diff --git a/Latex/Insight.bib b/Latex/Insight.bib index d4b370a67244dea1ad05159d60855908a481de24..99c82a4a51d0fa26e534d8f8cee341b9d48d399e 100644 --- a/Latex/Insight.bib +++ b/Latex/Insight.bib @@ -4836,3 +4836,42 @@ NUMBER=6, PAGES="764--773", YEAR=1988, } + +@ARTICLE{hu, +AUTHOR="M~-~K. Hu", +TITLE="{Visual Pattern Recognition by moment invariants}", +JOURNAL="IEEE Transactions on Information Theory", +VOLUME=8, +number =2, +YEAR=1962, +PAGES="179--187", +} + +@ARTICLE{flusserinv, +AUTHOR = "Jan Flusser", +TITLE = "{On the independence of rotation moment invariants}", +JOURNAL = "Pattern Recognition", +VOLUME = 33, +YEAR = 2000, +PAGES = "1405--1410", +} + +@ARTICLE{Dudani, +AUTHOR="S.A. Dudani and K.J. Breeding and R.B. McGhee", +TITLE="{Aircraft identification by moments invariants}", +JOURNAL="IEEE Transanctions on Computers", +VOLUME=26, +YEAR=1977, +PAGES="39--45", +} + +@ARTICLE{flusser_2, +AUTHOR="J.Flusser and T. Suk", +TITLE="{A moment based approach to registration of image with affine geometric distortion}", +JOURNAL="IEEE Transactions Geoscience Remote Sensing", +VOLUME=32, +number = 2, +YEAR=1994, +PAGES="382--387", +} + diff --git a/SoftwareGuide/Examples/CMakeLists.txt b/SoftwareGuide/Examples/CMakeLists.txt index 4110ab6f0c90f6ff2202356b0456b0b26913866a..6850b84986961c6b4f0aa34cd97150caec5cfbb7 100644 --- a/SoftwareGuide/Examples/CMakeLists.txt +++ b/SoftwareGuide/Examples/CMakeLists.txt @@ -165,6 +165,7 @@ SET( OTB_EXAMPLES_SRCS ${OTB_SOURCE_DIR}/Examples/FeatureExtraction/AlignmentsExample.cxx ${OTB_SOURCE_DIR}/Examples/FeatureExtraction/TouziEdgeDetectorExample.cxx ${OTB_SOURCE_DIR}/Examples/FeatureExtraction/HarrisExample.cxx + ${OTB_SOURCE_DIR}/Examples/FeatureExtraction/ComplexMomentImageExample.cxx ) diff --git a/SoftwareGuide/Latex/FeatureExtraction.tex b/SoftwareGuide/Latex/FeatureExtraction.tex index 282ced23c94c2f5b9ddcb99cbe14d864f4101c1c..8b78b57e28bf5db6bc566ee39cdd7d2b2047f52d 100644 --- a/SoftwareGuide/Latex/FeatureExtraction.tex +++ b/SoftwareGuide/Latex/FeatureExtraction.tex @@ -9,3 +9,57 @@ What is feature extraction \subsection{Alignments} \input{AlignmentsExample} \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: +\begin {equation} +c_{pq} = \int\limits_{-\infty}^{+\infty}\int\limits_{-\infty}^{+\infty}(x + iy)^p(x- iy)^qf(x,y)dxdy, +\label{2.2} +\end{equation} +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 +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 : + +\begin{equation} +\begin{array}{cccc} +\phi_1 = c_{11};& \phi_2 = c_{20}c_{02};& \phi_3 = c_{30}c_{03};& \phi_4 = c_{21}c_{12};\\ +\phi_5 = Re(c_{30}c_{12}^3);& \phi_6 = Re(c_{21}c_{12}^2);& \phi_7 = Im(c_{30}c_{12}^3).&\\ +\end{array} +\end{equation} + + +\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 +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 +rotation. They have the following expressions: +\begin {equation} +\begin{array}{ccc} +\psi_1 = c_{11} = \phi_1; & \psi_2 = c_{21}c_{12} = \phi_4; & \psi_3 = Re(c_{20}c_{12}^2) = \phi_6;\\ +\psi_4 = Im(c_{20}c_{12}^2); & \psi_5 = Re(c_{30}c_{12}^3) = \phi_5; +& \psi_6 = Im(c_{30}c_{12}^3) = \phi_7.\\ +\psi_7 = c_{22}; & \psi_8 = Re(c_{31}c_{12}^2); & \psi_9 = Im(c_{31}c_{12}~2);\\ +\psi_{10} = Re(c_{40}c_{12}^4); & \psi_{11} = Im(c_{40}c_{12}^2). &\\ + +\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} + +