WlzRegistration

Files
file	WlzAutoCor.c
	Functions to compute the autocorrelation of an object.
file	WlzPrinicipalAngle.c
	Calculates the angle which the long principal axis makes with the given object. The functions are based on a combination of methods by Rees and Hibbard. (D.W.A. Rees, Mechanics of Solids and Structures).
file	WlzRegCCor.c
	Functions to register two objects using frequency domain cross correlation.

Data Structures
struct	_WlzFeatureVector
	Finite element warping feature vector. Typedef: WlzFeatureVector. More...
struct	_WlzFeatValueLine
	A line of finite element warping feature vectors. Typedef: WlzFeatValueLine. More...
struct	_WlzFeatValues
	A ragged rectangular feature value table. Typedef: WlzFeatValues. More...
struct	_WlzRectFeatValues
	A rectangular feature value table. Typedef: WlzRectFeatValues. More...
struct	_WlzFMatchPoint
	Finite element warping feature match point. Typedef: WlzFMatchPoint. More...
struct	_WlzFMatchObj
	A finite element warping feature match, interesting points object. Typedef: WlzFMatchObj. More...
struct	_Wlz3DWarpTrans
	A plane-wise 3D finite element warping transform. Typedef: Wlz3DWarpTrans. More...

Enumerations
enum	_WlzMatchType {   WLZ_DISCARD_POINT = -1,   WLZ_NODE_ATTACH = 0,   WLZ_ELEMENT_ATTACH = 1 }
	Finite element warping match types. Typedef: WlzMatchType. More...

Functions
WlzObject *	WlzAutoCor (WlzObject *gObj, WlzErrorNum *dstErr)
	Computes the autocorrelation of the given object. The autocorrelation object will have double values, an origin of (0,0) and a column and line sizes which are the integer power of two greater than or equal to those of the given object. See AlgAutoCorrelate2D() for the organisation of the autocorrelation data. More...
double	WlzPrincipalAngle (WlzObject *srcObj, WlzDVertex2 cMass, int binObjFlag, WlzErrorNum *dstErrNum)
	Calculates the angle which the long principal axis makes with the x-axis in the given object. \[ \theta = \frac{1}{2} \arctan{(2 \frac{I_{xy}}{I_{yy}-I_{xx}})} \] where \[ I_{xx} = \sum_y \sum_x ((y - C_y) (y - C_y) G(x, y)) \] \[ I_{yy} = \sum_y \sum_x ((x - C_x) (x - C_x) G(x, y)) \] \[ I_{xy} = - \sum_y \sum_x (((x - C x) (y - C_y) G(x, y)) \] and \((C_x, C_y)\) are the coordinates of the centre of mass. More...
WlzAffineTransform *	WlzRegCCorObjs (WlzObject *tObj, WlzObject *sObj, WlzAffineTransform *initTr, WlzTransformType trType, WlzDVertex2 maxTran, double maxRot, int maxItr, WlzWindowFnType winFn, int noise, int inv, int *dstConv, double *dstCCor, WlzErrorNum *dstErr)
	Registers the two given objects using a frequency domain cross correlation. More...

Detailed Description

Enumeration Type Documentation

enum _WlzMatchType

Finite element warping match types. Typedef: WlzMatchType.

Enumerator
WLZ_DISCARD_POINT
WLZ_NODE_ATTACH
WLZ_ELEMENT_ATTACH

Function Documentation

WlzObject* WlzAutoCor	(	WlzObject *	gObj,
		WlzErrorNum *	dstErr
	)

Computes the autocorrelation of the given object. The autocorrelation object will have double values, an origin of (0,0) and a column and line sizes which are the integer power of two greater than or equal to those of the given object. See AlgAutoCorrelate2D() for the organisation of the autocorrelation data.

Returns

Autocorrelated object or NULL on error.

Parameters

gObj	Given object.
dstErr	Destination error pointer, may be NULL.

References Alc2Free(), ALC_ER_NONE, AlcDouble2Malloc(), AlgAutoCorrelate2D(), AlgBitNextPowerOfTwo(), _WlzValues::core, _WlzDomain::core, _WlzObject::domain, _WlzObject::type, _WlzObject::values, _WlzIVertex2::vtX, _WlzIVertex2::vtY, WLZ_2D_DOMAINOBJ, WLZ_ERR_DOMAIN_NULL, WLZ_ERR_MEM_ALLOC, WLZ_ERR_NONE, WLZ_ERR_OBJECT_NULL, WLZ_ERR_OBJECT_TYPE, WLZ_ERR_VALUES_NULL, WLZ_GREY_DOUBLE, WlzBoundingBox2I(), WlzFreeObj(), WlzFromArray2D(), WlzToArray2D(), _WlzIBox2::xMax, _WlzIBox2::xMin, _WlzIBox2::yMax, and _WlzIBox2::yMin.

Referenced by WlzRegCCorObjs().

double WlzPrincipalAngle	(	WlzObject *	srcObj,
		WlzDVertex2	cMass,
		int	binObjFlag,
		WlzErrorNum *	dstErrNum
	)

Calculates the angle which the long principal axis makes with the x-axis in the given object.

\[ \theta = \frac{1}{2} \arctan{(2 \frac{I_{xy}}{I_{yy}-I_{xx}})} \]

where

\[ I_{xx} = \sum_y \sum_x ((y - C_y) (y - C_y) G(x, y)) \]

\[ I_{yy} = \sum_y \sum_x ((x - C_x) (x - C_x) G(x, y)) \]

\[ I_{xy} = - \sum_y \sum_x (((x - C x) (y - C_y) G(x, y)) \]

and \((C_x, C_y)\) are the coordinates of the centre of mass.

Returns

Angle in radians.

Parameters

srcObj	Given object.
cMass	Center of mass of given object.
binObjFlag	Given object is binary if non zero.
dstErrNum	Destination pointer for error number, may be NULL if not required.

References _WlzValues::core, _WlzDomain::core, _WlzGreyP::dbp, _WlzObject::domain, _WlzGreyP::flp, _WlzGreyP::inp, _WlzIntervalWSpace::lftpos, _WlzIntervalWSpace::linpos, _WlzGreyWSpace::pixeltype, _WlzGreyP::rgbp, _WlzIntervalWSpace::rgtpos, _WlzGreyP::shp, _WlzObject::type, _WlzCoreDomain::type, _WlzCoreValues::type, _WlzGreyWSpace::u_grintptr, _WlzGreyP::ubp, _WlzObject::values, _WlzIVertex2::vtX, _WlzDVertex2::vtX, _WlzIVertex2::vtY, _WlzDVertex2::vtY, WLZ_2D_DOMAINOBJ, WLZ_ABS, WLZ_DBG, WLZ_DBG_LVL_1, WLZ_DBG_LVL_FN, WLZ_EMPTY_OBJ, WLZ_ERR_DOMAIN_NULL, WLZ_ERR_DOMAIN_TYPE, WLZ_ERR_EOO, WLZ_ERR_GREY_TYPE, WLZ_ERR_NONE, WLZ_ERR_OBJECT_NULL, WLZ_ERR_OBJECT_TYPE, WLZ_GREY_DOUBLE, WLZ_GREY_FLOAT, WLZ_GREY_INT, WLZ_GREY_RGBA, WLZ_GREY_SHORT, WLZ_GREY_UBYTE, WLZ_INTERVALDOMAIN_INTVL, WLZ_INTERVALDOMAIN_RECT, WLZ_M_PI_2, WLZ_RASTERDIR_ILIC, WLZ_RGBA_MODULUS, WlzEndGreyScan(), WlzInitGreyScan(), WlzInitRasterScan(), WlzNextGreyInterval(), and WlzNextInterval().

WlzAffineTransform* WlzRegCCorObjs	(	WlzObject *	tObj,
		WlzObject *	sObj,
		WlzAffineTransform *	initTr,
		WlzTransformType	trType,
		WlzDVertex2	maxTran,
		double	maxRot,
		int	maxItr,
		WlzWindowFnType	winFn,
		int	noise,
		int	inv,
		int *	dstConv,
		double *	dstCCor,
		WlzErrorNum *	dstErr
	)

Registers the two given objects using a frequency domain cross correlation.

Returns

Affine transform which brings the two objects into register.

    Registers the two given objects using a frequency domain
          cross correlation.  An affine transform is computed,
          which when applied to the source object takes it into
    register with the target object.
    Because frequency domain cross correlation (which relies on
    the FFT) is used the objects are padded out to arrays which
    are an integer power of two in size. This padding introduces
    significant influence of the objects boundaries and in many
    cases the registration will be dominated by the boundaries.
    To avoid the boundary problem, two methods are available -
    using a window function and adding Gaussian noise.
    The window functions apply a weight to objects values
    which is high at the objects centre of mass and decays
    towards the object boundary. Gaussian noise is added by
    placing the object on an array filled with with random
    values that have the same mean and varience as the object's
    values.

    The objects are assumed to have high foreground values and
    low background values. If this is no the case the invert
    grey values parameter should be set.

Parameters

tObj	The target object.
sObj	The source object to be registered with target object.
initTr	Initial affine transform to be applied to the source object prior to registration. May be NULL.
trType	Required transform type.
maxTran	Maximum translation.
maxRot	Maximum rotation.
maxItr	Maximum number of iterations, if \(\leq\) 0 then infinite iterations are allowed.
winFn	The window function to use.
noise	Use Gaussian noise if non-zero.
dstConv	Destination ptr for the convergence flag (non zero on convergence), may be NULL.
inv	Invert values of both objects if non-zero.
dstCCor	Destination ptr for the cross correlation value, may be NULL.
dstErr	Destination error pointer, may be NULL.

References AlcCalloc(), AlcDouble2Free(), AlcFree(), AlcMalloc(), AlgBitNextPowerOfTwo(), AlgCrossCorrelate2D(), AlgCrossCorrPeakXY(), _WlzValues::core, _WlzDomain::core, _WlzGreyV::dbv, _WlzObject::domain, _WlzGreyV::inv, _WlzAffineTransformPrim::theta, _WlzAffineTransformPrim::tx, _WlzAffineTransformPrim::ty, _WlzPixelV::type, _WlzObject::type, _WlzGreyV::ubv, _WlzPixelV::v, _WlzObject::values, _WlzIVertex2::vtX, _WlzDVertex2::vtX, _WlzIVertex3::vtX, _WlzIVertex2::vtY, _WlzDVertex2::vtY, _WlzIVertex3::vtY, WLZ_2D_DOMAINOBJ, WLZ_ERR_DOMAIN_NULL, WLZ_ERR_MEM_ALLOC, WLZ_ERR_NONE, WLZ_ERR_OBJECT_NULL, WLZ_ERR_OBJECT_TYPE, WLZ_ERR_VALUES_NULL, WLZ_GREY_DOUBLE, WLZ_GREY_INT, WLZ_GREY_UBYTE, WLZ_INTERPOLATION_NEAREST, WLZ_M_PI, WLZ_MAX, WLZ_MIN, WLZ_NINT, WLZ_SAMPLEFN_GAUSS, WLZ_TRANSFORM_2D_AFFINE, WLZ_TRANSFORM_2D_TRANS, WLZ_WINDOWFN_NONE, WlzAffineTransformFromPrimVal(), WlzAffineTransformIsIdentity(), WlzAffineTransformObj(), WlzAffineTransformPrimGet(), WlzAffineTransformProduct(), WlzArrayStats2D(), WlzAssignObject(), WlzAutoCor(), WlzBoundingBox2I(), WlzCopyObject(), WlzFreeAffineTransform(), WlzFreeObj(), WlzFromArray2D(), WlzGreySetRange(), WlzGreyStats(), WlzPolarSample(), WlzSampleObj(), WlzSetBackground(), WlzToArray2D(), WlzValueConvertPixel(), WlzWindow(), WlzWriteObj(), _WlzIBox2::xMax, _WlzIBox2::xMin, _WlzIBox2::yMax, and _WlzIBox2::yMin.