gsnake.tex

图像中非刚性曲线的蛇形检测算法

\rhead{Object class GSNAKE}

\section{GSNAKE : Generalized Active Contour Model} 
{\tt GSNAKE} is a class for modeling and extracting arbitrary deformable contours. It consists of {\tt PYRAMID} for external energy calculation and {\tt CONTOUR} class for internal energy calculation. {\tt GSNAKE} has the following structure :

\begin{verbatim}
class GSNAKE : public PYRAMID,
               public CONTOUR {

     protected :
        double global_lambda;   /* global regularization parameters */	
        double Eint;            /* Total internal energy of snake */
        double Eext;            /* Total external energy of snake */
        double Esnake;          /* Total snake energy */
        EEXTTYPE EextType;      /* external energy type */
        EDGE *EdgeMap;          /* edge map in current pyramid level */
        IMAGE *GaussImg;        /* gaussImg in current pyramid level */
};
\end{verbatim}

We initialize GSNAKE using generalized Hough transform (section 3.3 of \cite{kn:thesis}) and minimize its energy using dynamic programming with stratified line search (section 3.4 of\cite{kn:thesis}). The internal energy, {\tt Eint}, measures deviation in shape irregularities, while the external energy, {\tt Eext}, adjust the contour model to match the underlying image feature. Based on parameter selection strategy (section\ 2.2 of \cite{kn:thesis}), {\tt glabal\_lambda}, we regularize the tradeoff between {\tt Eint} and {\tt Eext}, and compute the total energy, {\tt Esnake}. Our implementation allows user to select minimax criterion ({\tt \_LOCAL\_MINMAX}), local regularization parameter ({\tt \_LOCAL\_LAMBDA}) or global lambda parameter selection strategy (within the range of 0.0 to 1.0). {\tt EextType} is the type of external energy used, which includes edge gradient ({\tt \_EDGE}), edge magnitude ({\tt \_EDGEMAG}) and image intensity ({\tt \_INTENSITY}).

%
\subsection{GSNAKE constructor}

\subsubsection*{Synopsis}
\begin{verbatim}
	GSNAKE(EextTYPE etype = _EDGE, double glambda = _LOCAL_MINMAX)
\end{verbatim}

\subsubsection*{Arguments}
\tb
	{\tt etype} & External energy type, includes intensity
		      (\_INTENSITY), edge \\
		    & magnitude only (\_EDGEMAG) and edge gradient (\_EDGE)
		      image energy.\\
	{\tt glambda} & Regularization parameter selection strategy, includes
			minmax criterion \\
		      & (\_LOCAL\_MINMAX) and  local regularization (\_LOCAL\_LAMBDA).
\te

\subsubsection*{Description}
The constructor selects {\em minimax} criterion as its parameter selection strategy, and uses edge gradient as its external energy type if user does not specify explicitly.


%
\subsection{GSNAKE destructor}

\subsubsection*{Synopsis}
\begin{verbatim}
	~GSNAKE(void)
\end{verbatim}

\subsubsection*{Description}
The destructor initializes {\tt EdgeMap} and {\tt GaussImg} to NULL.

%
\subsection{GSNAKE destructor}

\subsubsection*{Synopsis}
\begin{verbatim}
	void reset(void)
\end{verbatim}

\subsubsection*{Description}
{\tt reset} initializes {\tt EdgeMap} and {\tt GaussImg} to NULL

%
\subsection{Generating pyramid images}

\subsubsection*{Synopsis}
\begin{verbatim}
	int genPyramid(short level, short verbose)
\end{verbatim}

\subsubsection*{Arguments}
\tb
	{\tt level} & Levels of pyramid to be generated. \\
	{\tt verbose} & Verbose operation mode.
\te

\subsubsection*{Returns}
\tb
	{\tt NOERROR} & Successful Operation.\\
	{\tt MEMORYERROR} & Memory allocation error. 
\te

\subsubsection*{Description}
{\tt genPyramid} generate {\tt PYRAMID} object based on {\tt EextType} specified. To increase robustness, we use histogram equalization parameters ($high\_pct=1.0$, $low\_pct=1.0$, $ high\_val=1.0$, $low\_val=1.0$) for external energy of type \_INTENSITY, and use default condition parameters ($high\_pct=0.95$, $low\_pct=0.9$, $ high\_val=0.9$, $low\_val=0.2$) for external energy of type \_EDGE and \_EDGEMAG.


%
\subsection{Localization of contour}

\subsubsection*{Synopsis}
\begin{verbatim}
int localize( int _Qx=1, int _Qy=1, 
              int _NR=1, double  _QR=0.25, 
              int _Nrxy=1, double _Qrxy=0.1,
              int _Nt=1,  double _Qt=RADIAN(10),
              int _Ndx=1, double _Qdx=0.1,
              int _Ndy=1, double _Qdy=0.1,
              double _R=1.0, double _THETA=0.0 )
\end{verbatim}

\subsubsection*{Arguments}
\tb
	{\tt \_Qx, \_Qx}  &  X and Y resolution of {\tt GHOUGH} accumulator
			   space.\\
	{\tt \_NR} & Number of cells in scale change axis.\\
	{\tt \_QR} & Resolution for scale change.\\
	{\tt \_Nrxy} & Number of cells in diagonal stretching change.\\
	{\tt \_Qrxy} & Resolution for diagonal stretching.\\
	{\tt \_Nt}   & Number of cells in rotation axis.\\
	{\tt \_Qt}  & Resolution of rotation (in radian).\\
	{\tt \_Ndx, \_Ndy} & Number of cell in X and Y of dilution axis.\\
	{\tt \_Qdx, \_Qdy} & X and Y resolution of dilution.\\
	{\tt \_R} & Scaling factor.\\
	{\tt \_THETA} & Initial angle for reference line gsnake.
\te

\subsubsection*{Returns} 
\tb
	{\tt NOERROR} & Localisation performed successfully. \\
	{\tt MEMORYERROR} & Unable to allocate memory for GHOUGH objects.
\te

\subsubsection*{Description}
Based on resolution and allowable range of transformation specified by users, {\tt localize} performs rigid match of a contour with the underlying image by generalized Hough transform (GHT). If Gaussian image and edge map do not exist, it will generate level 1 {\tt PYRAMID}. Localization will only be performed at highest level of pyramid so as to reduce computational time. To increase accuracy, it activates {\tt fineLocalize} if {\tt \_Qx} or {\tt \_Qy} is greater than 1.


%
\subsection{Fine localization of GSNAKE template}

\subsubsection*{Synopsis}
\begin{verbatim}
	void fineLocalize( int _qx = 1, int _qy = 1, 
			   int _cg_col = 0, int _cg_row = 0 );
\end{verbatim}

\subsubsection*{Arguments}
\tb
	{\tt \_qx, \_qy} & X and Y resolution of translation. \\
	{\tt \_cg\_col, \_cg\_row} & Coordinate of center of gravity.
\te

\subsubsection*{Description}
{\tt fineLocalize} moves the localized contour in a small area of {\tt \_qx} x {\tt \_qy}. It calculates external energy during each move and then relocates the contour at place of lowest energy. To increase efficiency, user can also place contour at location with center ({\tt \_cg\_col, \_cg\_row}) before moving. This is useful when the contour can be in a fixed and small locality.


%
\subsection{Minimization of GSNAKE}

\subsubsection*{Synopsis}
\begin{verbatim}
int minimize( int segmentSpacing = 5, int numSearchSegment = 5,
              int snaxelSpacing  = 5, unsigned char blowup = 1,
              int verbose = 0, double theLambda = _DEFINED_LAMBDA,
              int showImg = 1,int img_Xoffset = 0, int img_Yoffset = 0 );
\end{verbatim}

\subsubsection*{Arguments}
\tb	
	{\tt segmentSpacing} & Coarse search spacing. \\
	{\tt numSearchSegment}  &  Number of searched segments around snaxel.\\
	{\tt snaxelSpacing} & Snaxel spacing. \\
	{\tt blowup} & Image magnification factor.\\
	{\tt verbose} & Verbose Flag. \\
	{\tt theLambda} & Lambda value. \\
	{\tt showImg} & Indication (0:off 1:on) of whether image is to be 
			shown. \\
	{\tt img\_Xoffset, img\_Yoffset} & Offset of a contour from
				 an showing image.
\te
	 
	 
\subsubsection*{Description}
Based on dynamic programming with stratified line search algorithm, {\tt minimize} performs coarse to fine energy minimization. As minimization progresses from the highest to lowest pyramid level, it inserts new snaxels at interval of {\tt snaxelSpacing} between two snaxels. The {\tt showImg}, {\tt img\_Xoffset} and {\tt img\_Yoffset} allow greater flexibility when applying minimization over a small region of image. In this case, we can cut image into portions and only perform minimization on portion of interest.


%
\subsection{Marginalizing gsnake to get probablity}
\begin{verbatim}
double marginalize(int nhoodTangent, int nhoodNormal)
\end{verbatim}

\subsubsection*{Arguments}
\tb
	{\tt nhoodTangent} & Number of searched segments along the tangent axis 
			     of snaxel.\\
	{\tt nhoodNormal} & Number of searched segments along the normal axis 
			    of snaxel.
\te

\subsubsection*{Returns} 
Probability of match.

\subsubsection*{Description}
{\tt marginalize} sums probablities and finds location that maximize probablity of matched contour operation. The summation is done in a small region of {\tt nhoodTangent} x {\tt nhoodNormal} around a contour.


%
\subsection{Calculating total energy of a gsnake}

\subsubsection*{Synopsis}
\begin{verbatim}
	double ESnake( short level, int verbose = 0 );
\end{verbatim}

\subsubsection*{Arguments}
\tb
	{\tt level} & Pyramid level of interest. \\
	{\tt verbose} & Flag (0:off 1:on) to operate verbose mode.
\te

\subsubsection*{Returns}
Total energy of {\tt GSNAKE}.

\subsubsection*{Description}
{\tt ESnake} compute the total energy of gsnake by regularizing the internal and external energy of each snaxel.


% 
\subsection{Calculating total energy of a snaxel}

\subsubsection*{Synopsis}
\begin{verbatim}
	double ESnaxel( SNAXEL *now,
		BOOLEAN store = _FALSE, int verbose = 0 ); 
\end{verbatim}

\subsubsection*{Arguments}
\tb
	{\tt *sxptr} & Pointer to target snaxel. \\
	{\tt store} & Flag to indicate whether to store snaxel energy. \\
	{\tt verbose} & Flag (0:off 1:on) to operate verbose mode.
\te

\subsubsection*{Returns}
Snaxel energy. Returns 1.0 if the snaxel coordinate is invalid.

\subsubsection*{Description}
{\tt Esnaxel} calculates the total energy of a snaxel by regularize its internal and external energy. 


%
\subsection{Calculating internal energy of a snaxel}

%
\subsection{Caluclating Internal energy at snaxel co-ordinates}
\begin{verbatim}
double EInternal(SNAXEL *now)
\end{verbatim}

\subsubsection*{Arguments}
\tb
	{\tt now} & Pointer to target snaxel. 
\te

\subsubsection*{Returns} 
Internal energy of a snaxel.

\subsubsection*{Description}
{\tt EInternal} computes the internal energy of a snaxel.


%
\subsection{Calculating external energy of a snaxel}

\subsubsection*{Synopsis}
\begin{verbatim}
  double EExternal(SNAXEL *now);
\end{verbatim}

\subsubsection*{Arguments}
\tb
	{\tt *now} & Pointer to the target snaxel. 
\te

\subsubsection*{Returns} 
External energy of a snaxel.

\subsubsection*{Description}
{\tt Eexternal} calculates the external energy of snaxel. If {\tt EextType} is {\tt \_INETNSITY}, it will return value $1-\mbox{intensity}$. If {\tt \_EDGEMAG}, it will return value $1-\mbox{edgeMag}$. Otherwise, it will consider both magnitude and direction of an edge point (Eqn 3.18 of \cite{kn:thesis}).

	
%	
\subsection{Showing GSNAKE}

\subsubsection*{Synopsis}
\begin{verbatim}
	void showLine( unsigned char blowup=1, int Xoffset=0, int Yoffset= 0)
\end{verbatim}		   

\subsubsection*{Arguments}
\tb
	{\tt blowup} & Image Magnification factor. \\
	{\tt Xoffset, Yoffset} & X and Y offset for image display.
\te

\subsubsection*{Description}