private static void applyLhs(
final float w1,
final float[][][] wp,
final float[][][] p2,
final float[][][] p3,
final float[][][] x,
final float[][][] y) {
final int n3 = x.length;
Parallel.loop(
1,
n3,
2,
new Parallel.LoopInt() { // i3 = 1, 3, 5, ...
public void compute(int i3) {
applyLhsSlice3(i3, w1, wp, p2, p3, x, y);
}
});
Parallel.loop(
2,
n3,
2,
new Parallel.LoopInt() { // i3 = 2, 4, 6, ...
public void compute(int i3) {
applyLhsSlice3(i3, w1, wp, p2, p3, x, y);
}
});
}
/**
* Applies the shifts {@code u} to the trace {@code g}.
*
* @param sf the sampling that {@code g} is being warped to.
* @param u the shifts to apply to {@code g}.
* @param sg the sampling of {@code g}.
* @param g the trace to be warped.
* @return the warped image.
*/
public static float[][][] applyShifts(
Sampling sf, final float[][][] u, Sampling sg, final float[][][] g) {
final int n1 = u[0][0].length;
final int n2 = u[0].length;
final int n3 = u.length;
final int ng = g[0][0].length;
final double dg = sg.getDelta();
final double df = sf.getDelta();
final double fg = sg.getDelta();
final double ff = sf.getDelta();
final float[][][] hf = new float[n3][n2][n1];
final SincInterp si = new SincInterp();
int n23 = n3 * n2;
Parallel.loop(
n23,
new Parallel.LoopInt() {
public void compute(int i23) {
int i2 = i23 % n2;
int i3 = i23 / n2;
double v = ff;
for (int i1 = 0; i1 < n1; i1++, v = ff + i1 * df) {
hf[i3][i2][i1] = si.interpolate(ng, dg, fg, g[i3][i2], (float) v + u[i3][i2][i1]);
}
}
});
return hf;
}
public float[][][][] flattenWithShifts(
final Sampling s1, final float[][][] r, final float[][][] f) {
cleanShifts(r);
final int n3 = r.length;
final int n2 = r[0].length;
final int n1 = r[0][0].length;
// Compute u1(x1,x2,x3).
final double f1 = s1.getFirst();
final double d1 = s1.getDelta();
final float[][][] u1 = r;
for (int i3 = 0; i3 < n3; ++i3) {
for (int i2 = 0; i2 < n2; ++i2) {
for (int i1 = 0; i1 < n1; ++i1) {
float x1i = (float) (f1 + i1 * d1);
u1[i3][i2][i1] = (float) (x1i + r[i3][i2][i1] * d1);
}
}
}
// Compute x1(u1,u2).
final float[][][] x1 = new float[n3][n2][n1];
final InverseInterpolator ii = new InverseInterpolator(s1, s1);
Parallel.loop(
n3,
new Parallel.LoopInt() {
public void compute(int i3) {
for (int i2 = 0; i2 < n2; ++i2) ii.invert(u1[i3][i2], x1[i3][i2]);
}
});
final SincInterpolator si = new SincInterpolator();
final float[][][] g = new float[n3][n2][n1];
Parallel.loop(
n3,
new Parallel.LoopInt() {
public void compute(int i3) {
for (int i2 = 0; i2 < n2; ++i2)
si.interpolate(n1, d1, f1, f[i3][i2], n1, x1[i3][i2], g[i3][i2]);
}
});
return new float[][][][] {g, u1};
}
private static void smooth2(final float sigma, final float[][][] s, final float[][][] x) {
final int n3 = x.length;
Parallel.loop(
n3,
new Parallel.LoopInt() {
public void compute(int i3) {
float[][] s3 = (s != null) ? s[i3] : null;
float[][] x3 = x[i3];
smooth2(sigma, s3, x3);
}
});
}
private void removeAverage(final float[][][] x) {
final int n1 = x[0][0].length;
Parallel.loop(
1,
n1,
2,
new Parallel.LoopInt() { // i1 = 1, 3, 5, ...
public void compute(int i1) {
removeAverage(i1, x);
}
});
Parallel.loop(
2,
n1,
2,
new Parallel.LoopInt() { // i1 = 2, 4, 6, ...
public void compute(int i1) {
removeAverage(i1, x);
}
});
}
/**
* Gets mappings computed from specified slopes and planarities.
*
* @param s1 sampling of 1st dimension.
* @param s2 sampling of 2nd dimension.
* @param p2 array of slopes of image features.
* @param ep array of planarities of image features.
*/
public Mappings getMappingsFromSlopes(
Sampling s1, Sampling s2, Sampling s3, float[][][] p2, float[][][] p3, float[][][] ep) {
// Sampling parameters.
final int n1 = s1.getCount();
final int n2 = s2.getCount();
final int n3 = s3.getCount();
float d1 = (float) s1.getDelta();
float d2 = (float) s2.getDelta();
float d3 = (float) s3.getDelta();
float f1 = (float) s1.getFirst();
// If necessary, convert units for slopes to samples per sample.
if (d1 != d2) p2 = mul(d2 / d1, p2);
if (d1 != d3) p3 = mul(d3 / d1, p3);
// Compute shifts r(x1,x2,x3), in samples.
float[][][] b = new float[n3][n2][n1]; // right-hand side
float[][][] r = new float[n3][n2][n1]; // shifts, in samples
VecArrayFloat3 vb = new VecArrayFloat3(b);
VecArrayFloat3 vr = new VecArrayFloat3(r);
Smoother3 smoother3 = new Smoother3(n1, n2, n3, _sigma1, _sigma2, _sigma3, ep);
A3 a3 = new A3(smoother3, _weight1, ep, p2, p3);
CgSolver cs = new CgSolver(_small, _niter);
makeRhs(ep, p2, p3, b);
smoother3.applyTranspose(b);
cs.solve(a3, vb, vr);
smoother3.apply(r);
cleanShifts(r);
// Compute u1(x1,x2,x3).
final float[][][] u1 = r;
for (int i3 = 0; i3 < n3; ++i3) {
for (int i2 = 0; i2 < n2; ++i2) {
for (int i1 = 0; i1 < n1; ++i1) {
float x1i = f1 + i1 * d1;
u1[i3][i2][i1] = x1i + r[i3][i2][i1] * d1;
}
}
}
// Compute x1(u1,u2).
final float[][][] x1 = b;
final InverseInterpolator ii = new InverseInterpolator(s1, s1);
Parallel.loop(
n3,
new Parallel.LoopInt() {
public void compute(int i3) {
for (int i2 = 0; i2 < n2; ++i2) ii.invert(u1[i3][i2], x1[i3][i2]);
}
});
return new Mappings(s1, s2, s3, u1, x1);
}
public static float[][] compositeShifts(
final Sampling sf, final float[][] u1, final float[][] u2) {
int n2 = u1.length;
final float[][] uc = new float[n2][];
Parallel.loop(
n2,
new Parallel.LoopInt() {
public void compute(int i2) {
uc[i2] = compositeShifts(sf, u1[i2], u2[i2]);
}
});
return uc;
}
@Deprecated
public static float[][][] transposeLag23(final float[][][] e) {
final int nl = e[0][0].length;
final int n1 = e[0].length;
final int n2 = e.length;
final float[][][] t = new float[n1][n2][nl];
Parallel.loop(
n1,
new Parallel.LoopInt() {
public void compute(int i1) {
for (int i2 = 0; i2 < n2; ++i2) t[i1][i2] = e[i2][i1];
}
});
return t;
}
@Deprecated
public static float[][][] transposeLag12(final float[][][] e) {
final int nl = e[0][0].length;
final int n1 = e[0].length;
final int n2 = e.length;
final float[][][] t = new float[n2][nl][n1];
Parallel.loop(
n2,
new Parallel.LoopInt() {
public void compute(int i2) {
for (int il = 0; il < nl; ++il)
for (int i1 = 0; i1 < n1; ++i1) t[i2][il][i1] = e[i2][i1][il];
}
});
return t;
}
// Smoothing for dimension 3.
private static void smooth3(final float sigma, final float[][][] s, final float[][][] x) {
final int n2 = x[0].length;
final int n3 = x.length;
Parallel.loop(
n2,
new Parallel.LoopInt() {
public void compute(int i2) {
float[][] s2 = (s != null) ? new float[n3][] : null;
float[][] x2 = new float[n3][];
for (int i3 = 0; i3 < n3; ++i3) {
if (s != null) s2[i3] = s[i3][i2];
x2[i3] = x[i3][i2];
}
smooth2(sigma, s2, x2);
}
});
}
private float[][][] apply(final float[][][] ux, final float[][][] f) {
final int n1 = s1.getCount();
final int n2 = s2.getCount();
final int n3 = s3.getCount();
final double d1 = s1.getDelta();
final double f1 = s1.getFirst();
final SincInterpolator si = new SincInterpolator();
final float[][][] g = new float[n3][n2][n1];
Parallel.loop(
n3,
new Parallel.LoopInt() {
public void compute(int i3) {
for (int i2 = 0; i2 < n2; ++i2)
si.interpolate(n1, d1, f1, f[i3][i2], n1, ux[i3][i2], g[i3][i2]);
}
});
return g;
}
public static void normalize(float[][] f, final float nmin, final float nmax) {
final int n1 = f[0].length;
final int n2 = f.length;
final float[][] ff = f;
final float vmin = min(f);
final float vmax = max(f);
final float range = vmax - vmin;
final float nrange = nmax - nmin;
Parallel.loop(
n2,
new Parallel.LoopInt() {
public void compute(int i2) {
for (int i1 = 0; i1 < n1; ++i1) {
float vi = ff[i2][i1];
ff[i2][i1] = nrange * (vi - vmin) / range + nmin;
}
}
});
}
/**
* Shifts and scales alignment errors to be in range [0,1].
*
* @param emin minimum alignment error before normalizing.
* @param emax maximum alignment error before normalizing.
* @param e input/output array of alignment errors.
*/
private static void shiftAndScale(float emin, float emax, float[][][] e) {
// System.out.println("shiftAndScale: emin="+emin+" emax="+emax);
final int nl = e[0][0].length;
final int n1 = e[0].length;
final int n2 = e.length;
final float eshift = emin;
final float escale = (emax > emin) ? 1.0f / (emax - emin) : 1.0f;
final float[][][] ef = e;
Parallel.loop(
n2,
new Parallel.LoopInt() {
public void compute(int i2) {
for (int i1 = 0; i1 < n1; ++i1) {
for (int il = 0; il < nl; ++il) {
ef[i2][i1][il] = (ef[i2][i1][il] - eshift) * escale;
}
}
}
});
}
public float[][][] findScreenPoints(
final float smin,
final float[][][] ss,
final float[][][] u1,
final float[][][] u2,
final float[][][] u3) {
final int n3 = ss.length;
final int n2 = ss[0].length;
final int n1 = ss[0][0].length;
final Sampling s1 = new Sampling(n1);
final Sampling s2 = new Sampling(n2);
final Sampling s3 = new Sampling(n3);
final float[][][] mk = new float[n3][n2][n1];
final SincInterpolator si = new SincInterpolator();
si.setExtrapolation(SincInterpolator.Extrapolation.CONSTANT);
Parallel.loop(
1,
n3 - 1,
new Parallel.LoopInt() {
public void compute(int i3) {
for (int i2 = 1; i2 < n2 - 1; ++i2) {
for (int i1 = 1; i1 < n1 - 1; ++i1) {
float sxi = ss[i3][i2][i1];
float u1i = u1[i3][i2][i1] * 2f;
float u2i = u2[i3][i2][i1] * 2f;
float u3i = u3[i3][i2][i1] * 2f;
float x1m = i1 - u1i;
float x2m = i2 - u2i;
float x3m = i3 - u3i;
float x1p = i1 + u1i;
float x2p = i2 + u2i;
float x3p = i3 + u3i;
float sxm = si.interpolate(s1, s2, s3, ss, x1m, x2m, x3m);
float sxp = si.interpolate(s1, s2, s3, ss, x1p, x2p, x3p);
if (sxi > sxm && sxi > sxp && sxi > smin) mk[i3][i2][i1] = sxi;
}
}
}
});
return mk;
}
public float[][][] scalarFieldM(
final int n1,
final int n2,
final int n3,
final FaultCell[] fc,
final float[][][] fp,
final float[][][] ft) {
final int d2 = 10;
final int d3 = 10;
final int d1 = 10;
// final float v = -1.f;
final float v = 0.0f;
float sigmaNor = 4.0f;
float sigmaPhi = 10.0f;
float sigmaTheta = 20.0f;
final float sw = 1.0f / (sigmaNor * sigmaNor);
final float sv = 1.0f / (sigmaPhi * sigmaPhi);
final float su = 1.0f / (sigmaTheta * sigmaTheta);
int nc = fc.length;
final float[] wp = new float[nc];
final float[][] xf = new float[3][nc];
final float[][] xs = new float[nc][3];
final float[][] ws = new float[nc][6];
final float[][] us = new float[nc][6];
final float[][] vs = new float[nc][6];
setKdTreePointsM(fc, xf, xs, ws, us, vs, wp);
final int[] bs1 = setBounds(n1, xf[0]);
final int[] bs2 = setBounds(n2, xf[1]);
final int[] bs3 = setBounds(n3, xf[2]);
final KdTree kt = new KdTree(xf);
final float[][][] sf = fillfloat(v, n1, n2, n3);
final float[][][] fpp = copy(fp);
final float[][][] ftp = copy(ft);
Parallel.loop(
bs3[0],
bs3[1],
1,
new Parallel.LoopInt() {
public void compute(int i3) {
float[] xmin = new float[3];
float[] xmax = new float[3];
System.out.println("i3=" + i3);
for (int i2 = bs2[0]; i2 < bs2[1]; ++i2) {
for (int i1 = bs1[0]; i1 < bs1[1]; ++i1) {
float[] y = new float[] {i1, i2, i3};
int ne = kt.findNearest(y);
float x1 = xf[0][ne];
float x2 = xf[1][ne];
float x3 = xf[2][ne];
float dd = distance(new float[] {x1, x2, x3}, y);
if (dd > 50.0f) {
continue;
}
getRange(d1, d2, d3, i1, i2, i3, n1, n2, n3, xmin, xmax);
int[] id = kt.findInRange(xmin, xmax);
int nd = id.length;
if (nd < 1) {
continue;
}
sf[i3][i2][i1] = 0.0f;
float wps = 0.0f;
float fpa = 0.0f;
float fta = 0.0f;
float fps = 0.0f;
float fts = 0.0f;
for (int ik = 0; ik < nd; ++ik) {
int ip = id[ik];
float wpi = pow(wp[ip], 8.0f);
float w1s = ws[ip][0];
float w2s = ws[ip][1];
float w3s = ws[ip][2];
float w12 = ws[ip][3];
float w13 = ws[ip][4];
float w23 = ws[ip][5];
float u1s = us[ip][0];
float u2s = us[ip][1];
float u3s = us[ip][2];
float u12 = us[ip][3];
float u13 = us[ip][4];
float u23 = us[ip][5];
float v1s = vs[ip][0];
float v2s = vs[ip][1];
float v3s = vs[ip][2];
float v12 = vs[ip][3];
float v13 = vs[ip][4];
float v23 = vs[ip][5];
float dx1 = i1 - xs[ip][0];
float dx2 = i2 - xs[ip][1];
float dx3 = i3 - xs[ip][2];
float d11 = dx1 * dx1;
float d12 = dx1 * dx2;
float d13 = dx1 * dx3;
float d22 = dx2 * dx2;
float d23 = dx2 * dx3;
float d33 = dx3 * dx3;
float g11 = w1s * d11 + w12 * d12 + w13 * d13;
float g12 = u1s * d11 + u12 * d12 + u13 * d13;
float g13 = v1s * d11 + v12 * d12 + v13 * d13;
float g21 = w12 * d12 + w2s * d22 + w23 * d23;
float g22 = u12 * d12 + u2s * d22 + u23 * d23;
float g23 = v12 * d12 + v2s * d22 + v23 * d23;
float g31 = w13 * d13 + w23 * d23 + w3s * d33;
float g32 = u13 * d13 + u23 * d23 + u3s * d33;
float g33 = v13 * d13 + v23 * d23 + v3s * d33;
float gss = 0.0f;
gss += (g11 + g21 + g31) * sw;
gss += (g12 + g22 + g32) * su;
gss += (g13 + g23 + g33) * sv;
float sfi = exp(-gss) * wpi;
sf[i3][i2][i1] += sfi;
int j1 = fc[ip].i1;
int j2 = fc[ip].i2;
int j3 = fc[ip].i3;
int k1 = fc[ne].i1;
int k2 = fc[ne].i2;
int k3 = fc[ne].i3;
float fpr = fpp[k3][k2][k1];
float fpi = fpp[j3][j2][j1];
if (abs(fpr - fpi) <= 30) {
fps += sfi;
fpa += fpp[j3][j2][j1] * sfi;
}
fts += sfi;
fta += ftp[j3][j2][j1] * sfi;
wps += wpi;
}
ft[i3][i2][i1] = fta / fts;
fp[i3][i2][i1] = fpa / fps;
sf[i3][i2][i1] /= wps;
}
}
}
});
return sf;
}
public float[][][] scalarField(final int n1, final int n2, final int n3, FaultCell[] fc) {
final int d2 = 10;
final int d3 = 10;
final int d1 = 20;
final float v = -1.f;
float sigmaNor = 4.0f;
float sigmaPhi = 6.0f;
float sigmaTheta = 20.0f;
final float sw = 1.0f / (sigmaNor * sigmaNor);
final float sv = 1.0f / (sigmaPhi * sigmaPhi);
final float su = 1.0f / (sigmaTheta * sigmaTheta);
int nc = fc.length;
final float[] wp = new float[nc];
final float[][] xf = new float[3][nc];
final float[][] xs = new float[nc][6];
final float[][] ws = new float[nc][6];
final float[][] us = new float[nc][6];
final float[][] vs = new float[nc][6];
setKdTreePoints(fc, xf, xs, ws, us, vs, wp);
final int[] bs1 = setBounds(n1, xf[0]);
final int[] bs2 = setBounds(n2, xf[1]);
final int[] bs3 = setBounds(n3, xf[2]);
final KdTree kt = new KdTree(xf);
final float[][][] sf = fillfloat(v, n1, n2, n3);
Parallel.loop(
bs3[0],
bs3[1],
1,
new Parallel.LoopInt() {
public void compute(int i3) {
float[] xmin = new float[3];
float[] xmax = new float[3];
System.out.println("i3=" + i3);
for (int i2 = bs2[0]; i2 < bs2[1]; ++i2) {
for (int i1 = bs1[0]; i1 < bs1[1]; ++i1) {
float[] y = new float[] {i1, i2, i3};
int ne = kt.findNearest(y);
float x1 = xf[0][ne];
float x2 = xf[1][ne];
float x3 = xf[2][ne];
float dd = distance(new float[] {x1, x2, x3}, y);
if (dd > 16.0f) {
continue;
}
getRange(d1, d2, d3, i1, i2, i3, n1, n2, n3, xmin, xmax);
int[] id = kt.findInRange(xmin, xmax);
int nd = id.length;
if (nd < 50) {
continue;
}
sf[i3][i2][i1] = 0.0f;
float wps = 0.0f;
for (int ik = 0; ik < nd; ++ik) {
int ip = id[ik];
float wpi = pow(wp[ip], 8.0f);
float w1s = ws[ip][0];
float w2s = ws[ip][1];
float w3s = ws[ip][2];
float w12 = ws[ip][3];
float w13 = ws[ip][4];
float w23 = ws[ip][5];
float u1s = us[ip][0];
float u2s = us[ip][1];
float u3s = us[ip][2];
float u12 = us[ip][3];
float u13 = us[ip][4];
float u23 = us[ip][5];
float v1s = vs[ip][0];
float v2s = vs[ip][1];
float v3s = vs[ip][2];
float v12 = vs[ip][3];
float v13 = vs[ip][4];
float v23 = vs[ip][5];
float x1m = i1 - xs[ip][0];
float x2m = i2 - xs[ip][1];
float x3m = i3 - xs[ip][2];
float x1p = i1 - xs[ip][3];
float x2p = i2 - xs[ip][4];
float x3p = i3 - xs[ip][5];
float x1sm = x1m * x1m;
float x2sm = x2m * x2m;
float x3sm = x3m * x3m;
float x12m = x1m * x2m;
float x13m = x1m * x3m;
float x23m = x2m * x3m;
float x1sp = x1p * x1p;
float x2sp = x2p * x2p;
float x3sp = x3p * x3p;
float x12p = x1p * x2p;
float x13p = x1p * x3p;
float x23p = x2p * x3p;
float g11m = w1s * x1sm + w12 * x12m + w13 * x13m;
float g12m = u1s * x1sm + u12 * x12m + u13 * x13m;
float g13m = v1s * x1sm + v12 * x12m + v13 * x13m;
float g21m = w12 * x12m + w2s * x2sm + w23 * x23m;
float g22m = u12 * x12m + u2s * x2sm + u23 * x23m;
float g23m = v12 * x12m + v2s * x2sm + v23 * x23m;
float g31m = w13 * x13m + w23 * x23m + w3s * x3sm;
float g32m = u13 * x13m + u23 * x23m + u3s * x3sm;
float g33m = v13 * x13m + v23 * x23m + v3s * x3sm;
float g11p = w1s * x1sp + w12 * x12p + w13 * x13p;
float g12p = u1s * x1sp + u12 * x12p + u13 * x13p;
float g13p = v1s * x1sp + v12 * x12p + v13 * x13p;
float g21p = w12 * x12p + w2s * x2sp + w23 * x23p;
float g22p = u12 * x12p + u2s * x2sp + u23 * x23p;
float g23p = v12 * x12p + v2s * x2sp + v23 * x23p;
float g31p = w13 * x13p + w23 * x23p + w3s * x3sp;
float g32p = u13 * x13p + u23 * x23p + u3s * x3sp;
float g33p = v13 * x13p + v23 * x23p + v3s * x3sp;
float gssm =
(g11m + g21m + g31m) * sw
+ (g12m + g22m + g32m) * su
+ (g13m + g23m + g33m) * sv;
float gssp =
(g11p + g21p + g31p) * sw
+ (g12p + g22p + g32p) * su
+ (g13p + g23p + g33p) * sv;
sf[i3][i2][i1] += (exp(-gssp) - exp(-gssm)) * wpi;
wps += wpi;
}
sf[i3][i2][i1] /= wps;
}
}
}
});
return sf;
}