From d7b0798050f72f08bcb3995c465efeb9bf9f516d Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Sun, 4 Mar 2012 13:01:08 -0800
Subject: Set font size, figsize, and bounding box of plots

Started taking Brano's comments into account (section 3)
---
 uniqueness.tex | 51 +++++++++++++++++++++++++++------------------------
 1 file changed, 27 insertions(+), 24 deletions(-)

(limited to 'uniqueness.tex')

diff --git a/uniqueness.tex b/uniqueness.tex
index 76b7461..2ed0f93 100644
--- a/uniqueness.tex
+++ b/uniqueness.tex
@@ -6,6 +6,7 @@ recognizable biometric is their uniqueness. Are skeletons consistently and
 sufficiently distinct to use them for person recognition?
 
 \subsection{Face recognition benchmark}
+\label{sec:frb}
 
 A good way to understand the uniqueness of a metric is to look at how
 well an algorithm based on it performs in the \emph{pair-matching
@@ -25,27 +26,30 @@ curve, which plots the true-positive rate against the false-positive rate as
 the threshold of the algorithm varies. Note that in this benchmark the identity
 information of the individuals appearing in the pairs is not available, which
 means that the algorithms cannot form additional image pairs from the input
-data. This is referred to as the \emph{Image-restricted} setting in the LFW
+data. This is referred to as the \emph{image-restricted} setting in the LFW
 benchmark.
 
 \subsection{Experiment design}
 
-In order to run an experiment similar to the one used in the face pair-matching
-problem, we use the Goldman Osteological Dataset \cite{deadbodies}. This
-dataset consists of skeletal measurements of 1538 skeletons uncovered around
-the world and dating from throughout the last several thousand years. Given the
-way these data were collected, only a partial view of the skeleton is
-available, we keep six measurements: the lengths of four bones (radius,
-humerus, femur, and tibia) and the breadth and height of the pelvis.  Because
-of missing values, this reduces the size of the dataset to 1191.
+In order to run an experiment similar to the one used in the face
+pair-matching problem (Section~\ref{sec:frb}), we use the Goldman
+Osteological Dataset \cite{deadbodies}. This dataset consists of
+skeletal measurements of 1538 skeletons uncovered around the world and
+dating from throughout the last several thousand years. Given the way
+these data were collected, only a partial view of the skeleton is
+available, we keep six measurements: the lengths of four bones
+(radius, humerus, femur, and tibia) and the breadth and height of the
+pelvis.  Because of missing values, this reduces the size of the
+dataset to 1191.
 
-From this dataset, 1191 matched pairs and 1191 unmatched pairs are generated.
-In practice, the exact measurements of the bones of living subjects are not
-directly accessible. Therefore, measurements are likely to have an error rate,
-whose variance depends on the method of collection (\eg measuring limbs over
-clothing versus on bare skin). Since there is only one sample per skeleton, we
-simulate this error by adding independent random Gaussian noise to each
-measurement of the pairs.
+From this dataset, 1191 matched pairs and 1191 unmatched pairs are
+generated.  In practice, the exact measurements of the bones of living
+subjects are not directly accessible. Therefore, measurements are
+likely to have an error rate, whose variance depends on the method of
+collection (\eg measuring limbs over clothing versus on bare
+skin). Since there is only one sample per skeleton, we simulate this
+error by adding independent random Gaussian noise to each measurement
+of the pairs.
 
 \subsection{Results}
 
@@ -53,26 +57,25 @@ We evaluate the performance of the pair-matching problem on the dataset by using
 threshold algorithm: for a given threshold, a pair will be classified
 as \emph{matched} if the Euclidean distance between the two skeletons is
 lower than the threshold, and \emph{unmatched} otherwise. Formally, let
-$(s_1,s_2)$ be an input pair of the algorithm
-($s_i\in\mathbf{R}_+^{6}$, these are the six bone measurements), 
+$(\bs_1,\bs_2)$ be an input pair of the algorithm
+($\bs_i\in\mathbf{R}_+^{6}$, these are the six bone measurements), 
 the output of the algorithm for the threshold $\delta$ is
 defined as:
 \begin{displaymath}
-  A_\delta(s_1,s_2) = \begin{cases}
-    1 & \text{if $d(s_1,s_2) < \delta$}\\
+  A_\delta(\bs_1,\bs_2) = \begin{cases}
+    1 & \text{if $d(\bs_1,\bs_2) < \delta$}\\
     0 & \text{otherwise}
   \end{cases}
 \end{displaymath}
 
 \begin{figure}[t]
   \begin{center}
-    \includegraphics[width=10cm]{graphics/roc.pdf}
+    \includegraphics[width=0.6\columnwidth]{graphics/roc.pdf}
   \end{center}
   \vspace{-1.5\baselineskip}
-  \caption{ROC curve (true positive rate
-  vs. false positive rate) for several standard deviations of the
+  \caption{ROC curve for several standard deviations of the
   noise and for the state-of-the-art \emph{Associate-Predict} face
-  detection algorithm}
+  detection algorithm. The standard deviation $\sigma$ is shown in millimeters}
   \label{fig:roc}
 \end{figure}
 
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