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Computer Vision and Image Processing: Homework 1⇤
Spatial Pyramid Matching for Scene Classification
Instructor: Kevin R. Keane
TAs: Radhakrishna Dasari, Yuhao Du, Niyazi Sorkunlu
Due Date: September 25, 2017

Figure 1: Scene Classification Given an image, can a computer program determine where it was taken?
In this homework, you will build a representation based on bags of visual words and use spatial pyramid
matching for classifying the scene categories.

1. Please pack your system and write-up into a single file named, see the
complete submission checklist at the end.
2. All questions marked with a Q require a submission.
3. For the implementation part, please stick to the headers, variable names, and file conventions provided.
4. Start early! This homework will take a long time to complete.
5. Attempt to verify your implementation as you proceed: If you don’t verify that your implementation is correct on toy examples, you will risk having a huge mess when you put everything
6. Try to use relative paths with respect to the working directory.
7. If you have any questions or need clarifications, please post in Piazza or visit the TAs during the office

⇤ Credit

to Deva Ramanan for this assignment.


The bag-of-words (BoW) approach, which you learned about in class, has been applied to a myriad of
recognition problems in computer vision. For example, two classic ones are object recognition [5, 7] and
scene classification [6, 8]1 .
Beyond that, the BoW representation has also been the subject of a great deal of study aimed at improving
it, and you will see a large number of approaches that remain in the spirit of bag-of-words but improve upon
the traditional approach which you will implement here. For example, two important extensions are pyramid
matching [2, 4] and feature encoding [1].
An illustrative overview of the homework is shown in Figure 2. In section 1, we will build the visual
words from the training set images. With the visual words, i.e. the dictionary, in section 2, we will represent
an image as a visual-word vector. Then the comparison between images is realized in the visual-word vector
space. Finally, we will build a scene recognition system based on the visual bag-of-words approach to classify
a given image into 8 types of scenes.

Figure 2: An overview of the bags-of-words approach to be implemented in the homework. Given the training
set of images, the visual features of the images are extracted. In our case, we will use the filter responses of
the pre-defined filter bank as the visual features. The visual words, i.e. dictionary, are built as the centers of
clusters of the visual features. During recognition, the image is first represented as a vector of visual words.
Then the comparison between images is realized in the visual-word vector space. Finally, we will build a
scene recognition system that classifies the given image into 8 types of scenes.

What you will be doing
1. You will implement a scene classification system that uses the bag-of-words approach with its spatial
pyramid extension. The paper that introduced the pyramid matching kernel [2] is:
Kristen Grauman and Trevor Darrell. The pyramid match kernel: Discriminative classification with sets of image features. In Computer Vision, 2005. ICCV 2005. Tenth IEEE
International Conference on, volume 2, pages 1458–1465. IEEE, 2005 PDF
1 This homework aims at being largely self-contained; however, reading the listed papers (even without trying to truly
understand them) is likely to be helpful.


Figure 3: The provided multi-scale filter bank.
Spatial pyramid matching [4] is presented at:
Svetlana Lazebnik, Cordelia Schmid, and Jean Ponce. Beyond bags of features: Spatial
pyramid matching for recognizing natural scene categories. In Computer Vision and Pattern
Recognition, 2006 IEEE Computer Society Conference on, volume 2, pages 2169–2178. IEEE,
2006 PDF
You will be working with a subset of the SUN database2 . The data set contains 1600 images from
various scene categories like “garden”, “library” and “ocean”. And to build a recognition system, you
• first, take responses of a filter bank on images and build a dictionary of visual words;
• then, learn a model for the visual world based on the bag of visual words (with spatial pyramid
matching [4]), and use nearest-neighbor to predict scene classes in a test set.
In terms of number of lines of code, this assignment is fairly small. However, it may take a few hours to
finish running the baseline system, so make sure you start early so that you have time to debug things.
Also, try each component on a subset of the data set first before putting everything together.
2. Extra Credit We ask you to try to improve the performance of your algorithm via a number of
di↵erent ways, and comment on the results you get.
We provide you with a number of functions and scripts in the hopes of alleviating some tedious or error-prone
sections of the implementation. You can find a list of files provided in section 3.


Representing the World with Visual Words

We have provided you with a multi-scale filter bank that you will use to understand the visual world. You
can create an instance of it with the following (provided) function:
[filterBank] = createFilterBank()

filterBank is a cell array , with the pre-defined filters in its entries. In our example, we are using 20
filters consisting of 4 types of filters in 5 scales.
Q1.0 (5 points) What properties do each of the filter functions (see Figure 3) pick up? You should
group the filters into broad categories (i.e., all the Gaussians). Answer in your write-up.
3 Look

at MATLABs documentation for more details, but filterBank{i} is a 2D matrix, and filterBank{i} and
filterBank{j} are not necessarily the same size.


Figure 4: An input image and filter responses for the filter bank illustrated in Figure 3 . (a) Input image of
an indoor ice rink. (b) Filter responses for the L*a*b* image.


Extracting Filter Responses

Q1.1 (10 points) We want to run our filter bank on an image by convolving each filter in the bank with
the image and concatenating all the responses into a vector for each pixel. Use the imfilter command in
a loop to do this. Since color images have 3 channels, you are going to have a total of 3F filter responses per
pixel if the filter bank is of size F . Note that in the given dataset, there are some gray-scale images. For
those gray-scale images, you can simply duplicated them into three channels using the command repmat.
Then output the result as a 3F channel image. Follow this function prototype
[filter response] = extractFilterResponses(I, filterBank)
We have provided you with a template code with detailed instructions in it. You will be required to
input a 3-channel RGB or gray-scale image and filter bank to get the responses of the filters on the image.
Remember to check the input argument I to make sure it is a floating point type and convert it if necessary.
Use the included helper function RGB2Lab to convert your image into L*a*b* space before applying the
filters. If I is an M ⇥ N ⇥ 3 matrix, then filter response should be a matrix of size M ⇥ N ⇥ 3F . Make
sure your convolution function call handles image padding along the edges sensibly.
Apply all 20 filters on a sample image, and visualize as a image collage (as shown in Figure 4). Submit
the collage of 20 images in the write-up. (Hint: Use montage MATLAB function to build the collage).


Creating Visual Words

You will now create a dictionary of visual words from the filter responses using k-means. After applying
k-means, similar filter responses will be represented by the same visual word. You will use a dictionary
with fixed-size. Instead of using all of the filter responses (that can exceed the memory capacity of your
computer), you will use responses at ↵ random pixels4 . If there are T training images, then you should
collect a matrix filter responses over all the images that is ↵T ⇥ 3F , where F is the filter bank size. Then,
to generate a visual words dictionary with K words, you will cluster the responses with k-means using the
built-in MATLAB function kmeans as follows:
[⇠, dictionary] = kmeans(filter responses, K, EmptyAction,drop);
Note that the output of the function kmeans is row-wise, i.e., each row is an sample/cluster. In our
following implementations, we will assume the dictionary matrix is column-wise. So you need to transpose
dictionary after it is estimated from the kmeans function.
Q1.2 (10 points) You should write the following functions to generate a dictionary given a list of images.
4 Try

using randperm


[filterBank, dictionary] = getFilterBankAndDictionary(image names)
As an input, getFilterBankAndDictionary takes a cell array of strings containing the full path to an image (or relative path wrt the working directory). You can load each file by iterating from 1:length(image names),
and doing imread(image namesi). Generate the ↵T filter responses over the training files and call kmeans. A sensible initial value to try for K is between 100 and 300, and for ↵ is between 50 and 200, but
they depend on your system configuration and you might want to play with these values.
Once you are done with getFilterBankAndDictionary, call the provided script computeDictionary,
which will pass in the file names, and go get a co↵ee. If all goes well, you will have a .mat file named
dictionary.mat that contains the filter bank as well as the dictionary of visual words. If all goes poorly,
you will have an error message5 . If the clustering takes too long, reduce the number of clusters and samples.
If you have debugging issues, try passing in a small number of training files manually.


Computing Visual Words

Figure 5: Visual words over images You will use the spatially un-ordered distribution of visual words in
a region (a bag of visual words) as a feature for scene classification, with some coarse information provided
by spatial pyramid matching [4].
Q1.3 (10 points) We want to map each pixel in the image to its closest word in the dictionary. Create
the following function to do this:
[wordMap] = getVisualWords(I, filterBank, dictionary)
wordMap is a matrix with the same width and height as I, where each pixel in wordMap is assigned the
closest visual word of the filter response at the respective pixel in I. We will use the standard Euclidean
distance to do this; to do this efficiently, use the MATLAB function pdist2. Some sample results are shown
in Figure 5.
Since this can be slow, we have provided a function batchToVisualWords(numberOfCores) that
will apply your implementation of the function getVisualWords to every image in the training and testing
set. This function will automatically6 use as many cores as you tell it to use. For every image “X.jpg”
in data/, there will be a corresponding file named “X.mat” in the same folder containing the variable
Visualize three wordmaps of three images from any one of the category and submit in the write-up along
with their original RGB image. Also, provide your comments about the visualization. They should look
similar to the ones in Figure 5. (Hint: use imagesc MATLAB function to visualize wordmap).
5 Dont

worry about “did-not-converge” errors.
parties should investigate batchToVisualWords.m and the MATLAB commands codepool and parfor.

6 Interested



Building a Recognition System

We have formed a convenient representation for recognition. We will now produce a basic recognition system
with spatial pyramid matching. The goal of the system is presented in Figure 1: given an image, classify
(colloquially, “name”) the scene where the image was taken.
Traditional classification problems follow two phases: training and testing. During training time, the
computer is given a pile of formatted data (i.e., a collection of feature vectors) with corresponding labels
(e.g., “beach”, “park”) and then builds a model of how the data relates to the labels: “if green, then park”.
At test time, the computer takes features and uses these rules to infer the label: e.g., “this is green, so
therefore it is park”.
In this assignment, we will use the simplest classification model: nearest neighbor. At test time, we will
simply look at the querys nearest neighbor in the training set and transfer that label. In this example, you
will be looking at the query image and looking up its nearest neighbor in a collection of training images
whose labels are already known. This approach works surprisingly well given a huge amount of data, e.g., a
very cool graphics applications from [3].
The components of any nearest-neighbor system are: features (how do you represent your instances?)
and similarity (how do you compare instances in the feature space?). You will implement both.


Extracting Features

We will first represent an image with a bag of words approach. In each image, we simply look at how often
each word appears.
Q2.1 (10 points) Create a function getImageFeatures that extracts the histogram7 of visual words
within the given image (i.e., the bag of visual words).
[h] = getImageFeatures(wordMap, dictionarySize)
As inputs, the function will take:
• wordMap is a H ⇥ W image containing the IDs of the visual words
• dictionarySize is the maximum visual word ID (i.e., the number of visual words)
P output, the function will return h, a dictionarySize ⇥ 1 histogram that is L1 normalized, (i.e.,
hi = 1). You may wish to load a single visual word map, visualize it, and verify that your function is
working correctly before proceeding.


Multi-resolution: Spatial Pyramid Matching

Bag of words is simple and efficient, but it discards information about the spatial structure of the image and
this information is often valuable. One way to alleviate this issue is to use spatial pyramid matching[4]. The
general idea is to divide the image into a small number of cells, and concatenate the histogram of each of
these cells to the histogram of the original image, with a suitable weight.
Here we will implement a popular scheme that chops the image into 2l ⇥ 2l cells where l is the layer
number. We treat each cell as a small image and count how often each visual word appears. This results in
a histogram for every single cell in every layer. Finally to represent the entire image, we concatenate all the
histograms together after normalization by the total number ofP
features in the image. If there are L layers
and K visual words, the resulting vector has dimensionality K l=0 4l = 13 (4(L+1) 1)K.
Now comes the weighting scheme. Note that when concatenating all the histograms, histograms from
di↵erent levels are assigned di↵erent weights. Typically (in [4]), a histogram from layer l gets half the weight
of a histogram from layer l + 1, with the exception of layer 0, which is assigned a weight equal to layer 1. A
popular choice is for layer 0 and layer 1 the weight is set to 2 L, and for the rest it is set to 2(l L 1) (e.g.,
in a three layer spatial pyramid, L = 2 and weights are set to 14 , 14 and 12 for layer 0, 1 and 2 respectively,
see Figure 6). Note that the L1 norm (absolute values of all dimensions summed up together) for the final
vector is 1.
7 Look

into hist in MATLAB.


Figure 6: Spatial Pyramid Matching From [4]. Toy example of a pyramid for L = 2. The image has
three visual words, indicated by circles, diamonds, and crosses. We subdivide the image at three di↵erent
levels of resolution. For each level of resolution and each channel, we count the features that fall in each
spatial bin. Finally, weight each spatial histogram.
Q2.2 (15 points) Create a function getImageFeaturesSPM that form a multi-resolution representation of the given image.
[h] = getImageFeaturesSPM(layerNum, wordMap, dictionarySize)
As inputs, the function will take:
• layerNum the number of layers in the spatial pyramid, i.e., L + 1
• wordMap is a H ⇥ W image containing the IDs of the visual words
• dictionarySize is the maximum visual word ID (i.e., the number of visual words)
As output, the function will return h, a vector that is L1 normalized. Please use a 3-layer spatial
pyramid (L = 2) for all the following recognition tasks.
One small hint for efficiency: a lot of computation can be saved if you first compute the histograms of
the finest layer, because the histograms of coarser layers can then be aggregated from finer ones.


Comparing images

We will also need a way of comparing images to find the “nearest” instance in the training data. In this
assignment, we’ll use the histogram intersection
Pn similarity. ThePhistogram intersection similarity between
two histograms x1:n and y1:n is defined as i=1 min(xi , yi ), or (min(x, y)) in MATLAB. Note that since
this is a similarity, you want the largest value to find the “nearest” instance.
Q2.3 (10 points) Create the function distanceToSet

[histInter] = distanceToSet(wordHist, histograms)
where wordHist is a K
1) ⇥ 1 vector and histograms is a K
1) ⇥ T matrix
3 (4(L + 1)
3 (4(L + 1)
containing 3 (4(L + 1) 1) features from T training samples concatenated along the columns. This function
returns the histogram intersection similarity between wordHist and each training sample as a 1⇥T vector.
Since this is called every time you want to look up a classification, you want this to be fast, and doing a
for-loop over tens of thousands of histograms is a very bad idea. Try repmat or (even faster) bsxfun8 .
8 As a recommendation: unless youre experienced with MATLAB or confident, make sure your optimization works before
moving on. Either use a few hand-made examples that you can manually verify or subtract the distances produced by the
unoptimized and optimized examples.



Building A Model of the Visual World

Now that we’ve obtained a representation for each image, and defined a similarity measure to compare two
spatial pyramids, we want to put everything up to now together.
You will need to load the training file names from traintest.mat and the filter bank and visual word
dictionary from dictionary.mat. You will save everything to a .mat file named vision.mat. Included
will be:
1. filterBank: your filterbank.
2. dictionary: your visual word dictionary.
3. train features: a K
1) ⇥ N matrix containing all of the histograms of the N training
3 (4(L + 1)
images in the data set. A dictionary with 150 words will make a train features matrix of size 3150⇥1349.
4. train labels: a 1⇥N vector containing the labels of each of the images (i.e., train features(:,i)
has label train labels(i)).
We have provided you with the names of the training and testing images in traintest.mat. You want
to use the cell array of files train imagenames for training, and the cell array of files test imagenames
for testing. You cannot use the testing images for training. To access the word maps created by
batchToVisualWords.m, you might need function strrep to modify the file names. You may also wish
to convert the labels to meaningful categories. Here is the mapping (a variable named mapping is included
in traintest.mat):
art gallery computer room garden ice skating library mountain ocean tennis court
Q2.4 (15 points) Write a script named buildRecognitionSystem.m that produces vision.mat,
and submit it as well as any helper functions you write. To qualitatively evaluate what you have done, we
have provided a helper function that will let you get the predictions on a new image given the training data.
This will give you a visual sanity check that you have implemented things correctly. Use the program as
The program will load the image, represent it with visual words, and get a prediction based on the histogram.
The predictions will appear inside your MATLAB command window as text.
Don’t worry if you get a fair amount of wrong answers. Do worry if the program crashes while calling
your code or if you get zero correct/all correct/all same answers. If you are getting 0% or 100% performance,
go back and verify (visually) that each of your components produces correct output, or check that testing
data are accidentally included during training (yet you can pick images from both training and testing set
for debugging purposes).


Quantitative Evaluation

Qualitative evaluation is all well and good (and very important for diagnosing performance gains and losses),
but we want some hard numbers. Load the corresponding test images and their labels, and compute the
predicted labels of each. To quantify the accuracy, you will compute a confusion matrix C: given a classification problem, the entry C(i,j) of a confusion matrix counts the number of instances of class i that
were predicted as class j. When things are going well, the elements on the diagonal of C are large, and
the o↵-diagonal elements are small. Since there are 8 classes, C will be 8 ⇥ 8. The accuracy, or percent of
correctly classified images, is given by trace(C) / sum(C(:)).
Q2.5 (10 points) Write a script named evaluateRecognitionSystem.m
[conf] = evaluateRecognitionSystem()


that tests the system and outputs the confusion matrix, and submit it as well as any helper functions you
write. Report the confusion matrix and accuracy for your results in your write-up. This does not have to be
formatted prettily: if you are using LaTeX, you can simply copy/paste it from MATLAB into a verbatim
environment. Additionally, do not worry if your accuracy is low: with 8 classes, chance is 12.5%. To give
you a more sensible number, a reference implementation without spatial pyramid matching gives an overall
accuracy of ⇠56%.


Find out the failed cases

There are some classes/samples that are more difficult to classify than the rest using the bags-of-words
approach. As a result, they are classified incorrectly into other categories.
Q2.6 (5 points) List some of these classes/samples and discuss why they are more difficult in your


Improving Performance (Extra Credit, upto 20 points)

So far you’ve implemented a baseline classification system. For extra credit, try make improvements to the
system either in terms of accuracy or speed. You are free to try anything you’d like, but some things you
could try include changing the feature bank (use new filters to improve accuracy or try running the features
on an image pyramid to decrease running time), replace the histogram intersection with a di↵erent similarity
measure or using a soft assignment scheme while mapping features to words. You can also explore di↵erent
variations of bag-of-words approach. If you attempt the extra credit section, include the entire code for the
extra credit classification system in a folder called custom. In your writeup explain what you tried, why you
thought it might work well and how much of a di↵erence it made to your system’s performance.


HW1 Distribution Checklist

After unpacking, you should have a folder hw1 containing one folder for the data (data) and one
for each system you might implement (code and custom). In the code folder, where you will primarily
work, you will find:
• batchToVisualWords.m: a provided script that will run your code to convert all the images to
visual word maps.
• computeDictionary.m: a provided script that will provide input for your visual word dictionary
• createFilterBank.m: a provided function that returns a cell array of 20 filters.
• guessImage.m: a provided script that will predict the class for given image.
• RGB2Lab.m: a provided helper function to convert RGB to Lab image space.
Apart from this, we have also provided the stub codes in code folder. The data folder contains:
• data/: a directory containing .jpg images from SUN database.
• data/traintest.mat: a .mat file with the filenames of the training and testing set.
• checkA1Submission.m: Script to verify that your submission ( is in
correct structure and contains all required files for submission.



HW1 Submission Checklist

The assignment should be submitted to UBlearns as a zip file named and a pdf
file named yourPersonNumber.pdf. By extracting the zip file, it should have the following files in the
structure defined below. (Note: Not following the structure will incur huge penalty in scores). When you
submit, remove the folder data/ , as well as any large temporary files that we did not ask
you to create.
• yourPersonNumber/ # A directory inside .zip file
– code/
⇤ dictionary.mat
⇤ vision.mat

– custom/ Matlab code for the custom system that you design to boost the performance of your
system (optional, extra credit);
Please run the provided script checkA1Submission(’yourPersonNumber’) before submission to
ensure that all the required files are available. It searches for a file in the current

[1] Ken Chatfield, Victor S Lempitsky, Andrea Vedaldi, and Andrew Zisserman. The devil is in the details:
an evaluation of recent feature encoding methods. In BMVC, volume 2, page 8, 2011.
[2] Kristen Grauman and Trevor Darrell. The pyramid match kernel: Discriminative classification with sets
of image features. In Computer Vision, 2005. ICCV 2005. Tenth IEEE International Conference on,
volume 2, pages 1458–1465. IEEE, 2005.
[3] James Hays and Alexei A Efros. Scene completion using millions of photographs. In ACM Transactions
on Graphics (TOG), volume 26, page 4. ACM, 2007.
[4] Svetlana Lazebnik, Cordelia Schmid, and Jean Ponce. Beyond bags of features: Spatial pyramid matching for recognizing natural scene categories. In Computer Vision and Pattern Recognition, 2006 IEEE
Computer Society Conference on, volume 2, pages 2169–2178. IEEE, 2006.
[5] David G Lowe. Object recognition from local scale-invariant features. In Computer vision, 1999. The
proceedings of the seventh IEEE international conference on, volume 2, pages 1150–1157. Ieee, 1999.
[6] Laura Walker Renninger and Jitendra Malik. When is scene identification just texture recognition?
Vision research, 44(19):2301–2311, 2004.
[7] John Winn, Antonio Criminisi, and Thomas Minka. Object categorization by learned universal visual
dictionary. In Computer Vision, 2005. ICCV 2005. Tenth IEEE International Conference on, volume 2,
pages 1800–1807. IEEE, 2005.
[8] Jianxiong Xiao, James Hays, Krista A Ehinger, Aude Oliva, and Antonio Torralba. Sun database: Largescale scene recognition from abbey to zoo. In Computer vision and pattern recognition (CVPR), 2010
IEEE conference on, pages 3485–3492. IEEE, 2010.



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