/**
* Compute the steepest descent images of the template at the identity warp. Each steepest descent
* image comprises the partial derivatives of template intensities with respect to one parameter
* of the warp function.
*
* <p>The result is stored in the <em>n+1</em> dimensional {@link #target} image. Dimension
* <em>n</em> is used to index the partial derivative. For example, the partial derivative by the
* second parameter of the warp function is stored in slice <em>n=1</em>.
*
* @param gradients n+1 dimensional image of partial derivatives of the template. Dimension n is
* used to index the partial derivative. For example, the partial derivative by Y is stored in
* slice n=1.
* @param warpFunction The warp function to be applied to the template. The partial derivatives of
* template intensities with respect to the parameters of this warp function are computed.
* @param target Image of <em>n+1</em> dimensions to store the steepest descent Dimension
* <em>n</em> is used to index the parameters of the warp function. For example, the partial
* derivative of the template image intensity by parameter 2 of the warp function at pixel
* <em>(x,y)</em> is stored at position <em>(x,y,1)</em>.
*/
public static <T extends NumericType<T>> void computeSteepestDescents(
final RandomAccessibleInterval<T> gradients,
final WarpFunction warpFunction,
final RandomAccessibleInterval<T> target) {
final int n = gradients.numDimensions() - 1;
final int numParameters = warpFunction.numParameters();
final T tmp = Util.getTypeFromInterval(gradients).createVariable();
for (int p = 0; p < numParameters; ++p) {
for (int d = 0; d < n; ++d) {
final Cursor<T> gd =
Views.flatIterable(Views.hyperSlice(gradients, n, d)).localizingCursor();
for (final T t : Views.flatIterable(Views.hyperSlice(target, n, p))) {
tmp.set(gd.next());
tmp.mul(warpFunction.partial(gd, d, p));
t.add(tmp);
}
}
}
}
double alignStep(final RandomAccessibleInterval<T> image) {
// compute error image = warped image - template
computeDifference(Views.extendBorder(image), currentTransform, template, error);
// compute transform parameter update
final double[] gradient = new double[numParameters];
for (int p = 0; p < numParameters; ++p) {
final Cursor<T> err = Views.flatIterable(error).cursor();
for (final T t : Views.flatIterable(Views.hyperSlice(descent, n, p)))
gradient[p] += t.getRealDouble() * err.next().getRealDouble();
}
final double[] dp = new double[numParameters];
LinAlgHelpers.mult(Hinv, gradient, dp);
// udpate transform
currentTransform.preConcatenate(warpFunction.getAffine(dp));
// return norm of parameter update vector
return LinAlgHelpers.length(dp);
}
public Align(final RandomAccessibleInterval<T> template, final ImgFactory<T> factory) {
this.template = template;
final T type = Util.getTypeFromInterval(template);
n = template.numDimensions();
warpFunction = new AffineWarp(n);
numParameters = warpFunction.numParameters();
currentTransform = new AffineTransform(n);
final long[] dim = new long[n + 1];
for (int d = 0; d < n; ++d) dim[d] = template.dimension(d);
dim[n] = n;
final Img<T> gradients = factory.create(dim, type);
gradients(Views.extendBorder(template), gradients);
dim[n] = numParameters;
descent = factory.create(dim, type);
computeSteepestDescents(gradients, warpFunction, descent);
Hinv = computeInverseHessian(descent);
error = factory.create(template, type);
}
