\chapter{Context-dependent trademark matching and retrieval}\label{chap:logo_cdk}
{

\begin{quote}
\textit{In this chapter we introduce a novel multiple-logo matching and detection algorithm based on a new class of  similarity functions referred to as context dependent. Our approach is based on designing a similarity measure, involving interest points, which takes into account not only their intrinsic visual features but also their context and spatial configuration. The main contribution of this work includes (i) a variational framework which makes it possible to design our similarity as the fixed point of an energy function mixing a visual ``data term'', a ``context criterion'' and a ``regularization term'' and, (ii)  a theoretical study of the consistency of logo matching/detection and its invariance to different transformations including similarity and occlusion. Finally, we will show the validity of the method through extensive experiments on challenging logo images.  
\footnote{Part of this work was conducted while the author was a visiting Ph.D. student at XXXXX XXXXX, City (Nation), from Month to Month YEAR (working with. Dr.~Xxxx Yyyy). This chapter previously appeared as research report n.~2010D009, Xxxxx XXX~\cite{logocdk10}.}
}
\end{quote}


%-------------------------------------------------------------------------
\section{Introduction}\label{sec:intro4}


%-------------------------------------------------------------------------
\section{Context-dependent similarity}\label{section2}

\subsection{Context}\label{sec2} 

\subsection{Similarity design}\label{minors}

\subsection{Solution}\label{soll}


%-------------------------------------------------------------------------
\section{Logo detection and consistency} 

\subsection{Matching}\label{cdk_matching} 
 
\subsection{Logo detection} 

\subsection{Similarity invariance} 


%-------------------------------------------------------------------------
\section{Benchmarking}\label{benchmark}

\subsection{Test data and settings} 

\subsection{Performance, comparison and discussion} 


%-------------------------------------------------------------------------
\section{Conclusion}\label{sec:conclusion4}

}