Bronger, thank you for your response.
But from the code of "mod-coord.cpp" (this file locates in
~/lensfun-0.2.7/libs/lensfun/mod-coord.cpp), we can see the following
code (for example for poly3 model, but the other models follow the
similar rule):
void lfExtModifier::ModifyCoord_Dist_Poly3 (void *data, float *iocoord, int
count)
{
const float inv_k1 = *(float *)data;
const float one_minus_k1_div_k1 = (1 - 1.0 / inv_k1) * inv_k1;
for (float *end = iocoord + count * 2; iocoord < end; iocoord += 2)
{
float x = iocoord [0];
float y = iocoord [1];
double ru = sqrt (x * x + y * y);
if (ru == 0.0)
continue;
float ru_div_k1 = ru * inv_k1;
// Use Newton's method to avoid dealing with complex numbers
// When carefully tuned this works almost as fast as Cardano's
// method (and we don't use complex numbers in it, which is
// required for a full solution!)
//
// Original function: Ru = k1 * Rd^3 + (1 - k1) * Rd
// Target function: k1 * Rd^3 + (1 - k1) * Rd - Ru = 0
// Divide by k1: Rd^3 + Rd * (1 - k1)/k1 - Ru/k1 = 0
// Derivative: 3 * Rd^2 + (1 - k1)/k1
double rd = ru;
for (int step = 0; ; step++)
{
double frd = rd * rd * rd + rd * one_minus_k1_div_k1 - ru_div_k1;
if (frd >= -NEWTON_EPS && frd < NEWTON_EPS)
break;
if (step > 5)
// Does not converge, no real solution in this area?
goto next_pixel;
rd -= frd / (3 * rd * rd + one_minus_k1_div_k1);
}
if (rd < 0.0)
continue; // Negative radius does not make sense at all
rd /= ru;
iocoord [0] = x * rd;
iocoord [1] = y * rd;
next_pixel:
;
}
}
void lfExtModifier::ModifyCoord_UnDist_Poly3 (void *data, float *iocoord, int
count)
{
// Ru = Rd * (1 - k1 + k1 * Rd^2)
const float k1 = *(float *)data;
const float one_minus_k1 = 1.0 - k1;
for (float *end = iocoord + count * 2; iocoord < end; iocoord += 2)
{
const float x = iocoord [0];
const float y = iocoord [1];
const float poly2 = one_minus_k1 + k1 * (x * x + y * y);
iocoord [0] = x * poly2;
iocoord [1] = y * poly2;
}
}
It seems that: given a distorted radius (Rd), we can directly compute
the undistorted radius (Ru), according the distortion forumula.
While given a undistorted radius (Ru), we need a Newton method to
solve the distorted radius (Rd).
So I think that Rd is measured in the original image (taken by the
camera), whereas Ru is measured in the destination picture (which is
supposed to be undistorted)?
Do you agree ? Anyone else have comments ?
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