Homework 4 Segmentation via Clustering Solution

Description

In this homework assignment, you will use clustering algorithms to segment images. You will then use these segmentations to identify foreground and background objects. And finally, you will transfer foreground objects from one image to another as shown in the figure below.

Provided files:

All of the image and Matlab files for this assignment are provided and they come from the Stanford Vision Lab (Prof. Fei Fei Li): https://github.com/oyzh/Feifeili-CV/tree/master/PA2/studentFiles.

There are 4 folders:

1. code: contains Matlab scripts and functions. Some functions have headers but are waiting for your function definition.

2. imgs: contains 17 images of cats

3. gt: contains 17 binary images representing the foreground/background segmentation for the images in the imgs folder

4. test_data: synthetic data you can use to test your clustering algorithm solution, as well as the feature normalization solution.

What You Have to Do:

Task 1 (20 points): Clustering Algorithms

1.1 K-Means Clustering

As discussed in class, K-Means is one of the most popular clustering algorithms. We have provided skeleton code for K-Means clustering in the file KMeansClustering.m. Your first task is to finish implementing the K- Means algorithm using the provided file. You can use KMeansClusteringTest.m to test your implementation.

1.2 Hierarchical Agglomerative Clustering

Another simple clustering algorithm is Hierarchical Agglomerative Clustering, which is sometimes abbreviated as HAC. In this algorithm, each point is initially assigned to its own cluster. Then cluster pairs are merged until we are left with the desired number of predetermined clusters (see Algorithm 1).

We have provided skeleton code for hierarchical agglomerative clustering in the file

HAClustering.m. Please finish the implementation in this file. You can use

HAClusteringTest.m to test your implementation.

Task 2 (15 points): Pixel Feature Vectors

Before we can use a clustering algorithm to segment an image, we must compute some feature vector for each pixel. The feature vector for each pixel should encode the qualities that we care about in a good segmentation. More concretely, for a pair of pixels pi and p j with corresponding feature vectors fi and fj, the distance between fi and fj should be small if we believe that pi and pj should be placed in the same segment and large otherwise.

2.1 Color Features

One of the simplest possible feature vectors for a pixel is simply the vector of colors for that pixel. This method has been implemented for you in the file ComputeColorFeatures.m.

2.2 Color and Position Features

Another simple feature vector for a pixel is to concatenate its color and its position

within the image. In other words, for a pixel of color (r,g,b) located at position (x,y)

in the image, its feature vector would be
(r, g, b, x, y). Implement this method of

computing feature vectors in the file ComputePositionColorFeatures.m. You

can test your implementation by running

ComputePositionColorFeaturesTest.m.

2.3 Feature Normalization

Sometimes we want to combine different types of features (such as color and position) into a single feature vector. Features from different sources may have drastically different ranges; for example each color channel of an image may be in the range [0, 1) while the position of each pixel may have a much wider range. Uneven scaling between different features in the feature vector may cause clustering algorithms to behave poorly.

One way to correct for uneven scaling between different features is to apply some sort of normalization to the feature vector. One of the simplest types of normalization is to force each feature to have zero mean and unit variance.

Suppose that we have a set of feature vectors f1 , . . . , fn where each fi ∈ R^m is the feature vector for a single pixel, and fij is the value of the jth feature for the ith pixel. We can then compute the mean μj and variance σ _j² of each feature as follows

1		n			1			n
		Xi						X
µj = n			σj2 = n		−	1
		fij						(fij − µj)2.
		=1						i=1

To force each feature to have zero mean and unit variance, we replace our feature vectors f1 , . . . , fn with a modified set of feature vectors

˜ f_ij − µ_j

f_ij = .

σ_j

Implement this method of feature vector normalization in the file NormalizeFeatures.m. You can test your implementation by running NormalizeFeaturesTest.m .

Task 3 (20 points): Optional for UG students, mandatory for Graduate students

For this programming assignment we have asked you to implement a very simple feature transform for each pixel. While it is not required, you should feel free to experiment with other feature transforms. Could your final segmentations be improved by adding gradients, edges, SIFT descriptors, or other information to your feature vectors? Could a different type of normalization give better results?

Depending on the creativity of your approach and the quality of your writeup, implementing extra feature vectors can be worth extra credit. You can use the function ComputeFeatures.m as a starting point to implement your own feature transforms.

Task 4 (5 points): Image Segmentations

After computing a feature vector for each pixel, we can compute a segmentation for the original image by applying a clustering algorithm to the computed feature vectors. Each cluster of feature vectors corresponds to a segment in the image, and each pair of pixels pi and pj in the image will be placed in the same segment if and only if their corresponding feature vectors fi and fj are located in the same cluster.

You can compute a segmentation for an image using the function ComputeSegmentation.m. This function allows you to specify the function used to compute features for each pixel, whether the features should be normalized, and the clustering method used to cluster the feature vectors.

For example, to compute a segmentation for the image img with 5 segments using K-Means clustering and using ComputeColorFeatures to compute pixel features with feature normalization you would write:

segments = ComputeSegmentation(img, 5, ’kmeans’, @ComputeColorFeatures, true);

You can read the full documentation for ComputeSegmentation by typing help ComputeSegmentation.

If you find that your segmentations take a long time to compute, you can set the optional resize argument of ComputeSegmentation. If this argument is set then the image will be shrunk before being segmented, and the segmentation will then be upsampled to the size of the original image. You will probably need to use this feature when segmenting images with hierarchical agglomerative clustering.

The syntax @ComputeColorFeatures creates a handle to the function ComputeColorFeatures; this mechanism allows functions to be passed as arguments to MATLAB functions.

At this point you have a lot of options for computing segmentations: you have two different clustering algorithms (K-Means and HAC), two choices of pixel features (just color features or color and position features), and the choice to either normalize or not normalize the features. You can also vary the number of segments that are computed.

Once you have computed a segmentation for an image, you can visualize it using the functions ShowSegmentation and ShowMeanColorImage. Read the documentation for these functions (using the help command) to see how they are used. Example output from these visualization tools can be seen in Figure 2.

You can use the script RunComputeSegmentation as a starting point to compute segmentations for images. Choose a few images (either your own or images from the

imgs folder) and compute segmentations for these images using different combinations of segmentation parameters (feature transform, normalization, clustering method, number of clusters). A successful segmentation will cleanly separate the objects in the image from each other, while an unsuccessful separation will not.

Task 5 (10 points): GrabCat: Transfer segments between images

A successful segmentation of an image should separate the objects from the background. Assuming that we compute such a successful segmentation, we can “transfer” objects from one image to another by transfer- ring the segments that make up the object. An example image produced using this procedure is shown in the first figure.

Once you have computed a successful segmentation for an image, you can use the ChooseSegments function to choose a subset of these segments to transfer to a background image. The documentation for the ChooseSegments function contains more details on how to use it.

Use some of your successful segmentations from the previous section to transfer objects from one image to another. You can use the provided foreground images of cats in the imgs directory and the provided background images in the imgs/backgrounds; also feel free to use your own images. You can use the script GrabCat.m as a starting point for this section.

Task 6 (50 points): Quantitative Evaluation. Write-up

Looking at images is a good way to get an idea for how well an algorithm is working, but the best way to evaluate an algorithm is to have some quantitative measure of its performance.

For this project we have supplied a small dataset of cat images and ground truth segmentations of these images into foreground (cats) and background (everything else). We will quantitatively evaluate your segmentations by evaluating their performance on this dataset.

To achieve good performance, you will probably need to divide each image into more than two segments. This means that you will need to combine multiple segments in order to reconstruct the foreground and the background. You can manually choose the foreground segments using ChooseSegments.m as in the previous sections. Alternatively, you can have the evaluation function

EvaluateSegmentation.m automatically choose which segments should be in the foreground and which segments should be in the background.

You can use the script EvaluateAllSegmentations.m to evaluate a segmentation method’s ability to separate foreground from background on the entire provided dataset. Use this script as a starting point to evaluate a variety of segmentation parameters. Note that you can toggle the chooseSegmentsManually variable to either choose foreground segments yourself or allow EvaluateSegmentation.m to automatically choose foreground segments for you.

What to include in your write-up:

1. In your writeup you should describe all methods of computing feature vectors that you use in your project. For each method of computing feature vectors, explain why you expect that this feature vector will or will not produce a good segmentation for an image (task 2-3).

In addition, you should describe all methods of feature normalization that you employ (task 2).

2. In your writeup you should include visualizations of at least 6 different segmentations (task 4). At least 3 of these segmentations should be successful, and at least 3 of these segmentations should be unsuccessful. Each of your examples should use different parameters for segmentation, and the parameters for each of your examples should be different.

3. You should also answer the following questions in your writeup (a few sentences for each question is sufficient):

1. 1. What effect do each of the segmentation parameters (feature transform, feature normalization, number of clusters, clustering method, resize) have on the quality of the final segmentation?

   2. How do each of these parameters affect the speed of computing a segmentation?

1. 3. How do the properties of an image affect the difficulty of computing a good segmentation for that image?

4. Include at least 2 examples of composite images produced by transferring segments from one image to another (task 5). For each composite image explain how you produced it (i.e. describe what the input images were and what segmentation parameters were used).

5. Include a detailed evaluation of the effect of varying segmentation parameters (feature transform, feature normalization, clustering method, number of clusters, resize) on the mean accuracy of foreground-background segmentations on the provided dataset. You should test a minimum of 10 combinations of parameters. To present your results, you might consider making a table similar to Table 1.

Feature	Feature	Clustering	Number	Resize	Mean
Transform	Normalization	Method	of clusters	(or max pixels)	accuracy
Position	Yes	K-Means	10	None	0.91
Position + Color	No	HAC	5	0.2	0.58
.	.	.	.	.	.
.	.	.	.	.	.
.	.	.	.	.	.

Table 1: Example table of results; the numbers are made up. You might want to make a table like this in your report.

You should expand upon the qualitative assessment of Section c) and try to answer the following question:

1. Based on your quantitative experiments, how do each of the segmentation parameters affect the quality of the final foreground-background segmentation? 


2. Are some images simply more difficult to segment correctly than others? If so, what are the qualities of these images that cause the segmentation algorithms to perform poorly? 


3. Also feel free to point out or discuss any other interesting observations that you made. 


Note: Overall for this assignment, we care more about your explanation and discussion than about your actual code or results (although those are important too!).

Submitting the assignment:

Make sure each script or function file is well commented and it includes a block comment with your name, course number, assignment number and instructor name. Zip all the .m and the write-up file together and submit the resulting .zip file through Moodle as homework 4 by Sunday, April 1st, by 11:55pm.