# Forulation of the Addresssed Machine Learning Problem

## Probelm Definition

The person re-identification problem presented in this paper requires mtatching 
pedestrian images from disjoint camera's by pedestrian detectors. This problem is 
challenging, as identities captured in photsos are subject to various lighting, pose, 
blur, background and oclusion from various camera views. This report considers 
features extracted from the CUHK03 dataset, following a 50 layer Residual network 
(Resnet50). This paper considers distance metrics techniques which can be used to 
perform person re-identification across **disjoint* cameras, using these features.

## Dataset - CUHK03  Summary

The dataset CUHK03 contains 14096 pictures of people captured from two 
different cameras. The feature vectors used, extracted from a trained ResNet50 model
, contain 2048 features that are used for identification.

The pictures represent 1467 different identities, each of which appears 9 to 10
times. Data is seperated in train, query and gallery sets with `train_idx`, 
`query_idx` and `gallery_idx` respectively, where the training set has been used 
to develop the ResNet50 model used for feature extraction. This procedure has 
allowed the evaluation of distance metric learning techniques on the query and 
gallery sets, without an overfit feature set a the set, as it was explicitly 
trained on the training set.

## Probelm to solve

The problem to solve is to create a ranklist for each image of the query set
by finding the nearest neighbor(s) within a gallery set. However gallery images
with the same label and taken from the same camera as the query image should
not be considered when forming the ranklist.

## Nearest Neighbor ranklist

Nearest Neighbor aims to find the gallery image whose feature are the closest to
the ones of a query image, predicting the class of the query image as the same 
of its nearest neighbor(s). The distance between images can be calculated through
different distance metrics, however one of the most commonly used is euclidean
distance:

$$ \textrm{NN}(x) = \operatorname*{argmin}_{i\in[m]} \|x-x_i\|^2 $$

*Square root when calculating euclidean distance is ommited as it does not 
affect ranking by distance*

Alternative distance metrics exist such as jaccardian and mahalanobis, which can
be used as an alternative to euclidiean distance.

# Baseline Evaluation

To evaluate improvements brought by alternative distance learning metrics a baseline 
is established as trough nearest neighbour identification as previously described.

\begin{figure}
\begin{center}
\includegraphics[width=20em]{fig/baseline.pdf}
\caption{Recognition accuracy of baseline Nearest Neighbor @rank k}
\label{fig:baselineacc}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=22em]{fig/eucranklist.png}
\caption{Ranklist @rank10 generated for 5 query images}
\label{fig:eucrank}
\end{center}
\end{figure}


# Suggested Improvement

## kMean Clustering


## k-reciprocal Reranking

\begin{figure}
\begin{center}
\includegraphics[width=24em]{fig/ranklist.png}
\caption{Ranklist (improved method) @rank10 generated for 5 query images}
\label{fig:ranklist2}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=20em]{fig/comparison.pdf}
\caption{Comparison of recognition accuracy @rank k (KL=0.3,K1=9,K2=3)}
\label{fig:baselineacc}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=17em]{fig/pqvals.pdf}
\caption{Identification accuracy varying K1 and K2}
\label{fig:pqvals}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=17em]{fig/cdist.pdf}
\caption{First two features of gallery(o) and query(x) feature data}
\label{fig:subspace}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=17em]{fig/clusteracc.pdf}
\caption{Top k identification accuracy for cluster count}
\label{fig:clustk}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=17em]{fig/jaccard.pdf}
\caption{Explained Jaccard}
\label{fig:jaccard}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=17em]{fig/kmeanacc.pdf}
\caption{Top 1 Identification accuracy varying kmeans cluster size}
\label{fig:kmeans}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=17em]{fig/lambda_acc.pdf}
\caption{Top 1 Identification Accuracy with Rerank (varying lambda)}
\label{fig:lambdagal}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=17em]{fig/lambda_acc_tr.pdf}
\caption{Top 1 Identification Accuracy with Rerank (varying lambda on train data)}
\label{fig:lambdatr}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=17em]{fig/mahalanobis.pdf}
\caption{Explained Mahalanobis}
\label{fig:mahalanobis}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=17em]{fig/trainpqvals.pdf}
\caption{Identification accuracy varying K1 and K2(train)}
\label{fig:pqtrain}
\end{center}
\end{figure}

# Comment on Mahalnobis Distance as a metric

We were not able to achieve significant improvements using mahalanobis for 
original distance ranking compared to square euclidiaen metrics. Results can 
be observed using the `-m|--mahalanobis` when running evalution with the 
repository complimenting this paper.

# Conclusion

# References

# Appendix