DataRepresentation.tex

\chapter{Data Representation}
\label{sec:DataRepresentation}

This chapter introduces the basic classes responsible
for representing data in ITK. The most common classes are
\doxygen{Image}, \doxygen{Mesh} and \doxygen{PointSet}.

\section{Image}
\label{sec:ImageSection}

The \doxygen{Image} class follows the spirit of
\href{https://www.boost.org/more/generic_programming.html}{Generic Programming},
where types are separated from the algorithmic behavior of the class.
ITK supports images with any pixel type and any spatial dimension.

\subsection{Creating an Image}\label{sec:CreatingAnImageSection}

\input{Image1.tex}

In practice it is rare to allocate and initialize an image directly.
Images are typically read from a source, such a file or data acquisition
hardware. The following example illustrates how an image can be read from
a file.


\subsection{Reading an Image from a File}
\label{sec:ReadingImageFromFile}

\input{Image2.tex}


\subsection{Accessing Pixel Data}
\label{sec:AccessingImagePixelData}

\input{Image3.tex}


\subsection{Defining Origin and Spacing}
\label{sec:DefiningImageOriginAndSpacing}

\input{Image4.tex}


\subsection{RGB Images}

The term RGB (Red, Green, Blue) stands for a color representation commonly used
in digital imaging. RGB is a representation of the human physiological
capability to analyze visual light using three spectral-selective
sensors~\cite{Malacara2002,Wyszecki2000}. The human retina possess different
types of light sensitive cells. Three of them, known as \emph{cones}, are
sensitive to color~\cite{Gray2003} and their regions of sensitivity loosely
match regions of the spectrum that will be perceived as red, green and blue
respectively. The \emph{rods} on the other hand provide no color discrimination
and favor high resolution and high sensitivity.\footnote{The human eye is
capable of perceiving a single isolated photon.} A fifth type of receptors,
the \emph{ganglion cells}, also known as circadian\footnote{The term
\emph{Circadian} refers to the cycle of day and night, that is, events that are
repeated with 24 hours intervals.} receptors are sensitive to the lighting
conditions that differentiate day from night. These receptors evolved as a
mechanism for synchronizing the physiology with the time of the day. Cellular
controls for circadian rythms are present in every cell of an organism and are
known to be exquisitively precise~\cite{Lodish2000}.

The RGB space has been constructed as a representation of a physiological
response to light by the three types of \emph{cones} in the human eye. RGB is
not a Vector space. For example, negative numbers are not appropriate in a
color space because they will be the equivalent of ``negative stimulation'' on
the human eye. In the context of colorimetry, negative color values are used
as an artificial construct for color comparison in the sense that

\begin{equation}
\label{eqn:ColorSubtraction}
         ColorA = ColorB - ColorC
\end{equation}

is just a way of saying that we can produce $ColorB$ by combining $ColorA$ and
$ColorC$. However, we must be aware that (at least in emitted light) it is not
possible to \emph{subtract light}. So when we mention
Equation~\ref{eqn:ColorSubtraction} we actually mean

\begin{equation}
\label{eqn:ColorAddition}
         ColorB = ColorA + ColorC
\end{equation}

On the other hand, when dealing with printed color and with paint, as opposed
to emitted light like in computer screens, the physical behavior of color
allows for subtraction. This is because strictly speaking the objects that we
see as red are those that absorb all light frequencies except those in the red
section of the spectrum~\cite{Wyszecki2000}.

The concept of addition and subtraction of colors has to be carefully
interpreted. In fact, RGB has a different definition regarding whether we are
talking about the channels associated to the three color sensors of the human
eye, or to the three phosphors found in most computer monitors or to the color
inks that are used for printing reproduction. Color spaces are usually non
linear and do not even from a group. For example, not all visible colors can be
represented in RGB space~\cite{Wyszecki2000}.

ITK introduces the \doxygen{RGBPixel} type as a support for representing the
values of an RGB color space. As such, the \code{RGBPixel} class embodies a different
concept from the one of an \doxygen{Vector} in space. For this reason, the
RGBPixel lacks many of the operators that may be naively expected from it. In
particular, there are no defined operations for subtraction or addition.

When you intend to find the ``Mean'' of two RGBType pixels, you are assuming that
the color in the visual ``middle'' of the two input pixels can be calculated through
a linear operation on their numerical representation. This is unfortunately not the
case in  color spaces due to the fact that they are based on a human physiological
response~\cite{Malacara2002}.

If you decide to interpret RGB images as simply three independent channels then
you should rather use the \doxygen{Vector} type as pixel type. In this way, you
will have access to the set of operations that are defined in Vector spaces.
The current implementation of the RGBPixel in ITK presumes that RGB color
images are intended to be used in applications where a formal interpretation of
color is desired, therefore only the operations that are valid in a color space
are available in the RGBPixel class.

The following example illustrates how RGB images can be represented in ITK.

\label{sec:DefiningRGBImages}
\input{RGBImage.tex}


\subsection{Vector Images}
\label{sec:DefiningVectorImages}

\input{VectorImage.tex}


\subsection{Importing Image Data from a Buffer}
\label{sec:ImportingImageDataFromABuffer}
\input{Image5.tex}


\section{PointSet}
\label{PointSetSection}

\subsection{Creating a PointSet}
\label{sec:CreatingAPointSet}

\input{PointSet1.tex}


\subsection{Getting Access to Points}
\label{sec:GettingAccessToPointsInThePointSet}

\input{PointSet2.tex}


\subsection{Getting Access to Data in Points}
\label{sec:GettingAccessToDataInThePointSet}

\input{PointSet3.tex}


\subsection{RGB as Pixel Type}
\label{sec:PointSetWithRGBAsPixelType}

\input{RGBPointSet.tex}


\subsection{Vectors as Pixel Type}
\label{sec:PointSetWithVectorsAsPixelType}

\input{PointSetWithVectors.tex}


\subsection{Normals as Pixel Type}
\label{sec:PointSetWithCovariantVectorsAsPixelType}

\input{PointSetWithCovariantVectors.tex}


\section{Mesh}\label{MeshSection}

\subsection{Creating a Mesh}
\label{sec:CreatingAMesh}

\input{Mesh1.tex}


\subsection{Inserting Cells}
\label{sec:InsertingCellsInMesh}

\input{Mesh2.tex}


\subsection{Managing Data in Cells}
\label{sec:ManagingCellDataInMesh}

\input{Mesh3.tex}


\subsection{Customizing the Mesh}
\label{sec:CustomizingTheMesh}

\input{MeshTraits.tex}


\subsection{Topology and the K-Complex}
\label{sec:MeshKComplex}

\input{MeshKComplex.tex}


\subsection{Representing a PolyLine}
\label{sec:MeshPolyLine}

\input{MeshPolyLine.tex}


\subsection{Simplifying Mesh Creation}
\label{sec:AutomaticMesh}

\input{AutomaticMesh.tex}


\subsection{Iterating Through Cells}
\label{sec:MeshCellsIteration}

\input{MeshCellsIteration.tex}


\subsection{Visiting Cells}
\label{sec:MeshCellVisitor}

\input{MeshCellVisitor.tex}


\subsection{More on Visiting Cells}
\label{sec:MeshCellVisitorMultipleType}

\input{MeshCellVisitor2.tex}


\section{Path}\label{PathSection}

\subsection{Creating a PolyLineParametricPath}
\label{sec:CreatingAPolyLineParametricPath}

\input{PolyLineParametricPath1.tex}