From b6842fee84ec43e2f4eec2ce2adcf3a97cfdad70 Mon Sep 17 00:00:00 2001 From: Thibaut Horel Date: Tue, 28 Feb 2012 03:00:42 -0800 Subject: Beginning of the uniqueness section. --- references.bib | 12 ++++++++++-- uniqueness.tex | 58 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++- 2 files changed, 67 insertions(+), 3 deletions(-) diff --git a/references.bib b/references.bib index 5cc5942..4615647 100644 --- a/references.bib +++ b/references.bib @@ -121,8 +121,8 @@ @misc{kinect, title = {Kinect for Xbox 360}, - institution = {Microsoft Corp.} - location = {Redmond, WA}, + institution = {Microsoft Corp.}, + location = {Redmond, WA} } @misc{comon, @@ -269,3 +269,11 @@ year={1991}, pages={71--86} } + +@article{deadbodies, +title={Human body mass estimation: a comparison of “morphometric” and “mechanical” methods}, +author="CB. Ruff and BM Auerbach", +journal = "American Journal of Physical Anthropology", +volume = "125", +pages = "331--342" +} diff --git a/uniqueness.tex b/uniqueness.tex index 765242b..9a89c6c 100644 --- a/uniqueness.tex +++ b/uniqueness.tex @@ -1,3 +1,59 @@ \section{Skeleton uniqueness} -\subsection{Face recognition benchmark} \ No newline at end of file +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? + +\subsection{Face recognition benchmark} + +A good way to understand the uniqueness of a metric is to look at the +performance it gives for the \emph{pair-matching 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 true-positive vs +false-positive curve (also known as ROC). + +\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. + +From this data set, 1191 matched pairs and 1191 unmatched +pairs are generated. 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. + +\subsection{Results} + +The pair-matching problem is then solved 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. + +This algorithm does not require any training, so it is run on the +whole set of pairs without doing cross-validation. Figure +\ref{fig:roc} shows the ROC of the proximity threshold algorithm for +varying variance of the noise added to the data. + + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "kinect" +%%% End: -- cgit v1.2.3-70-g09d2