Read in `hestain.png`, which is an image of tissue stained with hemotoxylin and eosin (H&E). This staining method helps pathologists distinguish different tissue types.

```he = imread('hestain.png'); imshow(he), title('H&E image'); text(size(he,2),size(he,1)+15,... 'Image courtesy of Alan Partin, Johns Hopkins University', ... 'FontSize',7,'HorizontalAlignment','right'); ```

### Step 2: Convert Image from RGB Color Space to L*a*b* Color Space

How many colors do you see in the image if you ignore variations in brightness? There are three colors: white, blue, and pink. Notice how easily you can visually distinguish these colors from one another. The L*a*b* color space (also known as CIELAB or CIE L*a*b*) enables you to quantify these visual differences.

The L*a*b* color space is derived from the CIE XYZ tristimulus values. The L*a*b* space consists of a luminosity layer 'L*', chromaticity-layer 'a*' indicating where color falls along the red-green axis, and chromaticity-layer 'b*' indicating where the color falls along the blue-yellow axis. All of the color information is in the 'a*' and 'b*' layers. You can measure the difference between two colors using the Euclidean distance metric.

Convert the image to L*a*b* color space using `makecform` and `applycform`.

```cform = makecform('srgb2lab'); lab_he = applycform(he,cform); ```

### Step 3: Classify the Colors in 'a*b*' Space Using K-Means Clustering

Clustering is a way to separate groups of objects. K-means clustering treats each object as having a location in space. It finds partitions such that objects within each cluster are as close to each other as possible, and as far from objects in other clusters as possible. K-means clustering requires that you specify the number of clusters to be partitioned and a distance metric to quantify how close two objects are to each other.

Since the color information exists in the 'a*b*' space, your objects are pixels with 'a*' and 'b*' values. Use `kmeans` to cluster the objects into three clusters using the Euclidean distance metric.

```ab = double(lab_he(:,:,2:3)); nrows = size(ab,1); ncols = size(ab,2); ab = reshape(ab,nrows*ncols,2); nColors = 3; % repeat the clustering 3 times to avoid local minima [cluster_idx, cluster_center] = kmeans(ab,nColors,'distance','sqEuclidean', ... 'Replicates',3); ```

### Step 4: Label Every Pixel in the Image Using the Results from KMEANS

For every object in your input, `kmeans` returns an index corresponding to a cluster. The `cluster_center` output from `kmeans` will be used later in the example. Label every pixel in the image with its `cluster_index`.

```pixel_labels = reshape(cluster_idx,nrows,ncols); imshow(pixel_labels,[]), title('image labeled by cluster index'); ```

### Step 5: Create Images that Segment the H&E Image by Color.

Using `pixel_labels`, you can separate objects in `hestain.png` by color, which will result in three images.

```segmented_images = cell(1,3); rgb_label = repmat(pixel_labels,[1 1 3]); for k = 1:nColors color = he; color(rgb_label ~= k) = 0; segmented_images{k} = color; end imshow(segmented_images{1}), title('objects in cluster 1'); ```

```imshow(segmented_images{2}), title('objects in cluster 2'); ```

```imshow(segmented_images{3}), title('objects in cluster 3'); ```

### Step 6: Segment the Nuclei into a Separate Image

Notice that there are dark and light blue objects in one of the clusters. You can separate dark blue from light blue using the 'L*' layer in the L*a*b* color space. The cell nuclei are dark blue.

Recall that the 'L*' layer contains the brightness values of each color. Find the cluster that contains the blue objects. Extract the brightness values of the pixels in this cluster and threshold them with a global threshold using `imbinarize`.

You must programmatically determine the index of the cluster containing the blue objects because `kmeans` will not return the same `cluster_idx` value every time. You can do this using the `cluster_center` value, which contains the mean 'a*' and 'b*' value for each cluster. The blue cluster has the smallest cluster_center value (determined experimentally).

```mean_cluster_value = mean(cluster_center,2); [tmp, idx] = sort(mean_cluster_value); blue_cluster_num = idx(1); L = lab_he(:,:,1); blue_idx = find(pixel_labels == blue_cluster_num); L_blue = L(blue_idx); is_light_blue = imbinarize(L_blue); ```

Use the mask `is_light_blue` to label which pixels belong to the blue nuclei. Then display the blue nuclei in a separate image.

```nuclei_labels = repmat(uint8(0),[nrows ncols]); nuclei_labels(blue_idx(is_light_blue==false)) = 1; nuclei_labels = repmat(nuclei_labels,[1 1 3]); blue_nuclei = he; blue_nuclei(nuclei_labels ~= 1) = 0; imshow(blue_nuclei), title('blue nuclei'); ```