From 79ce4cc4bff42b05d634f20a661197980031a03c Mon Sep 17 00:00:00 2001
From: Jon Whiteaker <jbw@berkeley.edu>
Date: Wed, 29 Feb 2012 12:06:50 -0800
Subject: jon's first pass on uniqueness section

---
 uniqueness.tex | 54 +++++++++++++++++++++++++++---------------------------
 1 file changed, 27 insertions(+), 27 deletions(-)

(limited to 'uniqueness.tex')

diff --git a/uniqueness.tex b/uniqueness.tex
index 2d6c3bf..dae88c3 100644
--- a/uniqueness.tex
+++ b/uniqueness.tex
@@ -1,10 +1,9 @@
 \section{Skeleton uniqueness}
 \label{sec:uniqueness}
 
-The most obvious concern raised by trying to use skeletons to
-recognize people is their uniqueness. Are skeletons consistently
-and sufficiently pairwise distinct to have reasonable hope of using
-them for people recognition?
+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?
 
 \subsection{Face recognition benchmark}
 
@@ -14,7 +13,7 @@ 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
+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
@@ -29,35 +28,35 @@ 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
-images pair from the input data. This is referred to as the
+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 Data Set
-\cite{deadbodies}. This data set consists of osteometric measurements
-of 1538 skeletons dating from throughout the Holocene. We keep from
-these measurements the lengths of six bones (radius, humerus, femur,
-tibia, left coxae, right coxae). 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, we use the Goldman Osteological Dataset \cite{deadbodies}. This
+dataset consists of osteometric measurements of 1538 skeletons dating from
+throughout the Holocene. We keep six measurements from the data: 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 data set, 1191 matched pairs and 1191 unmatched pairs are
-generated. In practice, the exact measurements of the bones are never
-directly accessible, but are always perturbed by a noise whose
-variance depends on the collection protocol. This is accounted for by
-adding independent random Gaussian noise to each constituents of the
-pairs.
+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.
 
 \subsection{Results}
 
-The pair-matching problem is then solved by using a proximity
+We evaluate the performance of the pair-matching problem on the dataset by using a proximity
 threshold algorithm: for a given threshold, a pair will be classified
-as \emph{matched} if the Euclidean distance of its two constituents is
-lower than the threshold and \emph{unmatched} otherwise. Formally, let
+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 measurements of the six
-bones), the output of the algorithm for the threshold $\delta$ is
+($s_i\in\mathbf{R}_+^{6}$, 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}
@@ -86,14 +85,15 @@ the Image-restricted LFW benchmark: \emph{Associate-Predict}
 The results show that with a standard deviation of 3mm, skeleton
 proximity thresholding performs quite similarly to face detection at
 low false-positive rate. At this noise level, the error is smaller
-than 1cm with 99.9\% probability smaller. Even with a standard
+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 identification
-setting. For this problem, a classifier can be built be first learning
+level can be interpreted as follows in the person recognition
+setting. 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
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