More efficient rigid 3D transformation in Java
I want to calculate a rigid 3D transformation between two sets of 3D points. I googled myself, found no suitable implementation and implemented it myself with the help of the Apache Commons Math library, based on this guide. The implementation can be seen below:
public static RigidTransformation3dAnswer computeRigidTransformation3D(RealMatrix src,
RealMatrix dst) {
if (src.getRowDimension() == dst.getRowDimension() && src.getColumnDimension() == dst
.getColumnDimension()) {
int n = src.getRowDimension();
RealMatrix centroidSrc = computeCentroid(src);
RealMatrix centroidDst = computeCentroid(dst);
RealMatrix aa = src.subtract(tile(centroidSrc, n));
RealMatrix bb = dst.subtract(tile(centroidDst, n));
RealMatrix h = aa.transpose().multiply(bb);
SingularValueDecomposition singularValueDecomposition = new SingularValueDecomposition(h);
RealMatrix u = singularValueDecomposition.getU();
RealMatrix vt = singularValueDecomposition.getVT();
RealMatrix rotationMatrix = vt.transpose().multiply(u.transpose());
if (new LUDecomposition(rotationMatrix).getDeterminant() < 0) {
vt.setColumn(2, vt.getColumnVector(2).mapMultiplyToSelf(-1).toArray());
rotationMatrix = vt.transpose().multiply(u.transpose());
}
RealMatrix transpose = (rotationMatrix.scalarMultiply(-1).multiply(centroidSrc.transpose()))
.add(centroidDst.transpose());
RigidTransformation3dAnswer answer = new RigidTransformation3dAnswer();
answer.setRotationMatrix(rotationMatrix);
answer.setTranslationMatrix(transpose);
return answer;
}
return null;
}
private static RealMatrix tile(RealMatrix a, int n) {
RealMatrix realMatrix = new Array2DRowRealMatrix(n, a.getColumnDimension());
for (int i = 0; i < n; i++) {
realMatrix.setEntry(i, 0, a.getEntry(0, 0));
realMatrix.setEntry(i, 1, a.getEntry(0, 1));
realMatrix.setEntry(i, 2, a.getEntry(0, 2));
}
return realMatrix;
}
private static RealMatrix computeCentroid(RealMatrix mat) {
double sumX = 0;
double sumY = 0;
double sumZ = 0;
double returnArray = new double[1][3];
for (int i = 0; i < mat.getRowDimension(); i++) {
double a = mat.getEntry(i, 0);
sumX = sumX + a;
a = mat.getEntry(i, 1);
sumY = sumY + a;
a = mat.getEntry(i, 2);
sumZ = sumZ + a;
}
double centroidX = sumX / (double) mat.getRowDimension();
double centroidY = sumY / (double) mat.getRowDimension();
double centroidZ = sumZ / (double) mat.getRowDimension();
returnArray[0][0] = centroidX;
returnArray[0][1] = centroidY;
returnArray[0][2] = centroidZ;
return new Array2DRowRealMatrix(returnArray);
}
Although this implementation works perfectly, it is not very efficient and takes around 50 ms on desktop, which is not suitable because I want to use it in an Android application.
So here are three question:
a) is there a more efficient library or framework method to use to compute a rigid 3D transformation?
b) If not, is there a heuristic, and therefore more efficient, implementation of such a transformation, if, for example, I exclude the translation and only want rotation around the Z (vertical) axis?
c) If neither of those two points has an answer, is there a way to improve my code efficiency-wise?
java math optimization geometry
add a comment |
I want to calculate a rigid 3D transformation between two sets of 3D points. I googled myself, found no suitable implementation and implemented it myself with the help of the Apache Commons Math library, based on this guide. The implementation can be seen below:
public static RigidTransformation3dAnswer computeRigidTransformation3D(RealMatrix src,
RealMatrix dst) {
if (src.getRowDimension() == dst.getRowDimension() && src.getColumnDimension() == dst
.getColumnDimension()) {
int n = src.getRowDimension();
RealMatrix centroidSrc = computeCentroid(src);
RealMatrix centroidDst = computeCentroid(dst);
RealMatrix aa = src.subtract(tile(centroidSrc, n));
RealMatrix bb = dst.subtract(tile(centroidDst, n));
RealMatrix h = aa.transpose().multiply(bb);
SingularValueDecomposition singularValueDecomposition = new SingularValueDecomposition(h);
RealMatrix u = singularValueDecomposition.getU();
RealMatrix vt = singularValueDecomposition.getVT();
RealMatrix rotationMatrix = vt.transpose().multiply(u.transpose());
if (new LUDecomposition(rotationMatrix).getDeterminant() < 0) {
vt.setColumn(2, vt.getColumnVector(2).mapMultiplyToSelf(-1).toArray());
rotationMatrix = vt.transpose().multiply(u.transpose());
}
RealMatrix transpose = (rotationMatrix.scalarMultiply(-1).multiply(centroidSrc.transpose()))
.add(centroidDst.transpose());
RigidTransformation3dAnswer answer = new RigidTransformation3dAnswer();
answer.setRotationMatrix(rotationMatrix);
answer.setTranslationMatrix(transpose);
return answer;
}
return null;
}
private static RealMatrix tile(RealMatrix a, int n) {
RealMatrix realMatrix = new Array2DRowRealMatrix(n, a.getColumnDimension());
for (int i = 0; i < n; i++) {
realMatrix.setEntry(i, 0, a.getEntry(0, 0));
realMatrix.setEntry(i, 1, a.getEntry(0, 1));
realMatrix.setEntry(i, 2, a.getEntry(0, 2));
}
return realMatrix;
}
private static RealMatrix computeCentroid(RealMatrix mat) {
double sumX = 0;
double sumY = 0;
double sumZ = 0;
double returnArray = new double[1][3];
for (int i = 0; i < mat.getRowDimension(); i++) {
double a = mat.getEntry(i, 0);
sumX = sumX + a;
a = mat.getEntry(i, 1);
sumY = sumY + a;
a = mat.getEntry(i, 2);
sumZ = sumZ + a;
}
double centroidX = sumX / (double) mat.getRowDimension();
double centroidY = sumY / (double) mat.getRowDimension();
double centroidZ = sumZ / (double) mat.getRowDimension();
returnArray[0][0] = centroidX;
returnArray[0][1] = centroidY;
returnArray[0][2] = centroidZ;
return new Array2DRowRealMatrix(returnArray);
}
Although this implementation works perfectly, it is not very efficient and takes around 50 ms on desktop, which is not suitable because I want to use it in an Android application.
So here are three question:
a) is there a more efficient library or framework method to use to compute a rigid 3D transformation?
b) If not, is there a heuristic, and therefore more efficient, implementation of such a transformation, if, for example, I exclude the translation and only want rotation around the Z (vertical) axis?
c) If neither of those two points has an answer, is there a way to improve my code efficiency-wise?
java math optimization geometry
2
Insrc.subtract(tile(centroidSrc, n))
you create a new matrix just for the subtraction and then a new one for the result, even though you don't usesrc
later. It would probably be faster to write a methodvoid subtractFromEachRow(RealMatrix minuend, RealMatrix subtrahendRow)
that does the subtraction without creating any new matrices. Modifysrc
using theaddToEntry
method.
– Socowi
Nov 22 at 14:26
Alsovt.transpose().multiply(u.transpose())
is the same asu.multiply(vt).transpose()
, but the latter is faster. However, sincevt
andu
are small, that shouldn't change much.
– Socowi
Nov 22 at 14:32
How many point pairs do you have?
– Nico Schertler
Nov 22 at 17:36
Normally around 7, 10 is the maximum
– Noltibus
Nov 22 at 18:14
1
Ok, then 50ms is very slow, indeed. I think the most important factor is the allocation of new memory as @Socowi pointed out. If that does not help, you need to profile where the time is spent. Minor thing: You can calculate the determinant of a 3x3 matrix directly and do not need to calculate a LU decomposition.
– Nico Schertler
Nov 22 at 18:37
add a comment |
I want to calculate a rigid 3D transformation between two sets of 3D points. I googled myself, found no suitable implementation and implemented it myself with the help of the Apache Commons Math library, based on this guide. The implementation can be seen below:
public static RigidTransformation3dAnswer computeRigidTransformation3D(RealMatrix src,
RealMatrix dst) {
if (src.getRowDimension() == dst.getRowDimension() && src.getColumnDimension() == dst
.getColumnDimension()) {
int n = src.getRowDimension();
RealMatrix centroidSrc = computeCentroid(src);
RealMatrix centroidDst = computeCentroid(dst);
RealMatrix aa = src.subtract(tile(centroidSrc, n));
RealMatrix bb = dst.subtract(tile(centroidDst, n));
RealMatrix h = aa.transpose().multiply(bb);
SingularValueDecomposition singularValueDecomposition = new SingularValueDecomposition(h);
RealMatrix u = singularValueDecomposition.getU();
RealMatrix vt = singularValueDecomposition.getVT();
RealMatrix rotationMatrix = vt.transpose().multiply(u.transpose());
if (new LUDecomposition(rotationMatrix).getDeterminant() < 0) {
vt.setColumn(2, vt.getColumnVector(2).mapMultiplyToSelf(-1).toArray());
rotationMatrix = vt.transpose().multiply(u.transpose());
}
RealMatrix transpose = (rotationMatrix.scalarMultiply(-1).multiply(centroidSrc.transpose()))
.add(centroidDst.transpose());
RigidTransformation3dAnswer answer = new RigidTransformation3dAnswer();
answer.setRotationMatrix(rotationMatrix);
answer.setTranslationMatrix(transpose);
return answer;
}
return null;
}
private static RealMatrix tile(RealMatrix a, int n) {
RealMatrix realMatrix = new Array2DRowRealMatrix(n, a.getColumnDimension());
for (int i = 0; i < n; i++) {
realMatrix.setEntry(i, 0, a.getEntry(0, 0));
realMatrix.setEntry(i, 1, a.getEntry(0, 1));
realMatrix.setEntry(i, 2, a.getEntry(0, 2));
}
return realMatrix;
}
private static RealMatrix computeCentroid(RealMatrix mat) {
double sumX = 0;
double sumY = 0;
double sumZ = 0;
double returnArray = new double[1][3];
for (int i = 0; i < mat.getRowDimension(); i++) {
double a = mat.getEntry(i, 0);
sumX = sumX + a;
a = mat.getEntry(i, 1);
sumY = sumY + a;
a = mat.getEntry(i, 2);
sumZ = sumZ + a;
}
double centroidX = sumX / (double) mat.getRowDimension();
double centroidY = sumY / (double) mat.getRowDimension();
double centroidZ = sumZ / (double) mat.getRowDimension();
returnArray[0][0] = centroidX;
returnArray[0][1] = centroidY;
returnArray[0][2] = centroidZ;
return new Array2DRowRealMatrix(returnArray);
}
Although this implementation works perfectly, it is not very efficient and takes around 50 ms on desktop, which is not suitable because I want to use it in an Android application.
So here are three question:
a) is there a more efficient library or framework method to use to compute a rigid 3D transformation?
b) If not, is there a heuristic, and therefore more efficient, implementation of such a transformation, if, for example, I exclude the translation and only want rotation around the Z (vertical) axis?
c) If neither of those two points has an answer, is there a way to improve my code efficiency-wise?
java math optimization geometry
I want to calculate a rigid 3D transformation between two sets of 3D points. I googled myself, found no suitable implementation and implemented it myself with the help of the Apache Commons Math library, based on this guide. The implementation can be seen below:
public static RigidTransformation3dAnswer computeRigidTransformation3D(RealMatrix src,
RealMatrix dst) {
if (src.getRowDimension() == dst.getRowDimension() && src.getColumnDimension() == dst
.getColumnDimension()) {
int n = src.getRowDimension();
RealMatrix centroidSrc = computeCentroid(src);
RealMatrix centroidDst = computeCentroid(dst);
RealMatrix aa = src.subtract(tile(centroidSrc, n));
RealMatrix bb = dst.subtract(tile(centroidDst, n));
RealMatrix h = aa.transpose().multiply(bb);
SingularValueDecomposition singularValueDecomposition = new SingularValueDecomposition(h);
RealMatrix u = singularValueDecomposition.getU();
RealMatrix vt = singularValueDecomposition.getVT();
RealMatrix rotationMatrix = vt.transpose().multiply(u.transpose());
if (new LUDecomposition(rotationMatrix).getDeterminant() < 0) {
vt.setColumn(2, vt.getColumnVector(2).mapMultiplyToSelf(-1).toArray());
rotationMatrix = vt.transpose().multiply(u.transpose());
}
RealMatrix transpose = (rotationMatrix.scalarMultiply(-1).multiply(centroidSrc.transpose()))
.add(centroidDst.transpose());
RigidTransformation3dAnswer answer = new RigidTransformation3dAnswer();
answer.setRotationMatrix(rotationMatrix);
answer.setTranslationMatrix(transpose);
return answer;
}
return null;
}
private static RealMatrix tile(RealMatrix a, int n) {
RealMatrix realMatrix = new Array2DRowRealMatrix(n, a.getColumnDimension());
for (int i = 0; i < n; i++) {
realMatrix.setEntry(i, 0, a.getEntry(0, 0));
realMatrix.setEntry(i, 1, a.getEntry(0, 1));
realMatrix.setEntry(i, 2, a.getEntry(0, 2));
}
return realMatrix;
}
private static RealMatrix computeCentroid(RealMatrix mat) {
double sumX = 0;
double sumY = 0;
double sumZ = 0;
double returnArray = new double[1][3];
for (int i = 0; i < mat.getRowDimension(); i++) {
double a = mat.getEntry(i, 0);
sumX = sumX + a;
a = mat.getEntry(i, 1);
sumY = sumY + a;
a = mat.getEntry(i, 2);
sumZ = sumZ + a;
}
double centroidX = sumX / (double) mat.getRowDimension();
double centroidY = sumY / (double) mat.getRowDimension();
double centroidZ = sumZ / (double) mat.getRowDimension();
returnArray[0][0] = centroidX;
returnArray[0][1] = centroidY;
returnArray[0][2] = centroidZ;
return new Array2DRowRealMatrix(returnArray);
}
Although this implementation works perfectly, it is not very efficient and takes around 50 ms on desktop, which is not suitable because I want to use it in an Android application.
So here are three question:
a) is there a more efficient library or framework method to use to compute a rigid 3D transformation?
b) If not, is there a heuristic, and therefore more efficient, implementation of such a transformation, if, for example, I exclude the translation and only want rotation around the Z (vertical) axis?
c) If neither of those two points has an answer, is there a way to improve my code efficiency-wise?
java math optimization geometry
java math optimization geometry
asked Nov 22 at 13:33
Noltibus
18615
18615
2
Insrc.subtract(tile(centroidSrc, n))
you create a new matrix just for the subtraction and then a new one for the result, even though you don't usesrc
later. It would probably be faster to write a methodvoid subtractFromEachRow(RealMatrix minuend, RealMatrix subtrahendRow)
that does the subtraction without creating any new matrices. Modifysrc
using theaddToEntry
method.
– Socowi
Nov 22 at 14:26
Alsovt.transpose().multiply(u.transpose())
is the same asu.multiply(vt).transpose()
, but the latter is faster. However, sincevt
andu
are small, that shouldn't change much.
– Socowi
Nov 22 at 14:32
How many point pairs do you have?
– Nico Schertler
Nov 22 at 17:36
Normally around 7, 10 is the maximum
– Noltibus
Nov 22 at 18:14
1
Ok, then 50ms is very slow, indeed. I think the most important factor is the allocation of new memory as @Socowi pointed out. If that does not help, you need to profile where the time is spent. Minor thing: You can calculate the determinant of a 3x3 matrix directly and do not need to calculate a LU decomposition.
– Nico Schertler
Nov 22 at 18:37
add a comment |
2
Insrc.subtract(tile(centroidSrc, n))
you create a new matrix just for the subtraction and then a new one for the result, even though you don't usesrc
later. It would probably be faster to write a methodvoid subtractFromEachRow(RealMatrix minuend, RealMatrix subtrahendRow)
that does the subtraction without creating any new matrices. Modifysrc
using theaddToEntry
method.
– Socowi
Nov 22 at 14:26
Alsovt.transpose().multiply(u.transpose())
is the same asu.multiply(vt).transpose()
, but the latter is faster. However, sincevt
andu
are small, that shouldn't change much.
– Socowi
Nov 22 at 14:32
How many point pairs do you have?
– Nico Schertler
Nov 22 at 17:36
Normally around 7, 10 is the maximum
– Noltibus
Nov 22 at 18:14
1
Ok, then 50ms is very slow, indeed. I think the most important factor is the allocation of new memory as @Socowi pointed out. If that does not help, you need to profile where the time is spent. Minor thing: You can calculate the determinant of a 3x3 matrix directly and do not need to calculate a LU decomposition.
– Nico Schertler
Nov 22 at 18:37
2
2
In
src.subtract(tile(centroidSrc, n))
you create a new matrix just for the subtraction and then a new one for the result, even though you don't use src
later. It would probably be faster to write a method void subtractFromEachRow(RealMatrix minuend, RealMatrix subtrahendRow)
that does the subtraction without creating any new matrices. Modify src
using the addToEntry
method.– Socowi
Nov 22 at 14:26
In
src.subtract(tile(centroidSrc, n))
you create a new matrix just for the subtraction and then a new one for the result, even though you don't use src
later. It would probably be faster to write a method void subtractFromEachRow(RealMatrix minuend, RealMatrix subtrahendRow)
that does the subtraction without creating any new matrices. Modify src
using the addToEntry
method.– Socowi
Nov 22 at 14:26
Also
vt.transpose().multiply(u.transpose())
is the same as u.multiply(vt).transpose()
, but the latter is faster. However, since vt
and u
are small, that shouldn't change much.– Socowi
Nov 22 at 14:32
Also
vt.transpose().multiply(u.transpose())
is the same as u.multiply(vt).transpose()
, but the latter is faster. However, since vt
and u
are small, that shouldn't change much.– Socowi
Nov 22 at 14:32
How many point pairs do you have?
– Nico Schertler
Nov 22 at 17:36
How many point pairs do you have?
– Nico Schertler
Nov 22 at 17:36
Normally around 7, 10 is the maximum
– Noltibus
Nov 22 at 18:14
Normally around 7, 10 is the maximum
– Noltibus
Nov 22 at 18:14
1
1
Ok, then 50ms is very slow, indeed. I think the most important factor is the allocation of new memory as @Socowi pointed out. If that does not help, you need to profile where the time is spent. Minor thing: You can calculate the determinant of a 3x3 matrix directly and do not need to calculate a LU decomposition.
– Nico Schertler
Nov 22 at 18:37
Ok, then 50ms is very slow, indeed. I think the most important factor is the allocation of new memory as @Socowi pointed out. If that does not help, you need to profile where the time is spent. Minor thing: You can calculate the determinant of a 3x3 matrix directly and do not need to calculate a LU decomposition.
– Nico Schertler
Nov 22 at 18:37
add a comment |
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2
In
src.subtract(tile(centroidSrc, n))
you create a new matrix just for the subtraction and then a new one for the result, even though you don't usesrc
later. It would probably be faster to write a methodvoid subtractFromEachRow(RealMatrix minuend, RealMatrix subtrahendRow)
that does the subtraction without creating any new matrices. Modifysrc
using theaddToEntry
method.– Socowi
Nov 22 at 14:26
Also
vt.transpose().multiply(u.transpose())
is the same asu.multiply(vt).transpose()
, but the latter is faster. However, sincevt
andu
are small, that shouldn't change much.– Socowi
Nov 22 at 14:32
How many point pairs do you have?
– Nico Schertler
Nov 22 at 17:36
Normally around 7, 10 is the maximum
– Noltibus
Nov 22 at 18:14
1
Ok, then 50ms is very slow, indeed. I think the most important factor is the allocation of new memory as @Socowi pointed out. If that does not help, you need to profile where the time is spent. Minor thing: You can calculate the determinant of a 3x3 matrix directly and do not need to calculate a LU decomposition.
– Nico Schertler
Nov 22 at 18:37