Cluster centers in k-means? - image-processing

Question

I have a 96x96 pixel grayscale facial images. i am trying to find the eye centers and lip corners. I applied one gabor filter (theta=pi/2, lamda=1.50) on the facial image and after convolving i get the filter output like this.
As you can see from the gabor output eyes and mouth corners are clearly distinguishable. i apply scikit kmeans clustering to group pixels together to 4 clusters (2 eyes and 2 lip corner)
data = output.reshape(-1,96*96)
estimator = KMeans(n_clusters=4)
estimator.fit(data)
centroids = np.asarray(estimator.cluster_centers_)
print 'Cluster centers', centroids.shape
print 'Labels', estimator.labels_, estimator.labels_.shape
Output
Input X,y: (100, 96, 96) (1783, 1)
Gabor Filters (1, 9, 9)
Final output X,y (100, 96, 96) (0,)
Shape estimator.cluster_centers_: (4, 9216)
Now comes the question: How do i plot the centroids x,y coordinates of the 4 cluster centers? Will i see the eye centers and mouth corners
Further information: I plot the estimator.cluster_centers_ and the output is like a code book. i see no coordinates of cluster centroids.
I am using the steps as described in this paper: http://jyxy.tju.edu.cn/Precision/MOEMS/doc/p36.pdf

Answer 1

I think there's some confusion here about the space in which you're doing your K-means clustering. In the code snippet that you included in your question, you're training up a KMeans model using the vectorized face images as data points. K-means clusters live in the same space as the data you give it, so (as you noticed) your cluster centroids will also be vectorized face images. Importantly, these face images have dimension 9216, not dimension 2 (i.e., x-y coordinates)!
To get 2-dimensional (x, y) coordinates as your K-means centroids, you need to run the algorithm using 2-dimensional input data. Just off the top of my head, it seems like you could apply a darkness threshold to your face images and assemble a clustering dataset of only the dark pixel locations. Then after you run K-means on this dataset, the centroids will hopefully be close to the pixel locations in your face images where there are the most dark pixels. These locations (assuming the face images in your training data were already somewhat registered) should be somewhat close to the eyes and mouth corners that you're hoping for.
This can be really confusing so I'll try to add an example. Let's say just for an example you have "face images" that are 3 pixels wide by 4 pixels tall. After thresholding the pixels in one of your images it might look like:
0 1 2 <-- x coordinates
0 0 0 0 ^ y coordinates
0 1 0 1 |
1 0 0 2 |
0 0 1 3 v
If you use this "image" directly in K-means, you're really running your K-means algorithm in a 12-dimensional space, and the image above would be vectorized as:
0 0 0 0 1 0 1 0 0 0 0 1
Then your K-means cluster centroids will also live in this same 12-dimensional space.
What I'm trying to suggest is that you could extract the (x, y) coordinates of the 1s in each image, and use those as the data for your K-means algorithm. So for the example image above, you'd get the following data points:
1 1
0 2
2 3
In this example, we've extracted 3 2-dimensional points from this one "image"; with more images you'd get more 2-dimensional points. After you run K-means with these 2-dimensional data points, you'll get cluster centroids that can also be interpreted as pixel locations in the original images. You could plot those centroid locations on top of your images and see where they correspond in the images.