diff --git a/SoftwareGuide/Latex/FeatureExtraction.tex b/SoftwareGuide/Latex/FeatureExtraction.tex index eee4091bb12abdba20af183c6c190fba30bfc11c..f4bbcdd6aca8ba46f03d090dd8331842c2d7cb98 100644 --- a/SoftwareGuide/Latex/FeatureExtraction.tex +++ b/SoftwareGuide/Latex/FeatureExtraction.tex @@ -12,10 +12,9 @@ What is feature extraction \subsection{Lines} \subsection{Geometric Moments} -Using the algebraic moment theory, H. Ming-Kuel obtained a family of 7 -invariants with respect to planar transformations called Hu invariants, -\cite{hu}. Those invariants can be seen as nonlinear combinations of -complex geometric moments: +\subsubsection{Complex Moments} +\label{sec:ComplexMoments} +The complex geometric moments are defined as: \begin {equation} c_{pq} = \int\limits_{-\infty}^{+\infty}\int\limits_{-\infty}^{+\infty}(x + iy)^p(x- iy)^qf(x,y)dxdy, \label{2.2} @@ -23,7 +22,18 @@ c_{pq} = \int\limits_{-\infty}^{+\infty}\int\limits_{-\infty}^{+\infty}(x + iy)^ where $x$ and $y$ are the coordinates of the image $f(x,y)$, $i$ is the imaginary unit and $p+q$ is the order of $c_{pq}$. The geometric moments are -particularly useful in the case of scale changes. Hu invariants have +particularly useful in the case of scale changes. + +\input{ComplexMomentImageExample} +\textbf{Example with paths} +%\input{ComplexMomentPathExample} + +\subsubsection{Hu Moments} +\label{sec:HuMoments} +Using the algebraic moment theory, H. Ming-Kuel obtained a family of 7 +invariants with respect to planar transformations called Hu invariants, +\cite{hu}. Those invariants can be seen as nonlinear combinations of +the complex moments. Hu invariants have been very much used in object recognition during the last 30 years, since they are invariant to rotation, scaling and translation. \cite{flusserinv} gives their expressions : @@ -37,7 +47,16 @@ since they are invariant to rotation, scaling and translation. \cite{flusserinv} \cite{dudani} have used these invariants for the recognition of aircraft silhouettes. Flusser and Suk have used them for image -registration, \cite{flusser_2}. They have been modified and +registration, \cite{flusser_2}. + +\textbf{Examples} +%\input{HuMomentImageExample} +%\input{HuMomentPathExample} + + +\subsubsection{Flusser Moments} +\label{sec:FlusserMoments} +The Hu invariants have been modified and improved by several authors. Flusser used these moments in order to produce a new family of descriptors of order higher than 3, \cite{flusserinv}. These descriptors are invariant to scale and @@ -53,14 +72,8 @@ rotation. They have the following expressions: \end{array} \end {equation} -OTB allows the computation of complex moments and Flusser and Hu -moments, and those can be computed on images and paths. - -\textbf{Mettra a jour quand la classe sera corrigee} -\input{ComplexMomentImageExample} -%% \input{ComplexMomentFunctionExample} - -%% \input{FlusserMomentImageExample} -%% \input{FlusserMomentFunctionExample} +\textbf{Examples} +%\input{FlusserMomentImageExample} +%\input{FlusserMomentPathExample}