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Computer Vision
Homework 4
Segmentation via Clustering
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/FeifeiliCV/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 pj 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 ∈ Rm 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 σj
2 of each feature as follows
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
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.
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 2 Rm 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 2
j of each feature as follows
µj = 1
n
X
n
i=1
fij 2
j = 1
n 1
X
n
i=1
(fij µj )
2.
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 ˜f1,…, ˜fn where
˜fij = fij µj
j
.
Implement this method of feature vector normalization in the file NormalizeFeatures.m. You can test your
implementation by running NormalizeFeaturesTest.m.
3.4 Get Creative!
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 di↵erent 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.
In Your Writeup
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.
In addition, you should describe all methods of feature normalization that you employ.
4 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);
3
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 2 Rm 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 2
j of each feature as follows
µj = 1
n
X
n
i=1
fij 2
j = 1
n 1
X
n
i=1
(fij µj )
2.
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 ˜f1,…, ˜fn where
˜fij = fij µj
j
.
Implement this method of feature vector normalization in the file NormalizeFeatures.m. You can test your
implementation by running NormalizeFeaturesTest.m.
3.4 Get Creative!
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 di↵erent 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.
In Your Writeup
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.
In addition, you should describe all methods of feature normalization that you employ.
4 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);
3
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:
a) 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).
b) 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.
c) You should also answer the following questions in your writeup (a few
sentences for each question is sufficient):
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?
3. How do the properties of an image affect the difficulty of computing
a good segmentation for that image?
d) 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).
e) 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.
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.
Feature
Transform
Feature
Normalization
Clustering
Method
Number
of clusters
Resize
(or max pixels)
Mean
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.
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.
In Your Writeup
Include a detailed evaluation of the e↵ect 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.
You should expand upon the qualitative assessment of Section 4 and try to answer the following question:
1. Based on your quantitative experiments, how do each of the segmentation parameters a↵ect the quality
of the final foreground-background segmentation?
2. Are some images simply more dicult 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.
You may combine your discussion in this section with your discussion from Section 4 if you like. However,
your grade for both sections will depend on the thoroughness and correctness of your discussion. Just as
a point of reference, we anticipate that none of the questions above can be answered in a single sentence;
you should back up all answers with either experimental data, or a convincing argument. Overall for this
assignment, we care more about your explanation and discussion than about your actual code or results
(although those are important too!).
6

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