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diff --git a/report/paper.md b/report/paper.md index 79d4183..79612c3 100755 --- a/report/paper.md +++ b/report/paper.md @@ -16,7 +16,7 @@ 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 +The pictures represent 1467 different identities, each of which appears 7 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 @@ -41,9 +41,6 @@ distance: $$ \textrm{NN}(x) = \operatorname*{argmin}_{i\in[m]} \|x-x_i\| $$ -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 @@ -105,21 +102,22 @@ We find that for the query and gallery set clustering does not seem to improve i \end{center} \end{figure} -# Suggested Improvement - ## Mahalanobis Distance We were not able to achieve significant improvements using mahalanobis for original distance ranking compared to square euclidiaen metrics. -The mahalanobis distance metric was used to create the ranklist as an alternative to euclidean distance. -When performing mahalanobis with the training set as the covariance matrix, reported accuracy is reduced to **38%** . +The mahalanobis distance metric was used to create the ranklist as an alternative to euclidean distance: + +$$ d_M(p,g_i) = (p-g_i)^TM(p-g_i). $$ + +When performing mahalanobis with the covariance matrix $M$ generated from the training set, reported accuracy is reduced to **38%** . We also attempted to perform the same mahalanobis metric on a reduced PCA featureset. This allowed for significant execution time improvements due to the greatly reduced computation requierments for smaller featurespace, but nevertheless demonstrated no improvements over an euclidean metric. -These results are likely due to the **extremely** low covariance of features in the training set. This is evident when looking at the Covariance matrix of the training data, and is also visible in figure \ref{fig:subspace}. This is likely the result of the feature transformations performed the the ResNet-50 convolution model the features were extracted from. +These results are likely due to the **extremely** low covariance of features in the training set. This is evident when looking at the covariance matrix of the training data, and is also visible in figure \ref{fig:subspace}. This is likely the result of the feature transformations performed the the ResNet-50 convolution model the features were extracted from. \begin{figure} \begin{center} @@ -130,6 +128,8 @@ These results are likely due to the **extremely** low covariance of features in \end{center} \end{figure} +# Suggested Improvement + ## $k$-reciprocal Re-ranking Formulation The approach addressed to improve the identification performance is based on @@ -167,11 +167,11 @@ e\textsuperscript{\textit{-d(p,g\textsubscript{i})}}, & \text{if}\ \textit{g\tex Through this transformation it is possible to reformulate the distance obtained through Jaccardian metric as: -$$ d_J(p,g_i)=1-\frac{\sum\limits_{j=1}^N min(V_{p,g_j},V_{g_i,g_j})}{\sum\limits_{j=1}^N max(V_{p,g_j},V_{g_i,g_j})} $$ +$$ d_J(p,g_i)=1-\frac{\sum\limits_{j=1}^N min(V_{p,g_j},V_{g_i,g_j})}{\sum\limits_{j=1}^N max(V_{p,g_j},V_{g_i,g_j})}. $$ It is then possible to perform a local query expansion using the g\textsubscript{i} neighbors of defined as: -$$ V_p=\frac{1}{|N(p,k_2)|}\sum\limits_{g_i\in N(p,k_2)}V_{g_i} $$. +$$ V_p=\frac{1}{|N(p,k_2)|}\sum\limits_{g_i\in N(p,k_2)}V_{g_i}. $$ We refer to $k_2$ since we limit the size of the nighbors to prevent noise from the $k_2$ neighbors. The dimension k of the *$R^*$* set will instead be defined as $k_1$: $R^*(g_i,k_1)$. |