Image Segmentation with Python
by Veronika Cheplygina

Step 1: Brainstorming

What problem(s) will students learn how to solve?

  • How to segment (medical) images with low-level techniques
  • How to represent pixels in a feature space
  • How to filter the image to extend the feature space
  • How to train simple classification techniques for segmentation
  • How to evaluate segmentation

What techniques or concepts will students learn?

  • Feature space
  • Class overlap
  • k-Means clustering
  • Nearest mean, nearest neighbor classifiers
  • Dice coefficient

What technologies, packages, or functions will students use?

Mostly NumPy supplemented with scikit-image and scikit-learn. Would like to use NumPy as much as possible to create understanding of what is going on in the algorithm, but it may be too much at the same time.

What terms or jargon will you define?

  • Accuracy, Dice coefficient
  • Gaussian blur/filtering
  • Overfitting
  • Supervised vs unsupervised
  • Dataset, image (vs volume)

What analogies or heuristics will you use?

What mistakes or misconceptions do you expect?

  • Mapping between the image (with spatial structure) and feature space (without)
  • That having ground truth for an image (for evaluation) doesn't mean we can use that ground truth to make the method better

What datasets will you use?

Step 2: Who Is This Course For?

  • Advanced Alex: Given Alex's background and experience, I don't think the course will be very relevant for him.

  • Starting Sindhu: Given her interest and experience in medical applications, the course might appeal to her. I think the course would also give her more confidence, since I intend to explain concepts that are sometimes considered "matter of fact", but that are not in fact obvious to everyone (and were not to me initially).

  • Coder Chen: It is difficult for me to assess whether Chen would be interested in image segmentation - given the increasing importance of image recognition in e-commerce, perhaps. Similarly to Sindhu, I think the course would fit in well with her background. I would like to intuitively explain mathematical concepts, that do not require advanced prerequisites.

  • Unaware Umberto: I don't think the course will be of interest to him.

Step 3: What Will Learners Do Along the Way?

Full Exercise 1

In this exercise, the goal is to create a feature space with two features by blurring the image (loaded as im) with a Gaussian, applying the k-Means algorithm to create two clusters of pixels, transform the cluster assignment back into an image, and visualize the result alongside the ground truth (loaded as segtrue).

The main concept is the transformation from image to feature space and back into image space. K-Means is used in a black box way, this could be a different technique.

The solution below gives the code, excluding imports and loading the data. Probably the code can be more compact. The starter code would have all of the methods, but the learner has to fill in the arguments.

The exercise is not so much about the exact code to create these plots, but understanding how the two representations relate. So after the plots are displayed, we can ask different questions.

Solution part 1

# Filter image with Gaussian of width 5
imgauss5 = ndimage.gaussian_filter(im, sigma=5)

# Put together original and blurred values into a dataset - surely there is a more compact way to do this?
pixeldata = np.append(np.expand_dims(im.ravel(), axis=1), np.expand_dims(imgauss5.ravel(), axis=1), axis=1)

# Visualize the scatterplot and the corresponding image
f, axes = plt.subplots(2,2)

axes[0, 0].scatter(pixeldata[:,0], pixeldata[:,1], c=segtrue.ravel())
axes[0, 1].imshow(segtrue, cmap=plt.cm.gray)
plt.show()

Questions after solution part 1:

  • What happens to the range of intensities after blurring? (Multiple choice: no change, lower, higher, not enough information? Correct: lower)

  • Which pixels (brain or non-brain) are displayed in yellow? (Multiple choice: A- Non-brain, because the blue pixels have the highest intensities and must belong to the brain, B - Brain, because the yellow pixels have the highest blurred intensities. Correct: B).

  • Where are the pixels of the skull in the scatterplot (Multiple choice: bottom left - low intensity & low blurred intensity, high & low, low & high, high & high. Correct: high & low.)

Solution part 2

# Do k-Means on this data (give approximate cluster centers so the ordering of the clusters is always the same)
kmeans = KMeans(n_clusters=2, init=np.array([[0.3, 0.3], [0.5, 0.1]])).fit(pixeldata)

# Transform the result into an image
kmeansresult = np.reshape(kmeans.labels_, im.shape)

axes[1, 0].scatter(pixeldata[:, 0], pixeldata[:, 1], c=kmeans.labels_)
axes[1, 1].imshow(kmeansresult, cmap=plt.cm.gray)
plt.show()

Questions after solution part 2:

  • What could happen if we do not initialize kMeans with approximate cluster centers? (Clusters could be reversed)

  • Why are some pixels classified incorrectly? Could kMeans have avoided these mistakes? (They have the same representation, no)

Full Exercise 2

In this exercise, the goal is to create a feature space with multiple features, select a subset of features and train a classifier on one subject's image, and then test out the classifier on another image.

Essentially the structure of this exercise is the same as the previous one, but

  • instead of a binary problem we have a multi-class problem
  • instead of an unsupervised case with 1 image, we go to a supervised
  • case where we need to have different images for training and testing
  • (optional) instead of using all the features, we will create a
  • selection based on some performance measure.

Part 1: Load images and create datasets. This is done twice, for the training and test image, but for the exercise, we could already explain what happened to the training image, and the student has to do it for the test image.

Solution part 1

test_imgauss5 = ndimage.gaussian_filter(test_im, sigma=5)
test_im_gm5 = ndimage.gaussian_gradient_magnitude(test_im, sigma=5)

num_test = len(test_im.ravel())
test_data = np.concatenate((test_im.reshape(num_test, 1), test_imgauss5.reshape(num_test, 1)), axis=1)
test_data = np.concatenate((test_data, test_im_gm5.reshape(num_test, 1)), axis=1)

Questions after part 1: we could look at the scatterplots of the training and test image to see if there are similar patterns. Since we have more than two features, need to look at a grid of scatterplots.

Could be an idea to look at three images in total - for example, from different locations in the brain, or from subjects of different ages, since they will have different distributions of classes.

Based on the scatterplots students could hypothesize which features (we could start with other ones than I've shown here, to create more interesting results) are likely to give better separation of the classes.

Part 2: Train a classifier using the training image, and apply it on the test image. Possibly this part could also incorporate feature selection, since now it is very similar to the k-Means from exercise 1.

Solution part 2

knn = KNeighborsClassifier(n_neighbors=3)

knn.fit(train_data, train_gt.ravel())
knnlabels = knn.predict(test_data)
knnresult = np.reshape(knnlabels, test_im.shape)
diceScores = diceMulticlass(test_gt,knnresult)

Questions after part 2: possible questions could include which classes are easier to classify and why, whether the hypothesis about which features would be better were correct, etc.

Other Exercises

Plotting 1D histogram of image intensities

Plot the intensities of an image, try to relate the pixels in the image (and the corresponding labels in the mask) to their positions in the histogram. See img/other_exercise1.png. Possible questions:

  • There are a lot of pixels of the blue class with low intensities - which pixels in the image are these? (Black background around the head)
  • The highest intensity pixels are also in the blue class - which pixels are these? (Skull)

Solution

imdata = im.ravel()
labels = segtrue.ravel()
class1 = imdata[labels==0]
class2 = imdata[labels==1]

bins = np.arange(0.0, 1.0, 0.05)

f, (ax1, ax2, ax3) = plt.subplots(nrows=1, ncols=3)

ax1.imshow(im, cmap=plt.cm.gray)
ax2.imshow(segtrue, cmap=plt.cm.gray)
ax3.hist(class1, bins, alpha=0.3)
ax3.hist(class2, bins, alpha=0.3)
plt.show()

Segmentation by thresholding intensity

Binarize the segmentation by selecting an intensity value (based on the histogram from the previous exercise) and comparing the image with it. Then display the image, the ground truth and your result. Add the Dice coefficient of the result in the plot title. Optional: could already provide the image of how the output should look like, see img/other_exercise2.png.

Solution

threshold = 0.1
segresult = im > threshold

f, (ax1, ax2, ax3) = plt.subplots(nrows=1, ncols=3)

ax1.imshow(im, cmap=plt.cm.gray)
ax2.imshow(segtrue, cmap=plt.cm.gray)
ax3.imshow(segresult, cmap=plt.cm.gray)
ax3.set_title('Result 1D threshold %.2f' % (diceCoefficient(segtrue, segresult)))
plt.show()

Dice coefficient

Create a function for computing the Dice coefficient for a binary segmentation problem.

Solution

def diceCoefficient(segmentationTrue, segmentationResult):
    overlap = np.logical_and(segmentationTrue, segmentationResult)
    dice = np.sum(overlap)*2 / (np.sum(segmentationTrue)+ np.sum(segmentationResult))
    return dice

Multi-class Dice coefficient

Create a function for computing multiple Dice coefficients for a problem with more than two classes. This function should loop through the possible classes, considering each in turn as the foreground class, and call the diceCoefficient function you implemented before.

First, imagine the foreground class is labeled by number 2. Write the lines of code needed to convert the ground truth, and the segmentation result to binary masks, on which you can then compute the Dice coefficient.

Solution part 1

# Convert the ground truth to a binary mask
binaryTrue = segmentationTrue == 2

# Convert the result to a binary mask
binaryResult = segmentationResult == 2

# Call the Dice function and store the result
diceCoeff = diceCoefficient(binaryTrue, binaryResult)

Next we will extend the previous exercise to multiple classes - instead of comparing the labels to the number 2, we can compare the labels to each of the classes present in the ground truth. In the next part of the exericse, get the list of classes from the ground truth using the np.unique() function, and initialize an empty vector that has as many cells as the number of classes.

Solution part 2

# Get list of classes you want to evaluate
classList = np.unique(segmentationTrue)

# Calculate the number of classes
numClasses = np.size(classList)

# Initialize vector to store Dice coefficients
diceCoeff = np.zeros(shape=(numClasses,1))

Now let's put everything from the first two steps together.

Solution part 3

def diceMulticlass(segmentationTrue, segmentationResult):

    # Get list of classes you want to evaluate
    classList = np.unique(segmentationTrue)

    # Calculate the number of classes
    numClasses = np.size(classList)

    # Initialize vector to store Dice coefficients
    diceCoeff = np.zeros(shape=(numClasses,1))

    # Loop over classes
    for i in range(0, numClasses):

       # Convert each image into background and foreground based on this class
       binaryTrue = segmentationTrue == classList[i]
       binaryTrue = binaryTrue.astype(int)

       binaryResult = segmentationResult == classList[i]
       binaryResult= binaryResult.astype(int)

       # Call the Dice function and store the result
       diceCoeff[i] = diceCoefficient(binaryTrue, binaryResult)

    # Finish
    return diceCoeff

Step 4: How Are the Concepts Connected?

  1. Segmentation in 1D
    1. Goal of segmentation, image vs mask
    2. Histogram of image
    3. Thresholding an image
    4. Unsupervised method in 1D (k-Means or mixture of Gaussians?)
    5. Class overlap
    6. Multi-class problem
  2. Evaluation
    1. Accuracy
    2. Dice coefficient
    3. Multi-class Dice
  3. Adding context to images
    1. Why context is needed, averaging neighborhood filter
    2. Gaussian blur
    3. Unsupervised method in 2D (k-Means or mixture of Gaussians?)
    4. Normalizing features
    5. Gaussian magnitude, other filters
    6. Unsupervised method in high-D
  4. Supervised segmentation
    1. Unsupervised vs supervised
    2. Supervised method in 2D and in high-D
    3. Feature selection
    4. Testing method on a different image
    5. Overfitting

The datasets are:

Step 5: Course Overview

Course Description

i. the process of identifying regions in an image that (hopefully) belong to the same object. It is a crucial step in almost all computer vision and image analysis applications, from finding pedestrians and signs on a road to identifying tumors in an X-ray. This course will teach you the basics underlying the important techniques and show you how to implement them in Python. The examples are drawn from medical image processing, but the ideas and methods apply to many other domains.

Learning Objectives

  • Write programs using the scientific Python stack to segment images using low-level techniques.
  • Understand how to represent pixels in a feature space and how to filter the image to extend that feature space.
  • Train simple classifiers to do image segmentation.
  • Evaluate segmentation results with a widely accepted metric.

Prerequisites

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