ThinPlateR2LogRSplineKernelTransform (Fiji Javadocs 0-SNAPSHOT API)

java.lang.Object
- jitk.spline.ThinPlateR2LogRSplineKernelTransform

All Implemented Interfaces:

Serializable
```
public class ThinPlateR2LogRSplineKernelTransform
extends Object
implements Serializable
```
Implements an n-dimensional thin plate spline transform. Began as a port of itk's itkKernelTransform.hxx
M. H. Davis, a Khotanzad, D. P. Flamig, and S. E. Harms, “A physics-based coordinate transformation for 3-D image matching.,” IEEE Trans. Med. Imaging, vol. 16, no. 3, pp. 317–28, Jun. 1997.

Author:

Kitware (ITK), John Bogovic

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`protected double[][]`	`aMatrix`
`protected double[]`	`bVector`
`protected boolean`	`computeAffine`
`protected org.ejml.data.DenseMatrix64F`	`dMatrix`
`protected static double`	`EPS`
`protected static org.apache.log4j.Logger`	`logger`
`protected int`	`ndims`
`protected int`	`nLandmarks`
`protected double[][]`	`sourceLandmarks`
`protected double`	`stiffness`
`protected double[]`	`tmpDisplacement`
`protected double[]`	`weights`
`protected boolean`	`wMatrixComputeD`

Constructor Summary

Constructors
Constructor and Description
`ThinPlateR2LogRSplineKernelTransform(double[][] srcPts, double[][] aMatrix, double[] bVector, double[] dMatrixData)` Constructor with transformation parameters.
`ThinPlateR2LogRSplineKernelTransform(int ndims)`
`ThinPlateR2LogRSplineKernelTransform(int ndims, double[][] srcPts, double[][] tgtPts)`
`ThinPlateR2LogRSplineKernelTransform(int ndims, double[][] srcPts, double[][] tgtPts, boolean computeAffine)`
`ThinPlateR2LogRSplineKernelTransform(int ndims, double[][] srcPts, double[][] tgtPts, double[] weights)` Constructor with weighted point matches
`ThinPlateR2LogRSplineKernelTransform(int ndims, float[][] srcPts, float[][] tgtPts)`
`ThinPlateR2LogRSplineKernelTransform(int ndims, float[][] srcPts, float[][] tgtPts, boolean computeAffine)`

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`double[]`	`apply(double[] pt)` Transforms the input point according to the thin plate spline stored by this object.
`void`	`apply(double[] pt, double[] result)`
`void`	`apply(double[] pt, double[] result, boolean debug)` Transform a source vector pt into a target vector result.
`void`	`applyInPlace(double[] pt)` Transform pt in place.
`org.ejml.data.DenseMatrix64F`	`buildDisplacements(double[][] targetLandmarks)`
`org.ejml.data.DenseMatrix64F`	`buildDisplacements(float[][] targetLandmarks)`
`jitk.spline.ThinPlateR2LogRSplineKernelTransform.IndexDistancePair`	`closestTargetLandmarkAndDistance(double[] target)` Returns the index of the target landmark closest to the input point as well as the distance to that landmark.
`void`	`computeDeformationContribution(double[] thispt, double[] result)`
`void`	`computeG(double[] pt, org.ejml.data.DenseMatrix64F mtx)`
`void`	`computeG(double[] pt, org.ejml.data.DenseMatrix64F mtx, double w)`
`protected void`	`computeK(org.ejml.data.DenseMatrix64F kMatrix)` Builds the K matrix from landmark points and G matrix.
`protected org.ejml.data.DenseMatrix64F`	`computeL(org.ejml.data.DenseMatrix64F kMatrix, org.ejml.data.DenseMatrix64F pMatrix)`
`protected void`	`computeP(org.ejml.data.DenseMatrix64F pMatrix)`
`protected org.ejml.data.DenseMatrix64F`	`computeReflexiveG()`
`protected void`	`computeW(org.ejml.data.DenseMatrix64F yMatrix)` The main workhorse method.
`double[][]`	`getAffine()`
`double[]`	`getKnotWeights()`
`int`	`getNumDims()`
`int`	`getNumLandmarks()`
`double[][]`	`getSourceLandmarks()`
`double[]`	`getTranslation()`
`double[]`	`initialGuessAtInverse(double[] target)` Approximates the inverse of the input target point by taking the best of several available approximation methods.
`double[]`	`inverse(double[] target, double tolerance)` Computes the inverse of this transformation.
`double`	`inverse(double[] target, double[] result, double tolerance, int maxIters)` Computes the inverse of this transformation.
`double[]`	`inverseGuessAffineInv(double[] target)` Quickly approximates the inverse of the input target point, using the affine portion of the transform only.
`double`	`inverseTol(double[] target, double[] guess, double tolerance, int maxIters)`
`double[][]`	`jacobian(double[] p)` Computes the jacobian of this tranformation around the point p.
`static double`	`normSqrd(double[] v)`
`void`	`printXfmBacks2d(int maxx, int maxy, int delx, int dely)`
`static double`	`r2Logr(double r)`
`double[][]`	`r2LogrDerivative(double[] p)` The derivative of component j of the output point, with respect to x_d (the dth component of the vector) is: \sum_i D[ d, l ] G'( r ) ( x_j - l_ij ) / ( sqrt( N_l(p) )) where: D is the D matrix i indexes the landmarks N_l(p) is the squared euclidean norm between landmark l and point p l_ij is the jth component of landmark i G' is the derivative of the kernel function.
`static double`	`r2LogrFromDisplacement(double[] displacement)`
`protected void`	`reorganizeW(org.ejml.data.DenseMatrix64F wMatrix)` Copies data from the W matrix to the D, A, and b matrices which represent the deformable, affine and translational portions of the transformation, respectively.
`void`	`setDoAffine(boolean estimateAffine)`
`protected void`	`srcPtDisplacement(int i, double[] pt, double[] res)` Computes the displacement between the i^th source point and the input point.
`protected void`	`srcPtDisplacement(int i, int j, double[] res)` Computes the displacement between the i^th and j^th source points.
`void`	`stepInDerivativeDirection(double[][] derivative, double[] start, double[] dest, double stepLength)`
`protected void`	`tgtPtDisplacement(int i, double[] pt, double[] res)` Computes the displacement between the i^th source point and the input point.
`double[]`	`transformPointAffine(double[] pt)` Transforms the input point according to the affine part of the thin plate spline stored by this object.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

ndims
```
protected final int ndims
```

dMatrix

protected org.ejml.data.DenseMatrix64F dMatrix

aMatrix
```
protected double[][] aMatrix
```

bVector
```
protected double[] bVector
```

stiffness
```
protected double stiffness
```

wMatrixComputeD
```
protected boolean wMatrixComputeD
```

computeAffine
```
protected boolean computeAffine
```

nLandmarks
```
protected int nLandmarks
```

sourceLandmarks

protected final double[][] sourceLandmarks

weights
```
protected double[] weights
```

tmpDisplacement
```
protected double[] tmpDisplacement
```

EPS
```
protected static final double EPS
```
See Also:

Constant Field Values

logger

protected static org.apache.log4j.Logger logger

Constructor Detail

ThinPlateR2LogRSplineKernelTransform

public ThinPlateR2LogRSplineKernelTransform(int ndims)

ThinPlateR2LogRSplineKernelTransform

public ThinPlateR2LogRSplineKernelTransform(int ndims,
                                            double[][] srcPts,
                                            double[][] tgtPts)

ThinPlateR2LogRSplineKernelTransform

public ThinPlateR2LogRSplineKernelTransform(int ndims,
                                            float[][] srcPts,
                                            float[][] tgtPts)

ThinPlateR2LogRSplineKernelTransform

public ThinPlateR2LogRSplineKernelTransform(int ndims,
                                            double[][] srcPts,
                                            double[][] tgtPts,
                                            boolean computeAffine)

ThinPlateR2LogRSplineKernelTransform

public ThinPlateR2LogRSplineKernelTransform(int ndims,
                                            float[][] srcPts,
                                            float[][] tgtPts,
                                            boolean computeAffine)

ThinPlateR2LogRSplineKernelTransform

public ThinPlateR2LogRSplineKernelTransform(int ndims,
                                            double[][] srcPts,
                                            double[][] tgtPts,
                                            double[] weights)

Constructor with weighted point matches

Parameters:: ndims - num dimensions; srcPts - source points; tgtPts - target points; weights - point weights

ThinPlateR2LogRSplineKernelTransform

public ThinPlateR2LogRSplineKernelTransform(double[][] srcPts,
                                            double[][] aMatrix,
                                            double[] bVector,
                                            double[] dMatrixData)

Constructor with transformation parameters. aMatrix and bVector are allowed to be null

Parameters:: srcPts - source points; aMatrix - A matrix; bVector - b vector; dMatrixData - D matrix

Method Detail
- getNumLandmarks
```
public int getNumLandmarks()
```
- getNumDims
```
public int getNumDims()
```
- getSourceLandmarks
```
public double[][] getSourceLandmarks()
```
- getAffine
```
public double[][] getAffine()
```
- getTranslation
```
public double[] getTranslation()
```
- getKnotWeights
```
public double[] getKnotWeights()
```
- setDoAffine
```
public void setDoAffine(boolean estimateAffine)
```
- computeReflexiveG
```
protected org.ejml.data.DenseMatrix64F computeReflexiveG()
```
- normSqrd
```
public static double normSqrd(double[] v)
```
- buildDisplacements
```
public org.ejml.data.DenseMatrix64F buildDisplacements(double[][] targetLandmarks)
```
- buildDisplacements
```
public org.ejml.data.DenseMatrix64F buildDisplacements(float[][] targetLandmarks)
```
- computeW
```
protected void computeW(org.ejml.data.DenseMatrix64F yMatrix)
```
  The main workhorse method.
  Implements Equation (5) in Davis et al. and calls reorganizeW.
  
  Parameters:
  
  yMatrix - the y matrix
- computeL
```
protected org.ejml.data.DenseMatrix64F computeL(org.ejml.data.DenseMatrix64F kMatrix,
                                                org.ejml.data.DenseMatrix64F pMatrix)
```
- computeP
```
protected void computeP(org.ejml.data.DenseMatrix64F pMatrix)
```
- computeK
```
protected void computeK(org.ejml.data.DenseMatrix64F kMatrix)
```
  Builds the K matrix from landmark points and G matrix.
  
  Parameters:
  
  kMatrix - the k matrix
- reorganizeW
```
protected void reorganizeW(org.ejml.data.DenseMatrix64F wMatrix)
```
  Copies data from the W matrix to the D, A, and b matrices which represent the deformable, affine and translational portions of the transformation, respectively.
  
  Parameters:
  
  wMatrix - the w matrix
- computeG
```
public void computeG(double[] pt,
                     org.ejml.data.DenseMatrix64F mtx)
```
- computeG
```
public void computeG(double[] pt,
                     org.ejml.data.DenseMatrix64F mtx,
                     double w)
```
- computeDeformationContribution
```
public void computeDeformationContribution(double[] thispt,
                                           double[] result)
```
- r2LogrDerivative
```
public double[][] r2LogrDerivative(double[] p)
```
  The derivative of component j of the output point, with respect to x_d (the dth component of the vector) is: \sum_i D[ d, l ] G'( r ) ( x_j - l_ij ) / ( sqrt( N_l(p) )) where: D is the D matrix i indexes the landmarks N_l(p) is the squared euclidean norm between landmark l and point p l_ij is the jth component of landmark i G' is the derivative of the kernel function. for a TPS, the kernel function is (r^2)logr, the derivative wrt r of which is: r( 2logr + 1 ) See the documentation for a derivation.
  
  Parameters:
  
  p - The point at which to evaluate the derivative
  
  Returns:
  
  The Jacobian matrix
- jacobian
```
public double[][] jacobian(double[] p)
```
  Computes the jacobian of this tranformation around the point p.
  The result is stored in a new double array where element [ i ][ j ] gives the derivative of variable i with respect to variable j
  
  Parameters:
  
  p - the point
  
  Returns:
  
  the jacobian array
- stepInDerivativeDirection
```
public void stepInDerivativeDirection(double[][] derivative,
                                      double[] start,
                                      double[] dest,
                                      double stepLength)
```
- printXfmBacks2d
```
public void printXfmBacks2d(int maxx,
                            int maxy,
                            int delx,
                            int dely)
```
- transformPointAffine
```
public double[] transformPointAffine(double[] pt)
```
  Transforms the input point according to the affine part of the thin plate spline stored by this object.
  
  Parameters:
  
  pt - the point to be transformed
  
  Returns:
  
  the transformed point
- apply
```
public void apply(double[] pt,
                  double[] result)
```
- apply
```
public void apply(double[] pt,
                  double[] result,
                  boolean debug)
```
  Transform a source vector pt into a target vector result. pt and result must NOT be the same vector.
  
  Parameters:
  
  pt - the point
  
  result - the result
  
  debug - do debug
- apply
```
public double[] apply(double[] pt)
```
  Transforms the input point according to the thin plate spline stored by this object.
  
  Parameters:
  
  pt - the point to be transformed
  
  Returns:
  
  the transformed point
- applyInPlace
```
public void applyInPlace(double[] pt)
```
  Transform pt in place.
  
  Parameters:
  
  pt - the point
- closestTargetLandmarkAndDistance
```
public jitk.spline.ThinPlateR2LogRSplineKernelTransform.IndexDistancePair closestTargetLandmarkAndDistance(double[] target)
```
  Returns the index of the target landmark closest to the input point as well as the distance to that landmark.
  
  Parameters:
  
  target - the point
  
  Returns:
  
  a pair containing the closest landmark point and its squared distance to that landmark
- initialGuessAtInverse
```
public double[] initialGuessAtInverse(double[] target)
```
  Approximates the inverse of the input target point by taking the best of several available approximation methods.
  
  Parameters:
  
  target - the target point
  
  Returns:
  
  the approximate inverse point
- inverseGuessAffineInv
```
public double[] inverseGuessAffineInv(double[] target)
```
  Quickly approximates the inverse of the input target point, using the affine portion of the transform only.
  
  Parameters:
  
  target - a point in the target space
  
  Returns:
  
  approximate inverse
- inverse
```
public double inverse(double[] target,
                      double[] result,
                      double tolerance,
                      int maxIters)
```
  Computes the inverse of this transformation.
  
  Parameters:
  
  target - the target point
  
  result - array in which to store the result
  
  tolerance - the desired precision - must be greater than zero
  
  maxIters - maximum number of iterations
  
  Returns:
  
  true if the result is within the specified tolerance, false otherwise
- inverse
```
public double[] inverse(double[] target,
                        double tolerance)
```
  Computes the inverse of this transformation. Performs a maximum of 100,000 iterations, returning whatever the estimate is at that point.
  
  Parameters:
  
  target - the target point
  
  tolerance - the desired precision - must be greater than zero
  
  Returns:
  
  the result of applying the inverse transform to the target point
- inverseTol
```
public double inverseTol(double[] target,
                         double[] guess,
                         double tolerance,
                         int maxIters)
```
- srcPtDisplacement
```
protected void srcPtDisplacement(int i,
                                 int j,
                                 double[] res)
```
  Computes the displacement between the i^th and j^th source points. Stores the result in the input array 'res' Does not validate inputs.
  
  Parameters:
  
  i - first index
  
  j - second index
  
  res - result
- srcPtDisplacement
```
protected void srcPtDisplacement(int i,
                                 double[] pt,
                                 double[] res)
```
  Computes the displacement between the i^th source point and the input point. Stores the result in the input array 'res'. Does not validate inputs.
  
  Parameters:
  
  i - first index
  
  pt - the point
  
  res - the result
- tgtPtDisplacement
```
protected void tgtPtDisplacement(int i,
                                 double[] pt,
                                 double[] res)
```
  Computes the displacement between the i^th source point and the input point. Stores the result in the input array 'res'. Does not validate inputs.
  
  Parameters:
  
  i - first index
  
  pt - the point
  
  res - the result
- r2Logr
```
public static double r2Logr(double r)
```
- r2LogrFromDisplacement
```
public static double r2LogrFromDisplacement(double[] displacement)
```

Class ThinPlateR2LogRSplineKernelTransform

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

ndims

dMatrix

aMatrix

bVector

stiffness

wMatrixComputeD

computeAffine

nLandmarks

sourceLandmarks

weights

tmpDisplacement

EPS

logger

Constructor Detail

ThinPlateR2LogRSplineKernelTransform

ThinPlateR2LogRSplineKernelTransform

ThinPlateR2LogRSplineKernelTransform

ThinPlateR2LogRSplineKernelTransform

ThinPlateR2LogRSplineKernelTransform

ThinPlateR2LogRSplineKernelTransform

ThinPlateR2LogRSplineKernelTransform

Method Detail

getNumLandmarks

getNumDims

getSourceLandmarks

getAffine

getTranslation

getKnotWeights

setDoAffine

computeReflexiveG

normSqrd

buildDisplacements

buildDisplacements

computeW

computeL

computeP

computeK

reorganizeW

computeG

computeG

computeDeformationContribution

r2LogrDerivative

jacobian

stepInDerivativeDirection

printXfmBacks2d

transformPointAffine

apply

apply

apply

applyInPlace

closestTargetLandmarkAndDistance

initialGuessAtInverse

inverseGuessAffineInv

inverse

inverse

inverseTol

srcPtDisplacement

srcPtDisplacement

tgtPtDisplacement

r2Logr

r2LogrFromDisplacement