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\newcommand{\secondsection}{Feature extraction using dense sampling}

\newcommand{\thirdsection}{Creating the codebooks}

\newcommand{\fourthsection}{Training binary classifiers}

\newcommand{\fifthsection}{Image segmentation}

\newcommand{\sixthsection}{Probability maps and evaluation}


\begin{document}
%
% paper title
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\title{CS484 - Image Analysis\\ Project Report}


% author names and affiliations
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\author{\IEEEauthorblockN{Özgür Taşlık}
\IEEEauthorblockA{Department of Computer Engineering\\
Bilkent University\\
Ankara, Turkey \\
ozgur.taslik@ug.bilkent.edu.tr}
\and
\IEEEauthorblockN{Çağdaş Öztekin}
\IEEEauthorblockA{Department of Computer Engineering\\
Bilkent University\\
Ankara, Turkey \\
cagdas.oztekin@ug.bilkent.edu.tr}}

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%\author{\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1},
%Homer Simpson\IEEEauthorrefmark{2},
%James Kirk\IEEEauthorrefmark{3}, 
%Montgomery Scott\IEEEauthorrefmark{3} and
%Eldon Tyrell\IEEEauthorrefmark{4}}
%\IEEEauthorblockA{\IEEEauthorrefmark{1}School of Electrical and Computer Engineering\\
%Georgia Institute of Technology,
%Atlanta, Georgia 30332--0250\\ Email: see http://www.michaelshell.org/contact.html}
%\IEEEauthorblockA{\IEEEauthorrefmark{2}Twentieth Century Fox, Springfield, USA\\
%Email: homer@thesimpsons.com}
%\IEEEauthorblockA{\IEEEauthorrefmark{3}Starfleet Academy, San Francisco, California 96678-2391\\
%Telephone: (800) 555--1212, Fax: (888) 555--1212}
%\IEEEauthorblockA{\IEEEauthorrefmark{4}Tyrell Inc., 123 Replicant Street, Los Angeles, California 90210--4321}}




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%\IEEEspecialpapernotice{(Invited Paper)}




% make the title area
\maketitle

% As a general rule, do not put math, special symbols or citations
% in the abstract
\begin{abstract}
Object recognition is a difficult problem and with the rapid growth of image data, it is impossible for objects in images to be manually labeled. In this project, we attempted to detect and classify objects using the bag-of-words method. We used dense sampling to create visual words and kmeans clustering to create a codebook for already labeled objects. And we attempted to classify segments of images in our test set using binary support vector machine classifiers on the basis of their codebooks. \\

\indent Keywords\\
\indent Computer vision, object recognition, bag-of-words
\end{abstract}

% no keywords


\section{Introduction}
% no \IEEEPARstart
% You must have at least 2 lines in the paragraph with the drop letter
% (should never be an issue)

In this project, our goal was to recognize objects in images using the bag-of-words model. First, we densely sampled our visual words from grids that were 10 pixels apart using Scale-invariant feature transform (SIFT)\cite{sift}. We extracted approximately \textbf{420,000} descriptors from \textbf{188} images. A more detailed discussion on feature extraction can be found in the second section, titled \textbf{\secondsection}. 

In the next step, we clustered the descriptors, in other words the visual words, in 500 clusters, using \textit{k}-means clustering\cite{kmeans-matlab} and created a codebook of words for each instance of an object in our training set. This part will be discussed in the third section titled \textbf{\thirdsection}. 

Consequentially, we trained binary support vector machine (SVM) classifiers for each object type in our training set, using the histograms of the visual words. As will be explained in more detail in the fourth section, \textbf{\fourthsection}, each bin in the histogram corresponded to a cluster from the previous step and the descriptors in these bins came from the given object. As the result of this step, we obtained \textbf{8} binary SVM classifiers, for 8 types of objects. 

In the next step, we first performed segmentation on the images in our test set, then, similar to the previous step, created histograms for each segment and attempted to predict the object type using the SVM classifiers, and assigned to it the class with the highest score. The result of this step was a probability map for each pixel in the images in the test set, whose probabilities came from the SVM classifiers' confidence of the corresponding segment's object type prediction. The segmentation of the images will be explained in more detail in the fifth section, \textbf{\fifthsection} followed by the sixth section, \textbf{\sixthsection} where we will talk about the probability maps and how we evaluated our project.

\section{\secondsection}

Our goal in this part was to extract features from the images, which could be later used in training models for object types and testing segments from the images to classify as objects. We used a method called dense sampling, chose the pixels from where the SIFT descriptors would come uniformly, on a regular grid. We used VLFeat's Dense SIFT implementation\cite{vlfeat-dsift}, which follows the dense sampling approach and extracts SIFT descriptors from an image with regular intervals between the grid positions. DSift function had two parameters, \textbf{size} and \textbf{step}. We used the default value, \textbf{8} for size, so that our SIFT descriptors would be vectors of length \textbf{128}. We tried several values for the step value, eventually picked \textbf{10}, which extracted a total of \textbf{424,652} SIFT descriptors from 188 images. In our data set, the images from 1 to 49, of size $256 \times 256$ each had 576 descriptors while the images from 50 to 188, of size $480 \times 640$ each had 2852 descriptors. 

\begin{figure}[!h]
    \centering
    \includegraphics[width=0.2\textwidth]{images/1.jpg}
    \includegraphics[width=0.2\textwidth]{images/dense_sampling.png}
    \caption{Original image from the data set on the left, and the grid positions when extracting SIFT descriptors on the right}
    \label{fig:my_label}
\end{figure}

Our main concerns while extracting features was to find a good step value so that we would have sufficiently many descriptors in total while avoiding having too many descriptors lest we have memory issues and a bad runtime performance.

\section{\thirdsection}

In this step, we clustered the SIFT descriptors. We used MATLAB's \textit{k}-means implementation\cite{kmeans-matlab} and had 500 clusters. Although we could opt for a larger number of clusters, our realization of the codebooks for individual objects being sparsely populated made us choose \textbf{500}, rather than 1000 or 2000.

\begin{table}[!h]
\caption{The distribution of visual words to the clusters}
\label{table_example}
\centering
\begin{tabular}{|c||c|}
\hline
Cluster labels & Number of visual words\\
\hline
1-100 & 90,973 \\
\hline
101-200 & 79,273 \\
\hline
201-300 & 84,601 \\
\hline
301-400 & 85,377 \\
\hline
401-500 & 84,428 \\
\hline
\end{tabular}
\end{table}

We observed that number of visual words in the clusters did not deviate greatly, which means that dense sampling had successfully obtained generalized features from the data set. We have found that, on the average, \textbf{450.36} bins in the histograms of the objects in the training set were empty, which means that only less than \bm{$10\%$} of the bins in the histograms were occupied. And we have also found that an object in the training set, had only \textbf{124.18} descriptors. In the light of these findings, we hope our decision to pick a rather smaller number of clusters is more clear.

\begin{figure}[!h]
    \centering
    \includegraphics[width=0.5\textwidth]{images/img1hist.png}
    \caption{A histogram for the first image in the data set, showing the number of descriptors in its histogram's bins.}
    \label{fig:my_label}
\end{figure}

\section{\fourthsection}

As mentioned earlier but not explained, we divided our data set into two halves, one being the training set and the other being the test set. We used MATLAB's dividerand\cite{dividerand} function to achieve this and passed the ratios for the two sets as \textbf{0.5}. After completing the third step, as we had our histograms for each instance of an object in the training set our data was ready for training. But not before we created 8 vectors of binary labels. We filled in the label vectors using the masks cell array, matching the names of classes to a list of indices we created in order to use as a lookup table. We labeled positive examples of a class in a given label vector as 1, and the negative examples as -1. In total, we trained 8 different binary SVM classifiers, each with the same training data but with respective training labels. We used MATLAB's own SVM library\cite{matlab-svm}.

\section{\fifthsection}

Before proceeding to test our models we first had to create meaningful segments from the images in the test set. Knowing that segmentation is a difficult problem, and takes a lot of runtime, we had performed the segmentation before doing the other parts. We used the normalized cut code that was recommended in the assignment sheet\cite{ncut}, which had its flaws too, a line of code where the eigenvalues were computed had to be changed.

\begin{figure}[!h]
    \centering
    \includegraphics[width=0.27\textwidth]{images/1.jpg} \\
    \includegraphics[width=0.4\textwidth]{images/seg1.png} \\
    \includegraphics[width=0.4\textwidth]{images/seg2.png} \\
    \includegraphics[width=0.4\textwidth]{images/seg3.png} \\
    \caption{The original image on the top, the following images belong to the first, the second and the third segments respectively, depicted in white.}
    \label{fig:my_label}
\end{figure}

As for how many segments we wanted to obtain from the images, we decided manually, by inspecting each image, number of cuts for each respective image can be found in \textbf{numcuts.mat} file in the compressed file. However, most of the segmentation results had much fewer segments than the parameter that was passed to the function, and we simply did not have the time to rerun the segmentation function for such images as performing the segmentation once for all the images took nearly 7 hours on Cagdas's computer. 

Our main concerns at this step was first to obtain meaningful segments, such as if there is a building in the image, obtain the whole of the building and nothing else in one segment. But the results were nowhere near that. We think that part of the reason for the accuracies to be low is that our segments turned out to be too large, encapsulating many visual words and therefore making it harder for our classifiers to predict a distinct class for the segments. That is also possibly why, the scores in the probability maps in the later section are quite low.

The segmentation results can be found in the file named \textbf{segments.mat} in the compressed file. We also read in the segmentation results, the labels for each pixels from the same file that we pre-computed, to alleviate the runtime.

\section{\sixthsection}

In this step we ran our classifiers on the test set. One remark is that, the total number of objects in the entire data set is \textbf{544}, and as we divide the data set in two halves randomly, we observed that the number of objects in our training set was usually around \textbf{270}. In the particular run I will be talking about in this section, we had \textbf{271} examples in the training set. That should naturally leave \textbf{273} objects in the test set, however, we had \textbf{2050} segments in total, in the images in the test set. 

\begin{algorithm}[!h]
 \KwData{Object histograms for each segment in the test set}
 \KwResult{Probability maps for each image and class}
 \For{each histogram \textbf{h} in the test set}{
   \Comment{\# Initialize max score and its index to 0}\\
    max\_score \leftarrow 0\\
    max\_score\_index \leftarrow 0\\
    \For{each binary classifier \textbf{c}}{
        [score, prediction] \leftarrow predict(c, h)\; \\
        \If{prediction = 1 \& score $>$ max\_score}{
            max\_score \leftarrow score\\
            max\_score\_ind \leftarrow index\_of\_c\\
        }
    }
    \# Assign the corresponding pixels with the score and class index \\
    prob\_maps \leftarrow max\_score \\
    prob\_maps\_inds \leftarrow max\_score\_ind \\
  }
 \caption{Our algorithm to create the probability maps, see the relevant part in our code for clarity}
\end{algorithm}

In testing, we tried to predict each segment with all of the 8 binary classifiers, and we said that the among the classifiers that say the given segment is an example of the positive class, we considered the classification with the highest score. We had initialized probabiltiy maps with zeros, whose size are the same as the image they correspond to. We had a probability map for each image and each class, during the testing of each segment, we updated pixels in the probability map that belonged to that segment with the classification score obtained for that image and that class.

As the scores from SVM's predictions differed too much, some being values between 0 and 1 but some being over 100, we did not apply a threshold when finding our confusion matrix, and as a result we do not have an ROC curve, but rather a confusion matrix as a result of accepting anything with a score greater than \textbf{0.9} as positive.

\begin{table}[!h]
\caption{The confusion matrix for each class, true positives, false positives, false negatives and true negatives in the order of columns, with the scores thresholded by \textbf{0.9}.}
\label{table_example}
\centering
\begin{tabular}{||c|c|c|c|c||}
\hline
Class & TP & FP & FN & TN \\
\hline
Screen & 286,659 & 2,994,407 & 786,161 & 18,526,309 \\
\hline
Keyboard & 0 & 0 & 703,722 & 21,889,814 \\
\hline
Mouse & 0 & 110,787 & 48,819 & 22,433,930 \\
\hline
Mug & 0 & 198,517 & 77,180 & 22,317,839 \\
\hline
Car & 4,983 & 173,210 & 135,668 & 22,279,675 \\
\hline
Tree & 16,537 & 33,501 & 668,673 & 21,874,825 \\
\hline
Person & 39 & 221,986 & 28,011 & 22,343,500 \\
\hline
Building & 1,466,606 & 14,679,762 & 281,482 & 6,165,686 \\
\hline
\end{tabular}
\end{table}

\begin{table}[!h]
\caption{The confusion matrix for each class, true positives, false positives, false negatives and true negatives in the order of columns, with the scores thresholded by \textbf{50}.}
\label{table_example}
\centering
\begin{tabular}{||c|c|c|c|c||}
\hline
Class & TP & FP & FN & TN \\
\hline
Screen & 286,659 & 2,994,407 & 786,161 & 18,526,309 \\
\hline
Keyboard & 0 & 0 & 703,722 & 21,889,814 \\
\hline
Mouse & 0 & 110,787 & 48,819 & 22,433,930 \\
\hline
Mug & 0 & 74,942 & 77,180 & 22,441,414 \\
\hline
Car & 0 & 0 & 140,651 & 22,452,885 \\
\hline
Tree & 0 & 0 & 685,210 & 21,908,326 \\
\hline
Person & 0 & 78,630 & 28,050 & 22,486,856 \\
\hline
Building & 1,466,606 & 14,679,762 & 281,482 & 6,165,686 \\
\hline
\end{tabular}
\end{table}

\begin{table}[!h]
\caption{Precision, recall and accuracy for each class, when the threshold values is \textbf{0.9}}
\label{table_example}
\centering
\begin{tabular}{||c|c|c|c|c||}
\hline
Class & Precision & Recall & Accuracy \\
\hline 
Screen & 0.087 & 0.267 & 0.832 \\
\hline
Keyboard & 0 & 0 & 0.968 \\
\hline
Mouse & 0 & 0 & 0.992 \\
\hline
Mug & 0 & 0 & 0.987 \\
\hline
Car & 0.027 & 0.035 & 0.986 \\
\hline
Tree & 0.330 & 0.024 & 0.68 \\
\hline
Person & 0 & 0.001 & 0.988 \\
\hline
Building & 0.090 & 0.843 & 0.337 \\
\hline
\end{tabular}
\end{table}

\section{Conclusion}

In conclusion, our model was simply awful. We could possibly achieve better precision and recall by just randomly guessing. In our defense, our segmentation code took a very long time, we did not have quite a long time to go through the segmentation process and obtain meaningful segments, that we think would drastically change our results. 


\begin{thebibliography}{20}


\bibitem{sift}
Lowe, David G. "Object recognition from local scale-invariant features." \textit{Computer vision, 1999. The proceedings of the seventh IEEE international conference on.} Vol. 2. Ieee, 1999.

\bibitem{kmeans-matlab} k-means clustering - MATLAB. \\
"https://www.mathworks.com/help/stats/kmeans.html", Accessed January 11, 2017.
  
\bibitem{vlfeat-dsift} VLFeat - Tutorials > Dense SIFT. \\
"http://www.vlfeat.org/overview/dsift.html", Accessed January 11, 2017.

\bibitem{dividerand} Divide targets into three sets using random indices - MATLAB. \\
"https://www.mathworks.com/help/nnet/ref/dividerand.html", Accessed January 11, 2017.

\bibitem{matlab-svm} Train support vector machine classifier - MATLAB. \\
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\end{thebibliography}

\section*{Appendix}

We did everything in intimate and equal collaboration.


% that's all folks
\end{document}