From 2fa61c47c9e93fdc4c4908dd9ee6e7885430e73b Mon Sep 17 00:00:00 2001
From: Jon Whiteaker <jbw@berkeley.edu>
Date: Sun, 4 Mar 2012 00:51:57 -0800
Subject: brano's comments

---
 conclusion.tex                          |   26 +
 data/combined/graphs/face.csv           | 1178 +++++++++++++++----------------
 data/combined/graphs/plots.py           |   35 +-
 data/face-frame-recognition-accuracy.py |   18 +-
 experimental.tex                        |  244 ++++---
 graphics/10fold-naive.pdf               |  Bin 16474 -> 0 bytes
 graphics/back.pdf                       |  Bin 15468 -> 19075 bytes
 graphics/face.pdf                       |  Bin 12536 -> 15440 bytes
 graphics/frames.pdf                     |  Bin 10896 -> 10940 bytes
 graphics/offline-nb.pdf                 |  Bin 0 -> 17290 bytes
 graphics/offline-sht.pdf                |  Bin 0 -> 21595 bytes
 graphics/online-nb.pdf                  |  Bin 0 -> 18224 bytes
 graphics/online-sht.pdf                 |  Bin 24198 -> 27848 bytes
 graphics/var.pdf                        |  Bin 16186 -> 17091 bytes
 intro.tex                               |   38 +-
 kinect.tex                              |    2 +
 related.tex                             |    4 +
 uniqueness.tex                          |   75 +-
 18 files changed, 844 insertions(+), 776 deletions(-)
 delete mode 100644 graphics/10fold-naive.pdf
 create mode 100644 graphics/offline-nb.pdf
 create mode 100644 graphics/offline-sht.pdf
 create mode 100644 graphics/online-nb.pdf

diff --git a/conclusion.tex b/conclusion.tex
index 3de1f74..1270fce 100644
--- a/conclusion.tex
+++ b/conclusion.tex
@@ -1,2 +1,28 @@
 \section{Conclusion}
 \label{sec:conclusion}
+
+In this paper, we introduce skeleton recognition.  We show that skeleton
+measurements are unique enough to distinguish individuals using a dataset of
+real skeletons.  We present an probabilistic model for recognition, and extend
+it to take advantage of consecutive frames. Finally we test our model by
+collecting data for a week in a real-world setting.  Our results show that
+skeleton recognition performs close to face recognition, and it can be used in
+many more scenarios.
+
+However, the Kinect SDK does have some limitations.  First of all, the Kinect
+SDK can only fit two skeletons at a time.  Therefore, when a group of people
+walk in front of the Kinect, not all of them can be recognized via skeleton,
+where they might be by face recognition.  Second, some times figure detection
+gives false positives, which caused skeletons to be fit on a window and a
+vacuum cleaner during our data collection (both of these are reflective
+surfaces, which might explain the failure).
+
+Skeleton recognition can only get more accurate as the resolution of range
+cameras increases and skeleton fitting algorithms improve.  Microsoft is
+planning on putting the Kinect technology inside
+laptops~\footnote{\url{http://www.thedaily.com/page/2012/01/27/012712-tech-kinect-laptop/}}
+and the Asus Xtion
+pro~\footnote{\url{http://www.asus.com/Multimedia/Motion_Sensor/Xtion_PRO/}} is
+a range camera like the Kinect designed for PCs. The increased usage of range
+cameras and competition among vendors can only lead to advancements in the
+associated technologies. 
diff --git a/data/combined/graphs/face.csv b/data/combined/graphs/face.csv
index 799f4ed..2f7ff26 100644
--- a/data/combined/graphs/face.csv
+++ b/data/combined/graphs/face.csv
@@ -36,267 +36,488 @@
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+0.000618811881188,1.0
+0.000618811881188,1.0
+0.000618811881188,1.0
+0.000618811881188,1.0
+0.000618811881188,1.0
+0.000618811881188,1.0
+0.000618811881188,1.0
+0.000618811881188,1.0
+0.000618811881188,1.0
+0.000618811881188,1.0
+0.000618811881188,1.0
+0.000618811881188,1.0
+0.000618811881188,1.0
+0.000618811881188,1.0
 0,1
 0,1
 0,1
diff --git a/data/combined/graphs/plots.py b/data/combined/graphs/plots.py
index 5fd3c2c..7b3bb3e 100755
--- a/data/combined/graphs/plots.py
+++ b/data/combined/graphs/plots.py
@@ -20,34 +20,45 @@ l = ["3","5","10","all"]
 
 #10-fold, naive
 plt.cla()
-ax = plt.subplot(121)
+#ax = plt.subplot(121)
 plt.axis([0,100,50,100])
-ax.set_aspect(2)
+#ax.set_aspect(2)
 for i in l:
     x,y = np.loadtxt(i+"_nb_off.mat",unpack=True)
-    plt.plot(100*x,100*y,label="$n=$ "+i,linewidth=0.8)
+    plt.plot(100*x,100*y,label="$n_p=$ "+i,linewidth=0.8)
     plt.xlabel("Recall [%]")
     plt.ylabel("Precision [%]")
     plt.legend(loc="best")
+plt.savefig("offline-nb.pdf")
 #10-fold, SHT
-ax = plt.subplot(122)
-plt.axis([0,100,50,100])
-ax.set_aspect(2)
+#ax = plt.subplot(122)
+#plt.axis([0,100,50,100])
+#ax.set_aspect(2)
+plt.cla()
 for i in l:
     x,y = np.loadtxt(i+"_sht_off.mat",unpack=True)
-    plt.plot(100*x,100*y,label="$n=$ "+i,linewidth=0.8)
+    plt.plot(100*x,100*y,label="$n_p=$ "+i,linewidth=0.8)
     plt.xlabel("Recall [%]")
     plt.ylabel("Precision [%]")
     plt.legend(loc="best")
 
 plt.axis([0,100,50,100])
-plt.savefig("10fold.pdf")
+plt.savefig("offline-sht.pdf")
 
+#online,NB
+plt.cla()
+for i in l:
+    x,y = np.loadtxt(i+"_nb_on.mat",unpack=True)
+    plt.plot(100*x,100*y,label="$n_p=$ "+i,linewidth=0.8,markersize=4)
+    plt.xlabel("Recall [%]")
+    plt.ylabel("Precision [%]")
+    plt.legend(loc="best")
+plt.savefig("online-nb.pdf")
 #online,SHT
 plt.cla()
 for i in l:
     x,y = np.loadtxt(i+"_sht_on.mat",unpack=True)
-    plt.plot(100*x,100*y,label="$n=$ "+i,linewidth=0.8,markersize=4)
+    plt.plot(100*x,100*y,label="$n_p=$ "+i,linewidth=0.8,markersize=4)
     plt.xlabel("Recall [%]")
     plt.ylabel("Precision [%]")
     plt.legend(loc="best")
@@ -69,8 +80,10 @@ plt.savefig("face.pdf")
 plt.cla()
 x,y = np.loadtxt("back_all_sht_on.mat",unpack=True)
 a,b = np.loadtxt("all_sht_on.mat",unpack=True)
-plt.plot(100*x,100*y,linewidth=0.8,label="Away")
-plt.plot(100*a,100*b,linewidth=0.8,label="Toward")
+c,d = np.loadtxt("front_back_all_sht.mat",unpack=True)
+plt.plot(100*a,100*b,linewidth=0.8,label="Train/test toward")
+plt.plot(100*x,100*y,linewidth=0.8,label="Train/test away")
+plt.plot(100*c,100*d,linewidth=0.8,label="Train toward test away")
 plt.xlabel("Recall [%]")
 plt.ylabel("Precision [%]")
 plt.legend(loc="best")
diff --git a/data/face-frame-recognition-accuracy.py b/data/face-frame-recognition-accuracy.py
index 7c53366..d32af9f 100755
--- a/data/face-frame-recognition-accuracy.py
+++ b/data/face-frame-recognition-accuracy.py
@@ -40,26 +40,24 @@ for line in open(sys.argv[2]):
         runs[prun] = recs.index(max(recs))+1
         recs = map(lambda x:0,users)
     recs[users.index(rec)] += 1
-    maxc = math.log(float(line[7])/100.0)
+    maxc = float(line[7])
     i = 9
-    cvec = []
-    while len(cvec) < len(users)-1:
-        if i < len(line):
-            cvec += [math.log(float(line[i])/100.0) - maxc]
-        else:
-            cvec += [-maxc]
-    conf[run] = math.log(np.sum(np.exp(cvec)))
+    cvec = [maxc]
+    while i < len(line):
+        cvec += [float(line[i])]
+        i += 2
+    conf[run] = (maxc/100.0)*(maxc/(np.sum(cvec)))
     prun = run
 
 for i in range(999)+list(np.arange(999,1000,0.01)):
-    thresh = 5-i/100.0
+    thresh = i/1000.0
     t=0.0
     tp=0.0
     fp=0.0
     fn=0.0
     for (k,v) in runs.items():
         #print v,labels[k]
-        if conf[k] > thresh:
+        if conf[k] < thresh:
             fn += 1
         elif v != labels[k]:
             fp += 1
diff --git a/experimental.tex b/experimental.tex
index 3c6547b..b30ba10 100644
--- a/experimental.tex
+++ b/experimental.tex
@@ -29,8 +29,7 @@ laboratory setting.  The Kinect is placed at the tee of a well traversed
 hallway.  The view of the Kinect is seen in \fref{fig:hallway}, showing the
 color image, the depth image, and the fitted skeleton of a person in a single
 frame.  For each frame where a person is detected and a skeleton is fitted we
-collect the 3D coordinates of 20 body joints, and the color image recorded by
-the RGB camera.
+capture the 3D coordinates of 20 body joints, and the color image.
 
 \begin{figure}[t]
   \begin{center}
@@ -57,19 +56,22 @@ is increasing.
 \subsection{Experiment design}
 \label{sec:experiment-design}
 
-Several reductions are then applied to the data set to extract \emph{features}
+We preprocess the data set to extract \emph{features}
 from the raw data.  First, the lengths of 15 body parts are computed from the
 joint coordinates. These are distances between two contiguous joints in the
 human body. If one of the two joints of a body part is not present or inferred
 in a frame, the corresponding body part is reported as absent for the frame.
-Second, the number of features is reduced to 9 by using the vertical symmetry
+Second, we reduce the number of features to nine by using the vertical symmetry
 of the human body: if two body parts are symmetric about the vertical axis, we
 bundle them into one feature by averaging their lengths. If only one of them is
-present, we take the value of its counterpart. If none of them are present, the
-feature is reported as missing for the frame. The resulting nine features are:
-Head-ShoulderCenter, ShoulderCenter-Shoulder, Shoulder-Elbow, Elbow-Wrist,
-ShoulderCenter-Spine, Spine-HipCenter, HipCenter-HipSide, HipSide-Knee,
-Knee-Ankle.  Finally, any frame with a missing feature is filtered out.
+present, we take its value. If neither of them is present, the feature is
+reported as missing for the frame.  The resulting nine features include the six
+arm, leg, and pelvis measurements from \xref{sec:uniqueness}, and three
+additional measurements: spine length, shoulder breadth, and head size.
+Finally, any frame with a missing feature is filtered out.
+%The resulting nine features are: Head-ShoulderCenter, ShoulderCenter-Shoulder,
+%Shoulder-Elbow, Elbow-Wrist, ShoulderCenter-Spine, Spine-HipCenter,
+%HipCenter-HipSide, HipSide-Knee, Knee-Ankle.  
 
 Each detected skeleton also has an ID number which identifies the figure it
 maps to from the figure detection stage. When there are consecutive frames with
@@ -77,35 +79,35 @@ the same ID, it means that the skeleton-fitting algorithm was able to detect
 the skeleton in a contiguous way. This allows us to define the concept of a
 \emph{run}: a sequence of frames with the same skeleton ID.
 
-\begin{table}
-\begin{center}
-\caption{Data set statistics. The right part of the table shows the
-average numbers for different intervals of $k$, the rank of a person
-in the ordering given by the number of frames}
-\label{tab:dataset}
-\begin{tabular}{|l|r||r|r|r|}
-\hline
-Number of people & 25 & $k\leq 5$ & $5\leq k\leq 20$ & $k\geq 20$\\
-\hline
-Number of frames & 15945 & 1211 & 561 & 291 \\
-\hline
-Number of runs & 244 & 18 & 8 & 4\\
-\hline
-\end{tabular}
-\end{center}
-\end{table}
+%\begin{table}
+%\begin{center}
+%\caption{Data set statistics. The right part of the table shows the
+%average numbers for different intervals of $k$, the rank of a person
+%in the ordering given by the number of frames}
+%\label{tab:dataset}
+%\begin{tabular}{|l|r||r|r|r|}
+%\hline
+%Number of people & 25 & $k\leq 5$ & $5\leq k\leq 20$ & $k\geq 20$\\
+%\hline
+%Number of frames & 15945 & 1211 & 561 & 291 \\
+%\hline
+%Number of runs & 244 & 18 & 8 & 4\\
+%\hline
+%\end{tabular}
+%\end{center}
+%\end{table}
 
 \begin{figure}[t]
   \begin{center}
-    \includegraphics[width=0.80\textwidth]{graphics/frames.pdf}
+    \includegraphics[width=0.49\textwidth]{graphics/frames.pdf}
   \end{center}
   \caption{Distribution of the frame ratio of each individual in the
   data set}
+  \label{fig:frames}
 \end{figure}
 
-\subsection{Results}
+\subsection{Offline learning setting}
 
-\paragraph{Offline setting.}
 
 The mixture of Gaussians model is evaluated on the whole dataset by
 doing 10-fold cross validation: the data set is partitioned into 10
@@ -115,7 +117,7 @@ repeated for the 10 possible testing subsample. Averaging the
 prediction rate over these 10 training-testing experiments yields the
 prediction rate for the chosen threshold.
 
-Figure \ref{fig:mixture} shows the precision-recall plot as the
+\fref{fig:offline} shows the precision-recall plot as the
 threshold varies. Several curves are obtained for different group
 sizes: people are ordered based on their numbers of frames, and all
 the frames belonging to someone beyond a given rank in this ordering
@@ -124,20 +126,37 @@ increasing the number of people in the data set can be explained
 by the overlaps between skeleton profiles due to the noise, as
 discussed in Section~\ref{sec:uniqueness}, but also by the very few
 number of runs available for the least present people, as seen in
-Table~\ref{tab:dataset}, which does not permit a proper training of
+\fref{fig:frames}, which does not permit a proper training of
 the algorithm.
 
-\begin{figure}[t]
-  \begin{center}
-    \includegraphics[width=0.80\textwidth]{graphics/10fold-naive.pdf}
-  \end{center}
-  \caption{Precision-Recall curve for the mixture of Gaussians model
+\begin{figure*}[t]
+\begin{center}
+\subfloat[Mixture of Gaussians]{
+    \includegraphics[width=0.49\textwidth]{graphics/offline-nb.pdf}
+    \label{fig:offline:nb}
+}
+\subfloat[Sequential Hypothesis Learning]{
+    \includegraphics[width=0.49\textwidth]{graphics/offline-sht.pdf}
+    \label{fig:offline:sht}
+}
+  \caption{Precision-recall curve for the mixture of Gaussians model
   with 10-fold cross validation. The data set is restricted to the top
-  $n$ most present people}
-  \label{fig:mixture}
-\end{figure}
+  $n_p$ most present people}
+\label{fig:offline}
+\end{center}
+\end{figure*}
 
-\paragraph{Online setting.}
+%\begin{figure}[t]
+%  \begin{center}
+%    \includegraphics[width=0.80\textwidth]{graphics/10fold-naive.pdf}
+%  \end{center}
+%  \caption{Precision-Recall curve for the mixture of Gaussians model
+%  with 10-fold cross validation. The data set is restricted to the top
+%  $n$ most present people}
+%  \label{fig:mixture}
+%\end{figure}
+
+\subsection{Online learning setting}
 
 Even though the previous evaluation is standard, it does not properly
 reflect the reality. A real-life setting could be the following: the
@@ -154,114 +173,127 @@ run. The analysis is therefore performed by partitioning the dataset
 into 10 subsamples of equal size. For a given threshold, the algorithm
 is trained and tested incrementally: trained on the first $k$
 subsamples (in the chronological order) and tested on the $(k+1)$-th
-subsample. Figure~\ref{fig:sequential} shows the prediction-recall
+subsample. \fref{fig:online} shows the prediction-recall
 curve when averaging the prediction rate of the 10 incremental
 experiments.
 
-\begin{figure}[t]
-  \begin{center}
-    \includegraphics[width=0.80\textwidth]{graphics/online-sht.pdf}
-  \end{center}
-  \caption{Precision-Recall curve for the sequential hypothesis
-  testing algorithm in the online setting. $n$ is the size of the
-  group as in Figure~\ref{fig:mixture}}
-  \label{fig:sequential}
-\end{figure}
+\begin{figure*}[t]
+\begin{center}
+\subfloat[Mixture of Gaussians]{
+    \includegraphics[width=0.49\textwidth]{graphics/online-nb.pdf}
+    \label{fig:online:nb}
+}
+\subfloat[Sequential Hypothesis Learning]{
+    \includegraphics[width=0.49\textwidth]{graphics/online-sht.pdf}
+    \label{fig:online:sht}
+}
+\caption{Precision-recall curves for the online setting. $n_p$ is the size of
+the group as in Figure~\ref{fig:offline}}
+\label{fig:online}
+\end{center}
+\end{figure*}
 
-\paragraph{Face recognition.}
+\subsection{Face recognition}
 
-We then compare the performance of skeleton recognition with the
-performance of face recognition as given by \textsf{face.com}
-\todo{REFERENCE NEEDED}. At the time of writing, this is the best
-performing face recognition algorithm on the LFW data set
-\cite{face-com}.
+We then compare the performance of skeleton recognition with the performance of
+face recognition as given by \textsf{face.com}.  At the time of writing, this
+is the best performing face recognition algorithm on the LFW data set
+~\cite{face-com}.
 
 We use the publicly available REST API of \textsf{face.com} to do face
-recognition on our data set: the training is done on half of the data
-and the testing is done on the remaining half. For comparison, the
-Gaussian mixture algorithm is run with the same training-testing
-partitioning of the data set. In this setting, the Sequential
-Hypothesis Testing algorithm is not relevant for the comparison,
-because \textsf{face.com} does not give the possibility to mark a
-sequence of frames as belonging to the same run. This additional
-information would be used by the SHT algorithm and would thus bias the
-results in favor of skeleton recognition.
+recognition on our data set.  Due to the restrictions of the API, for this
+experiment we train on one half of the data and test on the remaining half. For
+comparison, the Gaussian mixture algorithm is run with the same
+training-testing partitioning of the data set. In this setting, the Sequential
+Hypothesis Testing algorithm is not relevant for the comparison, because
+\textsf{face.com} does not give the possibility to mark a sequence of frames as
+belonging to the same run. This additional information would be used by the SHT
+algorithm and would thus bias the results in favor of skeleton recognition.
 
 \begin{figure}[t]
+\parbox[t]{0.49\linewidth}{
   \begin{center}
-    \includegraphics[width=0.80\textwidth]{graphics/face.pdf}
+    \includegraphics[width=0.49\textwidth]{graphics/face.pdf}
   \end{center}
-  \caption{Precision-Recall curve for face recognition and skeleton recognition}
+  \caption{Precision-recall curve for face recognition and skeleton recognition}
   \label{fig:face}
-\end{figure}
-
-\paragraph{People walking away from the camera.}
-
-The performance of face recognition and skeleton recognition are
-comparable in the previous setting \todo{is that really
-true?}. However, there are many cases where only skeleton recognition
-is possible. The most obvious one is when people are walking away from
-the camera. Coming back to the raw data collected during the
-experiment design, we manually label the runs of people walking away
-from the camera. In this case, it is harder to get the ground truth
-classification and some of runs are dropped because it is not possible
-to recognize the person. Apart from that, the data set reduction is
-performed exactly as explained in Section~\ref{sec:experiment-design}.
-
-\begin{figure}[t]
+}
+\parbox[t]{0.49\linewidth}{
   \begin{center}
-    \includegraphics[width=0.80\textwidth]{graphics/back.pdf}
+    \includegraphics[width=0.49\textwidth]{graphics/back.pdf}
   \end{center}
-  \caption{Precision-Recall curve for the sequential hypothesis
-  testing algorithm in the online setting with people walking away
-  from and toward the camera. All the people are included}
+  \caption{Precision-recall curve 
+  with people walking away
+  from and toward the camera}
   \label{fig:back}
+}
 \end{figure}
 
-Figure~\ref{fig:back} compares the curve obtained in the online
+\subsection{Walking away}
+
+The performance of face recognition and skeleton recognition are comparable in
+the previous setting.  However, there are many cases where only skeleton
+recognition is possible. The most obvious one is when people are walking away
+from the camera. Coming back to the raw data collected during the experiment
+design, we manually label the runs of people walking away from the camera. In
+this case, it is harder to get the ground truth classification and some of runs
+are dropped because it is not possible to recognize the person. Apart from
+that, the data set reduction is performed exactly as explained in
+Section~\ref{sec:experiment-design}.
+
+%\begin{figure}[t]
+%  \begin{center}
+%    \includegraphics[width=0.80\textwidth]{graphics/back.pdf}
+%  \end{center}
+%  \caption{Precision-Recall curve for the sequential hypothesis
+%  testing algorithm in the online setting with people walking away
+%  from and toward the camera. All the people are included}
+%  \label{fig:back}
+%\end{figure}
+
+\fref{fig:back} compares the curve obtained in the online
 setting with people walking toward the camera, with the curve obtained
 by running the same experiment on the data set of runs of people
 walking away from the camera. The two curves are sensibly the
 same. However, one could argue that as the two data sets are
 completely disjoint, the SHT algorithm is not learning the same
 profile for a person walking toward the camera and for a person
-walking away from the camera. Figure~\ref{fig:back2} shows the
-Precision-Recall curve when training on runs toward the camera and
+walking away from the camera. \fref{fig:back} shows the
+Precision-recall curve when training on runs toward the camera and
 testing on runs away from the camera.
 
-\todo{PLOT NEEDED}
+\subsection{Reducing the noise} 
 
-\paragraph{Reducing the noise.} Predicting potential improvements of
-the prediction rate of our algorithm is straightforward. The algorithm
-relies on 9 features only. Section~\ref{sec:uniqueness} shows that
-6 of these features alone are sufficient to perfectly distinguish two
-different skeletons at a low noise level. Therefore, the only source
-of classification error in our algorithm is the dispersion of the
-observed limbs' lengths away from the exact measurements.
+Predicting potential improvements of the prediction rate of our algorithm is
+straightforward. The algorithm relies on 9 features only.
+\xref{sec:uniqueness} shows that 6 of these features alone are
+sufficient to perfectly distinguish two different skeletons at a low noise
+level. Therefore, the only source of classification error in our algorithm is
+the dispersion of the observed limbs' lengths away from the exact measurements.
 
 To simulate a possible reduction of the noise level, the data set is
 modified as follows: all the observations for a given person are
 homothetically contracted towards their average so as to divide their
-empirical variance by 2. Formally, if $x$ is an observation in the
-9-dimensional feature space for the person $i$, and if $\bar{x}$ is
+empirical variance by 2. Formally, if $\bx$ is an observation in the
+9-dimensional feature space for the person $i$, and if $\bar{\bx}$ is
 the average of all the observations available for this person in the
-data set, then $x$ is replaced by $x'$ defined by:
+data set, then $\bx$ is replaced by $\bx'$ defined by:
 \begin{equation}
-  x' = \bar{x} + \frac{x-\bar{x}}{\sqrt{2}}
+  \bx' = \bar{\bx} + \frac{\bx-\bar{\bx}}{\sqrt{2}}
 \end{equation}
 We believe that a reducing factor of 2 for the noise's variance is
 realistic given the relative low resolution of the Kinect's infrared
 camera. 
 
-Figure~\ref{fig:var} compares the Precision-Recall curve of
-Figure~\ref{fig:sequential} to the curve of the same experiment run on
+\fref{fig:var} compares the Precision-recall curve of
+\fref{fig:sequential} to the curve of the same experiment run on
 the newly obtained data set.
 
 \begin{figure}[t]
   \begin{center}
-    \includegraphics[width=0.80\textwidth]{graphics/var.pdf}
+    \includegraphics[width=0.49\textwidth]{graphics/var.pdf}
   \end{center}
-  \caption{Precision-Recall curve for the sequential hypothesis
+  \caption{Precision-recall curve for the sequential hypothesis
   testing algorithm in the online setting for all the people with and
   without halving the variance of the noise}
   \label{fig:var}
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diff --git a/intro.tex b/intro.tex
index 5e51a36..bd643e2 100644
--- a/intro.tex
+++ b/intro.tex
@@ -1,7 +1,7 @@
 \section{Introduction}
 \label{sec:intro}
 
-Person identification has become a valuable asset, whether for means of
+Person recognition has become a valuable asset, whether for means of
 authentication, personalization, or other applications.  Previous work revolves
 around either physiological biometrics, such as face recognition, or behavioral
 biometrics such as gait recognition.  In this paper, we propose using
@@ -11,35 +11,31 @@ In recent years, advances in range cameras have given us access to increasingly
 accurate real-time depth imaging.  Furthermore, the low-cost and widely
 available Kinect~\cite{kinect} has brought range imaging to the masses.  In
 parallel, the automatic detection of body parts from depth images has led to
-real-time skeleton mapping.  As the resolution and accuracy of range cameras
-improve, so will the accuracy and precision of skeleton mapping algorithms.  
+real-time skeleton fitting.  
 
-In this paper we show that skeleton mapping is accurate and unique enough in
-individuals to be used for person recognition.  We make the following two
+In this paper we show that skeleton fitting is accurate and unique enough in
+individuals to be used for person recognition.  We make the following
 contributions.  First, we show that ground truth skeleton measurements can
-uniquely identify a person.  We model how the accuracy of skeleton recognition
-decreases as simulated error increases, and find it is still possible to use
-for recognition.  Second, we evaluate our hypothesis using real-world data
-collected with the Kinect.  Our results show that skeleton recognition performs
-well, particularly in situations where face recognition cannot be performed.
+uniquely identify a person.  Second, we evaluate our hypothesis using
+real-world data collected with the Kinect.  Our results show that skeleton
+recognition performs quite well, particularly in situations where face
+recognition cannot be performed.
+%As the resolution and accuracy of range cameras improve, so will the accuracy
+%and precision of skeleton fitting algorithms.  
 
 Much of the prior work in person recognition focuses on data gathered from
-other sensors, such as face recognition with color cameras and voice
+other sensors, such as face recognition with color images and voice
 recognition with microphones.  In the realm of depth imaging, most of the work
-surrounds behavioral recognition, continuing work in gait recognition.  The
-Xbox 360~\cite{} does use the height inferred from the Kinect as part of its
-user identification algorithm, albeit in addition to other attributes including
-face recognition.
+surrounds behavioral recognition, continuing work in gait recognition.  
 
 The paper is organized as follows.  First we discuss prior methods of
-person identification, in addition to the advances in the technologies
-pertaining to skeleton mapping (Section~\ref{sec:related}).  Next we
+person recognition, in addition to the advances in the technologies
+pertaining to skeleton fitting (Section~\ref{sec:related}).  Next we
 use a dataset of actual skeletal measurements to show that
-identification by skeleton is feasible, even when we simulate the
-error of measuring skeletons with a Kinect
+recognition by skeleton is feasible
 (Section~\ref{sec:uniqueness}). We then discuss an error model and the
-resulting algorithm to do person identification
-(Section~\ref{sec:algorithm}).  Finally, we collect skeleton data with
+resulting algorithm to do person recognition
+(Section~\ref{sec:algorithms}).  Finally, we collect skeleton data with
 a Kinect in an uncontrolled setting and we apply preprocessing and
 classification algorithms to this dataset
 (Section~\ref{sec:experiment}).  We evaluate the performance of
diff --git a/kinect.tex b/kinect.tex
index 1e87cc8..5407ddd 100644
--- a/kinect.tex
+++ b/kinect.tex
@@ -19,6 +19,8 @@
 \usepackage{colortbl} % required for cell backgrounds
 %\usepackage{psfrag}
 \usepackage{pifont}
+\usepackage{subfig}
+\usepackage{url}
 
 %\usepackage{times}
 % substitutes normal through postscript fonts (\texttt) use \mathptmx
diff --git a/related.tex b/related.tex
index a772a32..f7b9a1e 100644
--- a/related.tex
+++ b/related.tex
@@ -66,6 +66,10 @@ Kinect.  Given the maturity of the solutions, we will use implementations of
 figure detection and skeleton fitting.  Therefore this paper will focus
 primarily on the classification part of skeleton recognition.
 
+%The
+%Xbox 360~\cite{} does use the height inferred from the Kinect as part of its
+%user recognition algorithm, albeit in addition to other attributes including
+%face recognition.
 
 %a person from an image to measure gait, but can also be measured from floor
 %sensors or wearable sensors~\cite{gait-survey}.  
diff --git a/uniqueness.tex b/uniqueness.tex
index 854e4c2..927421a 100644
--- a/uniqueness.tex
+++ b/uniqueness.tex
@@ -1,9 +1,9 @@
 \section{Skeleton uniqueness}
 \label{sec:uniqueness}
 
-The most obvious concern raised by trying to use skeletons as a recognizable
-biometric is their uniqueness. Are skeletons consistently and sufficiently
-distinct to use them for person recognition?
+The most obvious concern raised by trying to use skeleton measurements as a
+recognizable biometric is their uniqueness. Are skeletons consistently and
+sufficiently distinct to use them for person recognition?
 
 \subsection{Face recognition benchmark}
 
@@ -13,41 +13,39 @@ problem}. In this problem you are given two measurements of the metric
 and you want to decide whether they come from the same individual
 (matched pair) or from two different individuals (unmatched pair).
 
-The \emph{Labeled Faces in the Wild} \cite{lfw} database is
-specifically suited to study the face pair matching problem and has
-been used to benchmark several face recognition algorithms. Raw data
-of this benchmark is publicly available and has been derived as
-follows: the database is split into 10 subsets. From each of these
-subsets, 300 matched pairs and 300 unmatched pairs are randomly
-chosen. Each algorithm runs 10 separate leave-one-out cross-validation
-experiments on these sets of pairs. Averaging the number of true
-positives and false positives across the 10 experiments for a given
-threshold then yields one point on the receiver operating
-characteristic curve (ROC curve: this is the curve of the
-true-positive rate vs. 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 benchmark.
+This benchmark is standard for face recognition using the \emph{Labeled Faces
+in the Wild} \cite{lfw} database.  Raw data of this benchmark is publicly
+available and has been derived as follows: the database is split into 10
+subsets. From each of these subsets, 300 matched pairs and 300 unmatched pairs
+are randomly chosen. Each algorithm runs 10 separate leave-one-out
+cross-validation experiments on these sets of pairs. Averaging the number of
+true positives and false positives across the 10 experiments for a given
+threshold then yields one point on the receiver operating characteristic (ROC)
+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
+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 osteometric measurements of 1538 skeletons dating from
-throughout the Holocene. 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.
+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.
-With exact measurements, all skeletons are distinct and therefore every pair is
-correctly classified.  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). We simulate this error
-by adding independent random Gaussian noise to each measurement of the pairs.
+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}
 
@@ -70,7 +68,7 @@ defined as:
   \begin{center}
     \includegraphics[width=10cm]{graphics/roc.pdf}
   \end{center}
-  \caption{Receiver operating characteristic (true positive rate
+  \caption{ROC curve (true positive rate
   vs. false positive rate) for several standard deviations of the
   noise and for the state-of-the-art \emph{Associate-Predict} face
   detection algorithm}
@@ -90,23 +88,22 @@ than 1cm with 99.9\% probability. Even with a standard
 deviation of 5mm, it is still possible to detect 90\% of the matched
 pairs with a false positive rate of 6\%.
 
-\todo{We should unify the language here with that in the related work (and intro)}
 This experiment gives an idea of the noise variance level above which
-it is not possible to consistently distinguish skeletons. This noise
-level can be interpreted as follows in the person recognition
-problem. For this problem, a classifier can be built be first learning
+it is not possible to consistently distinguish skeletons. 
+For this problem, a classifier can be built by first learning
 a \emph{skeleton profile} for each individual from all the
 measurements in the training set. Then, given a new skeleton
 measurement, the algorithm classifies it to the individual whose
 skeleton profile is closest to the new measurement. In this case,
 there are two distinct sources of noise:
 \begin{itemize}
-\item the absolute deviation of the estimator: how far is the
-  estimated profile from the exact skeleton profile of the person.
+\item the absolute deviation of the estimator: how far is the estimated profile
+  from the exact skeleton profile of the person due to figure position or
+  motion (\ie from walking).
 \item the noise of the new measurement: this comes from the device
   doing the measurement.
 \end{itemize}
-the combination of these two noises is what can be compared to the
+The combination of these two noise sources is what can be compared to the
 noise represented on the ROC curves. Section \label{sec:kinect} will
 give more insight on the structure of the noise.
 
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