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%     http://www.itk.org/

\documentclass{InsightArticle}


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\usepackage[dvips,
bookmarks,
bookmarksopen,
backref,
colorlinks,linkcolor={blue},citecolor={blue},urlcolor={blue},
]{hyperref}
% to be able to use options in graphics
\usepackage{graphicx}
% for pseudo code
\usepackage{listings}
% subfigures
\usepackage{subfigure}


%  This is a template for Papers to the Insight Journal. 
%  It is comparable to a technical report format.

% The title should be descriptive enough for people to be able to find
% the relevant document. 
\title{Grayscale morphological attribute operations}

% Increment the release number whenever significant changes are made.
% The author and/or editor can define 'significant' however they like.
\release{0.00}

% At minimum, give your name and an email address.  You can include a
% snail-mail address if you like.
\author{Richard Beare}
\authoraddress{Richard.Beare@med.monash.edu.au\\Department of Medicine\\Monash University\\Melbourne\\Australia}

\begin{document}
\maketitle

\ifhtml
\chapter*{Front Matter\label{front}}
\fi


\begin{abstract}
\noindent
% The abstract should be a paragraph or two long, and describe the
% scope of the document.
Morphological area attribute openings and closings\cite{Cheng92,Vincent93a} are connected set
operations that are able to remove parts of an image that meet certain
criteria without changing the rest of the image. This article describes a number of
classes that implement morphological area attribute operations using
the methods described by Meijster and Wilkinson \cite{meijster02}.
\end{abstract}

\tableofcontents


% \url{http://www.itk.org}
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% \section{Principles of Solar Spot Detection}
% \cite{ITKSoftwareGuide}.
% \doxygen{ImageToImageFilter}

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% The {itemize} environment uses a bullet for each \item.  If you want the 
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%   \item  Insight Toolkit 2.4.
%   \item  CMake 2.2
% \end{itemize}

% \ref{cthead1}
\section{Introduction}
A morphological attribute opening is probably best described by
considering application to a binary image, in which case all blobs
(aka connected components) with attributes meeting specific criteria
will be removed and all others retained. The most common and useful
criteria is the number of voxels (i.e. area or volume) - an opening by
area attributes with a threshold of 20 will remove all blobs
containing fewer than 20 voxels. This operation can be implemented
using connected component labelling approaches for binary
images. Alternative attribute measures are possible, including
perimeter and minimum enclosing rectangle\cite{Breen96}. Some of these
attributes are not increasing so the resulting operations aren't
strictly openings, but are idempotent.  There simplest way of
extending this concept to gray scale images is to generate a series of
binary images by thresholding at each distinct gray level. The binary
image created by thresholding at gray level $j$ will be a subset of
the image formed by thresholding at level $j-1$. The binary area
opening described above can then be applied independently to each
binary image and the output grayscale image computed as a union of the
results.  An alternative description is to treat each peak
independently. If the peak is smaller than the threshold area then
form a region by collecting the all voxels with the next highest grey
level that are connected to the peak. Repeat this process until the
area exceeds the threshold. Set all pixels in the resulting region to
the grey level of the most recently connected pixels. The algorithm
described in \cite{meijster02} is an efficient way of doing this.

The most recent version of this package can be obtained from
\url{http://voxel.jouy.inra.fr/darcsweb/}\footnote{The most recent
versions can be obtained using darcs \cite{DarcsWebSite} with the
command {\em darcs get
http://voxel.jouy.inra.fr/\\darcs/contrib-itk/attributeMorphology}},


\section{Comparison of area attribute and traditional openings}
The operation of traditional openings is based on the shape of a
structuring element, with any feature where the structuring element
doesn't ``fit'' being removed. Area attributes, on the other hand, are
independent of shape and therefore can perform better in some
circumstances. For example, an area attribute opening could retain
long, linear structures and reject a range of compact
objects. Connected set operations, such as area attribute openings,
are dependent on connectivity. This can lead to undesirable results --
e.g. a blob touching a linear structure would be retained in the
previous example. In addition, breaks in connectivity could lead to
parts of a linear structure being removed
unexpectedly\footnote{Unexpected in the sense that a person probably
wouldn't notice such breaks}. The ability to remove some parts of an
image while leaving the rest unchanged in especially useful in top hat
filters.

\subsection{Examples}
\begin{figure}[htbp]
\begin{center}
\subfigure[50 pixel opening]{\includegraphics[scale=0.7]{opening-50-1}}
\subfigure[100 pixel opening]{\includegraphics[scale=0.7]{opening-100-1}}
\subfigure[200 pixel opening]{\includegraphics[scale=0.7]{opening-200-1}}
\subfigure[1000 pixel opening]{\includegraphics[scale=0.7]{opening-1000-1}}
\caption{A series of area openings applied to the cthead image\label{fig:ctheadopening}}
\end{center}
\end{figure}
\begin{figure}[htbp]
\begin{center}
\subfigure[50 pixel closing]{\includegraphics[scale=0.7]{closing-50-1}}
\subfigure[100 pixel closing]{\includegraphics[scale=0.7]{closing-100-1}}
\subfigure[200 pixel closing]{\includegraphics[scale=0.7]{closing-200-1}}
\subfigure[1000 pixel closing]{\includegraphics[scale=0.7]{closing-1000-1}}
\caption{A series of area closings applied to the cthead image\label{fig:ctheadclosing}}
\end{center}
\end{figure}

Figures \ref{fig:ctheadopening} and \ref{fig:ctheadclosing} illustrate
a series of progressively larger area openings and closings applied to
the cthead image. In Figure \ref{fig:ctheadopening} progressively
larger bright regions are removed from the image while progressively
larger dark regions are removed in Figure \ref{fig:ctheadclosing}. In
both cases the rest of the image is left unchanged. It is especially
important to note that contours are preserved.

If the peaks being removed were actually of interest then a top hat
filter would be appropriate. The white top hat filter is the
difference between the original image and the opened version, while
the black top hat filter is the difference between the closed version
of the image and the original -- see Figure \ref{fig:ctheadtophat}.
\begin{figure}[htbp]
\begin{center}
\subfigure[White top hat of cthead1]{\includegraphics[scale=0.7]{wth}}
\subfigure[Black top hat of cthead1]{\includegraphics[scale=0.7]{bth}}
\caption{White and black top hat filter results with area attribute of 50.\label{fig:ctheadtophat}}
\end{center}
\end{figure}

\section{Filter documentation}
The filters described here implement the area attribute opening or
closing using the method described by Meijster and Wilkinson
\cite{meijster02}. The base class is {\em
itkAttributeMorphologyBaseImageFilter}. There are two sets of
subclasses -- {\em itkAreaOpeningImageFilter} and {\em
itkAreaClosingImageFilter} and {\em itkPhysicalSizeOpeningImageFilter}
and {\em itkPhysicalSizeClosingImageFilter}. The first two filters
compute area/volume operations using units of voxel counts while the
last two use physical units.

These classes are templated on input and output image type and are
controlled by two methods:
\begin{itemize}
\item {\bf [Set/Get]FullyConnected} : define whether the neighborhood used to define a region is fully or face connected.
\item {\bf [Set/Get]Lambda} : set the area attribute.
\end{itemize}


\appendix



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\nocite{ITKSoftwareGuide}

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