/**
* Converts an {@link Img} into a matrix
*
* @param maxtrixImg - the input {@link Img}
* @return a {@link Matrix} or null if the {@link Img} is not one or two-dimensional
*/
public static <S extends RealType<S>> Matrix getMatrix(final Img<S> maxtrixImg) {
final int numDimensions = maxtrixImg.numDimensions();
if (numDimensions > 2) return null;
final Matrix matrix;
if (numDimensions == 1) {
matrix = new Matrix((int) maxtrixImg.dimension(0), 1);
final Cursor<S> cursor = maxtrixImg.localizingCursor();
while (cursor.hasNext()) {
cursor.fwd();
matrix.set(cursor.getIntPosition(0), 0, cursor.get().getRealDouble());
}
} else {
matrix = new Matrix((int) maxtrixImg.dimension(0), (int) maxtrixImg.dimension(1));
final Cursor<S> cursor = maxtrixImg.localizingCursor();
while (cursor.hasNext()) {
cursor.fwd();
matrix.set(
cursor.getIntPosition(0), cursor.getIntPosition(1), cursor.get().getRealDouble());
}
}
return matrix;
}
private static final <R extends RealType<R>> Img<R> processReal(
final Img<R> img, final float[] m, final Mode mode, final OutOfBoundsFactory<R, Img<R>> oobf)
throws Exception {
final InterpolatorFactory<R, RandomAccessible<R>> inter;
switch (mode) {
case LINEAR:
inter = new NLinearInterpolatorFactory<R>();
break;
case NEAREST_NEIGHBOR:
inter = new NearestNeighborInterpolatorFactory<R>();
break;
default:
throw new IllegalArgumentException("Scale: don't know how to scale with mode " + mode);
}
final ImageTransform<R> transform;
final ExtendedRandomAccessibleInterval<R, Img<R>> imgExt = Views.extend(img, oobf);
if (2 == img.numDimensions()) {
// Transform the single-plane image in 2D
AffineModel2D aff = new AffineModel2D();
aff.set(m[0], m[4], m[1], m[5], m[3], m[7]);
transform = new ImageTransform<R>(imgExt, aff, (InterpolatorFactory) inter);
} else if (3 == img.numDimensions()) {
// Transform the image in 3D, or each plane in 2D
if (m.length < 12) {
throw new IllegalArgumentException(
"Affine transform in 3D requires a matrix array of 12 elements.");
}
AffineModel3D aff = new AffineModel3D();
aff.set(m[0], m[1], m[2], m[3], m[4], m[5], m[6], m[7], m[8], m[9], m[10], m[11]);
transform = new ImageTransform<R>(imgExt, aff, (InterpolatorFactory) inter);
// Ensure Z dimension is not altered if scaleZ is 1:
if (Math.abs(m[10] - 1.0f) < 0.000001 && 0 == m[8] && 0 == m[9]) {
long[] d = transform.getNewImageSize();
d[2] = img.dimension(2); // 0-based: '2' is the third dimension
transform.setNewImageSize(d);
}
} else {
throw new Exception("Affine transform: only 2D and 3D images are supported.");
}
if (!transform.checkInput() || !transform.process()) {
throw new Exception("Could not affine transform the image: " + transform.getErrorMessage());
}
return transform.getResult();
}
@Override
public boolean process() {
final int numDimensions = img.numDimensions();
final long integralSize[] = new long[numDimensions];
// the size of the first dimension is changed
for (int d = 0; d < numDimensions; ++d) integralSize[d] = img.dimension(d) + 1;
final Img<T> integral = imgFactory.create(integralSize, type);
// not enough RAM or disc space
if (integral == null) return false;
this.integral = integral;
if (numDimensions > 1) {
final long[] fakeSize = new long[numDimensions - 1];
// the size of dimension 0
final long size = integralSize[0];
for (int d = 1; d < numDimensions; ++d) fakeSize[d - 1] = integralSize[d];
final long imageSize = getNumPixels(fakeSize);
final AtomicInteger ai = new AtomicInteger(0);
final Thread[] threads = SimpleMultiThreading.newThreads();
final Vector<Chunk> threadChunks =
SimpleMultiThreading.divideIntoChunks(imageSize, threads.length);
for (int ithread = 0; ithread < threads.length; ++ithread)
threads[ithread] =
new Thread(
new Runnable() {
@Override
public void run() {
// Thread ID
final int myNumber = ai.getAndIncrement();
// get chunk of pixels to process
final Chunk myChunk = threadChunks.get(myNumber);
final long loopSize = myChunk.getLoopSize();
final LocalizingZeroMinIntervalIterator cursorDim =
new LocalizingZeroMinIntervalIterator(fakeSize);
// location for the input location
final long[] tmpIn = new long[numDimensions];
// location for the integral location
final long[] tmpOut = new long[numDimensions];
final long[] tmp = new long[numDimensions - 1];
final RandomAccess<R> cursorIn = img.randomAccess();
final RandomAccess<T> cursorOut = integral.randomAccess();
final T tmpVar = integral.firstElement().createVariable();
final T sum = integral.firstElement().createVariable();
cursorDim.jumpFwd(myChunk.getStartPosition());
// iterate over all dimensions except the one we are computing the integral in,
// which is dim=0 here
main:
for (long j = 0; j < loopSize; ++j) {
cursorDim.fwd();
// get all dimensions except the one we are currently doing the integral on
cursorDim.localize(tmp);
tmpIn[0] = 0;
tmpOut[0] = 1;
for (int d = 1; d < numDimensions; ++d) {
tmpIn[d] = tmp[d - 1] - 1;
tmpOut[d] = tmp[d - 1];
// all entries of position 0 are 0
if (tmpOut[d] == 0) continue main;
}
// set the cursor to the beginning of the correct line
cursorIn.setPosition(tmpIn);
// set the cursor in the integral image to the right position
cursorOut.setPosition(tmpOut);
// integrate over the line
integrateLineDim0(converter, cursorIn, cursorOut, sum, tmpVar, size);
}
}
});
SimpleMultiThreading.startAndJoin(threads);
} else {
final T tmpVar = integral.firstElement().createVariable();
final T sum = integral.firstElement().createVariable();
// the size of dimension 0
final long size = integralSize[0];
final RandomAccess<R> cursorIn = img.randomAccess();
final RandomAccess<T> cursorOut = integral.randomAccess();
cursorIn.setPosition(0, 0);
cursorOut.setPosition(1, 0);
// compute the first pixel
converter.convert(cursorIn.get(), sum);
cursorOut.get().set(sum);
for (long i = 2; i < size; ++i) {
cursorIn.fwd(0);
cursorOut.fwd(0);
converter.convert(cursorIn.get(), tmpVar);
sum.add(tmpVar);
cursorOut.get().set(sum);
}
return true;
}
for (int d = 1; d < numDimensions; ++d) {
final int dim = d;
final long[] fakeSize = new long[numDimensions - 1];
// the size of dimension d
final long size = integralSize[d];
// get all dimensions except the one we are currently doing the integral on
int countDim = 0;
for (int e = 0; e < numDimensions; ++e) if (e != d) fakeSize[countDim++] = integralSize[e];
final long imageSize = getNumPixels(fakeSize);
final AtomicInteger ai = new AtomicInteger(0);
final Thread[] threads = SimpleMultiThreading.newThreads();
final Vector<Chunk> threadChunks =
SimpleMultiThreading.divideIntoChunks(imageSize, threads.length);
for (int ithread = 0; ithread < threads.length; ++ithread)
threads[ithread] =
new Thread(
new Runnable() {
@Override
public void run() {
// Thread ID
final int myNumber = ai.getAndIncrement();
// get chunk of pixels to process
final Chunk myChunk = threadChunks.get(myNumber);
final long loopSize = myChunk.getLoopSize();
final LocalizingZeroMinIntervalIterator cursorDim =
new LocalizingZeroMinIntervalIterator(fakeSize);
// local instances
final long[] tmp2 = new long[numDimensions - 1];
final long[] tmp = new long[numDimensions];
final RandomAccess<T> cursor = integral.randomAccess();
final T sum = integral.firstElement().createVariable();
cursorDim.jumpFwd(myChunk.getStartPosition());
for (long j = 0; j < loopSize; ++j) {
cursorDim.fwd();
// get all dimensions except the one we are currently doing the integral on
cursorDim.localize(tmp2);
tmp[dim] = 1;
int countDim = 0;
for (int e = 0; e < numDimensions; ++e)
if (e != dim) tmp[e] = tmp2[countDim++];
// update the cursor in the input image to the current dimension position
cursor.setPosition(tmp);
// sum up line
integrateLine(dim, cursor, sum, size);
}
}
});
SimpleMultiThreading.startAndJoin(threads);
}
return true;
}
public boolean analyzePeak(final DifferenceOfGaussianPeak<T> peak) {
final int numDimensions = laPlacian.numDimensions();
// the subpixel values
final double[] subpixelLocation = new double[numDimensions];
// the current position for the quadratic fit
final long[] currentPosition = new long[numDimensions];
peak.localize(currentPosition);
// the cursor for the computation (one that cannot move out of Img)
final RandomAccess<T> cursor;
if (canMoveOutside) cursor = Views.extendPeriodic(laPlacian).randomAccess();
else cursor = laPlacian.randomAccess();
// the current hessian matrix and derivative vector
Img<DoubleType> hessianMatrix =
doubleArrayFactory.create(
new int[] {cursor.numDimensions(), cursor.numDimensions()}, new DoubleType());
Img<DoubleType> derivativeVector =
doubleArrayFactory.create(new int[] {cursor.numDimensions()}, new DoubleType());
// the inverse hessian matrix
Matrix A, B, X;
// the current value of the center
T value = peak.value.createVariable();
boolean foundStableMaxima = true, pointsValid = false;
int numMoves = 0;
// fit n-dimensional quadratic function to the extremum and
// if the extremum is shifted more than 0.5 in one or more
// directions we test wheather it is better there
// until we
// - converge (find a stable extremum)
// - move out of the Img
// - achieved the maximal number of moves
do {
++numMoves;
// move the cursor to the current positon
cursor.setPosition(currentPosition);
// store the center value
value.set(cursor.get());
// compute the n-dimensional hessian matrix [numDimensions][numDimensions]
// containing all second derivatives, e.g. for 3d:
//
// xx xy xz
// yx yy yz
// zx zy zz
hessianMatrix = getHessianMatrix(cursor, hessianMatrix);
// compute the inverse of the hessian matrix
A = invertMatrix(hessianMatrix);
if (A == null) return handleFailure(peak, "Cannot invert hessian matrix");
// compute the n-dimensional derivative vector
derivativeVector = getDerivativeVector(cursor, derivativeVector);
B = getMatrix(derivativeVector);
if (B == null) return handleFailure(peak, "Cannot compute derivative vector");
// compute the extremum of the n-dimensinal quadratic fit
X = (A.uminus()).times(B);
for (int d = 0; d < numDimensions; ++d) subpixelLocation[d] = X.get(d, 0);
// test all dimensions for their change
// if the absolute value of the subpixel location
// is bigger than 0.5 we move into that direction
foundStableMaxima = true;
for (int d = 0; d < numDimensions; ++d) {
// Normally, above an offset of 0.5 the base position
// has to be changed, e.g. a subpixel location of 4.7
// would mean that the new base location is 5 with an offset of -0.3
//
// If we allow an increasing maxima tolerance we will
// not change the base position that easily. Sometimes
// it simply jumps from left to right and back, because
// it is 4.51 (i.e. goto 5), then 4.49 (i.e. goto 4)
// Then we say, ok, lets keep the base position even if
// the subpixel location is 0.6...
final double threshold = allowMaximaTolerance ? 0.5 + numMoves * maximaTolerance : 0.5;
if (Math.abs(subpixelLocation[d]) > threshold) {
if (allowedToMoveInDim[d]) {
// move to another base location
currentPosition[d] += Math.signum(subpixelLocation[d]);
foundStableMaxima = false;
} else {
// set it to the position that is maximally away when keeping the current base position
// e.g. if (0.7) do 4 -> 4.5 (although it should be 4.7, i.e. a new base position of 5)
// or if (-0.9) do 4 -> 3.5 (although it should be 3.1, i.e. a new base position of 3)
subpixelLocation[d] = Math.signum(subpixelLocation[d]) * 0.5;
}
}
}
// check validity of the new location if there is a need to move
pointsValid = true;
if (!canMoveOutside)
if (!foundStableMaxima)
for (int d = 0; d < numDimensions; ++d)
if (currentPosition[d] <= 0 || currentPosition[d] >= laPlacian.dimension(d) - 1)
pointsValid = false;
} while (numMoves <= maxNumMoves && !foundStableMaxima && pointsValid);
if (!foundStableMaxima) return handleFailure(peak, "No stable extremum found.");
if (!pointsValid) return handleFailure(peak, "Moved outside of the Img.");
// compute the function value (intensity) of the fit
double quadrFuncValue = 0;
for (int d = 0; d < numDimensions; ++d) quadrFuncValue += X.get(d, 0) * B.get(d, 0);
quadrFuncValue /= 2.0;
// set the results if everything went well
// subpixel location
for (int d = 0; d < numDimensions; ++d)
peak.setSubPixelLocationOffset((float) subpixelLocation[d], d);
// pixel location
peak.setPixelLocation(currentPosition);
// quadratic fit value
final T quadraticFit = peak.getImgValue().createVariable();
quadraticFit.setReal(quadrFuncValue);
peak.setFitValue(quadraticFit);
// normal value
peak.setImgValue(value);
return true;
}
@Override
public boolean process() {
/* 0. Instantiate tensor holder, and initialize cursors. */
long[] tensorDims = new long[input.numDimensions() + 1];
for (int i = 0; i < input.numDimensions(); i++) {
tensorDims[i] = input.dimension(i);
}
tensorDims[input.numDimensions()] = 3;
try {
D = input.factory().imgFactory(new FloatType()).create(tensorDims, new FloatType());
} catch (IncompatibleTypeException e) {
errorMessage = BASE_ERROR_MESSAGE + "Failed to create tensor holder:\n" + e.getMessage();
return false;
}
/* 1. Create a smoothed version of the input. */
Img<FloatType> smoothed = Gauss.toFloat(new double[] {sigma, sigma}, input);
/* 2. Compute the gradient of the smoothed input, but only algon X & Y */
boolean[] doDimension = new boolean[input.numDimensions()];
doDimension[0] = true;
doDimension[1] = true;
Gradient<FloatType> gradientCalculator = new Gradient<FloatType>(smoothed, doDimension);
gradientCalculator.process();
final Img<FloatType> gradient = gradientCalculator.getResult();
/* 3. Compute the structure tensor. */
final Img<FloatType> J = D.factory().create(D, new FloatType());
final int newDim = input.numDimensions();
final Vector<Chunk> chunks = SimpleMultiThreading.divideIntoChunks(input.size(), numThreads);
Thread[] threads = SimpleMultiThreading.newThreads(numThreads);
for (int i = 0; i < threads.length; i++) {
final Chunk chunk = chunks.get(i);
threads[i] =
new Thread("" + BASE_ERROR_MESSAGE + "thread " + i) {
@Override
public void run() {
float ux, uy;
Cursor<T> cursor = input.localizingCursor();
RandomAccess<FloatType> grad_ra = gradient.randomAccess();
RandomAccess<FloatType> J_ra = J.randomAccess();
cursor.jumpFwd(chunk.getStartPosition());
for (long k = 0; k < chunk.getLoopSize(); k++) {
cursor.fwd();
for (int i = 0; i < input.numDimensions(); i++) {
grad_ra.setPosition(cursor.getLongPosition(i), i);
J_ra.setPosition(cursor.getLongPosition(i), i);
}
grad_ra.setPosition(0, newDim);
ux = grad_ra.get().get();
grad_ra.fwd(newDim);
uy = grad_ra.get().get();
J_ra.setPosition(0, newDim);
J_ra.get().set(ux * ux);
J_ra.fwd(newDim);
J_ra.get().set(ux * uy);
J_ra.fwd(newDim);
J_ra.get().set(uy * uy);
}
}
};
}
SimpleMultiThreading.startAndJoin(threads);
/* 3.5 Smoooth the structure tensor. */
Gauss.inFloat(new double[] {rho, rho, 0}, J);
/* 4. Construct Diffusion tensor. */
for (int i = 0; i < threads.length; i++) {
final Chunk chunk = chunks.get(i);
threads[i] =
new Thread("" + BASE_ERROR_MESSAGE + "thread " + i) {
@Override
public void run() {
Cursor<T> cursor = input.localizingCursor();
RandomAccess<FloatType> J_ra = J.randomAccess();
RandomAccess<FloatType> D_ra = D.randomAccess();
float Jxx, Jxy, Jyy;
double tmp, v1x, v1y, v2x, v2y, mag, mu1, mu2, lambda1, lambda2, di;
double newLambda1, newLambda2, Dxx, Dxy, Dyy;
double scale;
cursor.jumpFwd(chunk.getStartPosition());
for (long k = 0; k < chunk.getLoopSize(); k++) {
cursor.fwd();
for (int j = 0; j < input.numDimensions(); j++) {
D_ra.setPosition(cursor.getLongPosition(j), j);
J_ra.setPosition(cursor.getLongPosition(j), j);
}
// Compute eigenvalues
J_ra.setPosition(0, newDim);
Jxx = J_ra.get().get();
J_ra.fwd(newDim);
Jxy = J_ra.get().get();
J_ra.fwd(newDim);
Jyy = J_ra.get().get();
tmp = Math.sqrt((Jxx - Jyy) * (Jxx - Jyy) + 4 * Jxy * Jxy);
v2x = 2 * Jxy;
v2y = Jyy - Jxx + tmp;
mag = Math.sqrt(v2x * v2x + v2y * v2y);
v2x /= mag;
v2y /= mag;
v1x = -v2y;
v1y = v2x;
mu1 = 0.5 * (Jxx + Jyy + tmp);
mu2 = 0.5 * (Jxx + Jyy - tmp);
// Large one in abs values must be the 2nd
if (Math.abs(mu2) > Math.abs(mu1)) {
lambda1 = mu1;
lambda2 = mu2;
} else {
lambda1 = mu2;
lambda2 = mu1;
}
di = lambda2 - lambda1;
scale = Util.pow(di * di, m);
newLambda1 = alpha + (1 - alpha) * Math.exp(-C / scale);
newLambda2 = alpha;
Dxx = newLambda1 * v1x * v1x + newLambda2 * v2x * v2x;
Dxy = newLambda1 * v1x * v1y + newLambda2 * v2x * v2x;
Dyy = newLambda1 * v1y * v1y + newLambda2 * v2y * v2y;
D_ra.setPosition(0, 2);
D_ra.get().setReal(Dxx);
D_ra.fwd(2);
D_ra.get().setReal(Dxy);
D_ra.fwd(2);
D_ra.get().setReal(Dyy);
}
}
};
}
SimpleMultiThreading.startAndJoin(threads);
return true;
}