bool searchModel_minimalSamples(const Kernel &kernel,
typename Kernel::Model* bestModel,
InliersVec *bestInliers = 0,
double *bestRMS = 0)
{
assert(kernel.NumSamples() == Kernel::MinimumSamples());
InliersVec isInlier(kernel.NumSamples());
int best_score = 0;
bool bestModelFound = false;
std::vector<typename Kernel::Model> possibleModels;
kernel.ComputeModelFromMinimumSamples(&possibleModels);
for (std::size_t i = 0; i < possibleModels.size(); ++i) {
double rms;
int model_score = kernel.ComputeInliersForModel(possibleModels[i], &isInlier, bestRMS ? &rms : 0);
if (model_score > best_score) {
if (bestRMS) {
*bestRMS = rms;
}
best_score = model_score;
*bestModel = possibleModels[i];
bestModelFound = true;
}
}
if (!bestModelFound) {
return false;
}
if (bestInliers) {
*bestInliers = isInlier;
}
if (bestRMS) {
*bestRMS = kernel.ScalarUnormalize(*bestRMS);
}
kernel.Unnormalize(bestModel);
return true;
}
ProsacReturnCodeEnum prosac(const Kernel &kernel,
typename Kernel::Model* bestModel,
InliersVec *bestInliers = 0,
double *bestRMS = 0)
{
assert(bestModel);
const int N = (int)std::min(kernel.NumSamples(), (std::size_t)RAND_MAX);
// For us, the draw set is the same as the verification set
const int N_draw = N;
const int m = (int)Kernel::MinimumSamples();
// Test if we have sufficient points for the kernel.
if (N < m) {
return eProsacReturnCodeNotEnoughPoints;
} else if (N == m) {
bool ok = searchModel_minimalSamples(kernel, bestModel, bestInliers, bestRMS);
return ok ? eProsacReturnCodeFoundModel : eProsacReturnCodeNoModelFound;
}
InliersVec isInlier(N);
#ifndef PROSAC_DISABLE_LO_RANSAC
InliersVec isInlierLO(N);
#endif
/* NOTE: the PROSAC article sets T_N (the number of iterations before PROSAC becomes RANSAC) to 200000,
but that means :
- only 535 correspondences out of 1000 will be used after 2808 iterations (60% outliers)
- 395 588 (50%)
- 170 163 (40%)
(the # of iterations is the # of RANSAC draws for a 0.99 confidence
of finding the right model given the percentage of outliers)
QUESTION: Is it more reasonable to set it to the maximum number of iterations we plan to
do given the percentage of outlier?
MY ANSWER: If you know that you won't draw more than XX samples (say 2808, because you only
accept 60% outliers), then it's more reasonable to set N to that value, in order to give
all correspondences a chance to be drawn (even if that chance is very small for the last ones).
Anyway, PROSAC should find many inliers in the first rounds and stop right away.
T_N=2808 gives:
- only 961 correspondences out of 1000 will be used after 2808 iterations (60% outliers)
- 595 588 (50%)
- 177 163 (40%)
*/
const int T_N = kernel.maxOutliersProportion >= 1. ? std::numeric_limits<int>::max() : niter_RANSAC(kernel.probability, kernel.maxOutliersProportion, m, kernel.iMaxIter);
const int t_max = kernel.iMaxIter > 0 ? kernel.iMaxIter : T_N;
const double beta = kernel.getProsacBetaParam();
assert(beta > 0. && beta < 1.);
int n_star = N; // termination length (see sec. 2.2 Stopping criterion)
int I_n_star = 0; // number of inliers found within the first n_star data points
int I_N_best = 0; // best number of inliers found so far (store the model that goes with it)
const int I_N_min = (1. - kernel.maxOutliersProportion) * N; // the minimum number of total inliers
int t = 0; // iteration number
int n = m; // we draw samples from the set U_n of the top n data points
double T_n = T_N; // average number of samples {M_i}_{i=1}^{T_N} that contain samples from U_n only
int T_n_prime = 1; // integer version of T_n, see eq. (4)
for(int i = 0; i < m; ++i) {
T_n *= (double)(n - i) / (N - i);
}
int k_n_star = T_N; // number of samples to draw to reach the maximality constraint
bool bestModelFound = false;
std::vector<std::size_t> sample(m);
// Note: the condition (I_N_best < I_N_min) was not in the original paper, but it is reasonable:
// we sholdn't stop if we haven't found the expected number of inliers
while (((I_N_best < I_N_min) || t <= k_n_star) && t < T_N && t <= t_max) {
int I_N; // total number of inliers for that sample
// Choice of the hypothesis generation set
t = t + 1;
// from the paper, eq. (5) (not Algorithm1):
// "The growth function is then defined as
// g(t) = min {n : T′n ≥ t}"
// Thus n should be incremented if t > T'n, not if t = T'n as written in the algorithm 1
if ((t > T_n_prime) && (n < n_star)) {
double T_nplus1 = (T_n * (n+1)) / (n+1-m);
n = n+1;
T_n_prime = T_n_prime + std::ceil(T_nplus1 - T_n);
T_n = T_nplus1;
}
// Draw semi-random sample (note that the test condition from Algorithm1 in the paper is reversed):
if (t > T_n_prime) {
// during the finishing stage (n== n_star && t > T_n_prime), draw a standard RANSAC sample
// The sample contains m points selected from U_n at random
deal(n, m, sample);
} else {
// The sample contains m-1 points selected from U_{n−1} at random and u_n
deal(n - 1, m - 1, sample);
sample[m - 1] = n - 1;
}
// INSERT Compute model parameters p_t from the sample M_t
std::vector<typename Kernel::Model> possibleModels;
kernel.ComputeModelFromMinimumSamples(sample, &possibleModels);
for (std::size_t modelNb = 0; modelNb < possibleModels.size(); ++modelNb) {
// Find support of the model with parameters p_t
// From first paragraph of section 2: "The hypotheses are verified against all data"
double RMS;
I_N = kernel.ComputeInliersForModel(possibleModels[modelNb], &isInlier, bestRMS ? &RMS : 0);
if (I_N > I_N_best) {
int n_best; // best value found so far in terms of inliers ratio
int I_n_best; // number of inliers for n_best
int I_N_draw; // number of inliers withing the N_draw first data
// INSERT (OPTIONAL): Test for degenerate model configuration (DEGENSAC)
// (i.e. discard the sample if more than 1 model is consistent with the sample)
// ftp://cmp.felk.cvut.cz/pub/cmp/articles/matas/chum-degen-cvpr05.pdf
// Do local optimization, and recompute the support (LO-RANSAC)
// http://cmp.felk.cvut.cz/~matas/papers/chum-dagm03.pdf
// for the fundamental matrix, the normalized 8-points algorithm performs very well:
// http://axiom.anu.edu.au/~hartley/Papers/fundamental/ICCV-final/fundamental.pdf
// Store the best model
*bestModel = possibleModels[modelNb];
bestModelFound = true;
if (bestRMS) {
*bestRMS = RMS;
}
#ifndef PROSAC_DISABLE_LO_RANSAC
int loransac_iter = 0;
while (I_N > I_N_best) {
I_N_best = I_N;
if (kernel.iMaxLOIter < 0 || loransac_iter < kernel.iMaxLOIter) {
// Continue while LO-ransac finds a better support
typename Kernel::Model modelLO;
double RMS_L0;
bool modelOptimized = kernel.OptimizeModel(*bestModel, isInlier, &modelLO);
if (modelOptimized) {
// IN = findSupport(/* model, sample, */ N, isInlier);
int I_N_LO = kernel.ComputeInliersForModel(modelLO, &isInlierLO, bestRMS ? &RMS_L0 : 0);
if (I_N_LO > I_N_best) {
isInlier = isInlierLO;
*bestModel = modelLO;
if (bestRMS) {
*bestRMS = RMS_L0;
}
I_N = I_N_LO;
}
}
++loransac_iter;
} // LO-RANSAC
}
#else
if (I_N > I_N_best) {
I_N_best = I_N;
}
#endif
if (bestInliers) {
*bestInliers = isInlier;
}
// Select new termination length n_star if possible, according to Sec. 2.2.
// Note: the original paper seems to do it each time a new sample is drawn,
// but this really makes sense only if the new sample is better than the previous ones.
n_best = N;
I_n_best = I_N_best;
I_N_draw = std::accumulate(isInlier.begin(), isInlier.begin() + N_draw, 0);
#ifndef PROSAC_DISABLE_N_STAR_OPTIMIZATION
int n_test; // test value for the termination length
int I_n_test; // number of inliers for that test value
double epsilon_n_best = (double)I_n_best/n_best;
for (n_test = N, I_n_test = I_N_draw; n_test > m; n_test--) {
// Loop invariants:
// - I_n_test is the number of inliers for the n_test first correspondences
// - n_best is the value between n_test+1 and N that maximizes the ratio I_n_best/n_best
assert(n_test >= I_n_test);
// * Non-randomness : In >= Imin(n*) (eq. (9))
// * Maximality: the number of samples that were drawn so far must be enough
// so that the probability of having missed a set of inliers is below eta=0.01.
// This is the classical RANSAC termination criterion (HZ 4.7.1.2, eq. (4.18)),
// except that it takes into account only the n first samples (not the total number of samples).
// kn_star = log(eta0)/log(1-(In_star/n_star)^m) (eq. (12))
// We have to minimize kn_star, e.g. maximize I_n_star/n_star
//printf("n_best=%d, I_n_best=%d, n_test=%d, I_n_test=%d\n",
// n_best, I_n_best, n_test, I_n_test);
// a straightforward implementation would use the following test:
//if (I_n_test > epsilon_n_best*n_test) {
// However, since In is binomial, and in the case of evenly distributed inliers,
// a better test would be to reduce n_star only if there's a significant improvement in
// epsilon. Thus we use a Chi-squared test (P=0.10), together with the normal approximation
// to the binomial (mu = epsilon_n_star*n_test, sigma=sqrt(n_test*epsilon_n_star*(1-epsilon_n_star)).
// There is a significant difference between the two tests (e.g. with the findSupport
// functions provided above).
// We do the cheap test first, and the expensive test only if the cheap one passes.
if (( I_n_test * n_best > I_n_best * n_test ) &&
( I_n_test > epsilon_n_best * n_test + std::sqrt(n_test * epsilon_n_best * (1. - epsilon_n_best) * 2.706) )) {
if (I_n_test < Prosac_Imin(m,n_test,beta)) {
// equation 9 not satisfied: no need to test for smaller n_test values anyway
break; // jump out of the for(n_test) loop
}
n_best = n_test;
I_n_best = I_n_test;
epsilon_n_best = (double)I_n_best / n_best;
}
// prepare for next loop iteration
I_n_test -= isInlier[n_test - 1];
} // for(n_test ...
#endif // #ifndef PROSAC_DISABLE_N_STAR_OPTIMIZATION
// is the best one we found even better than n_star?
if ( I_n_best * n_star > I_n_star * n_best ) {
assert(n_best >= I_n_best);
// update all values
n_star = n_best;
I_n_star = I_n_best;
k_n_star = niter_RANSAC(1. - kernel.eta0, 1. - I_n_star / (double)n_star, m, T_N);
}
} // if (I_N > I_N_best)
} //for (modelNb ...
} // while(t <= k_n_star ...
if (!bestModelFound) {
return eProsacReturnCodeNoModelFound;
}
if (bestRMS) {
*bestRMS = kernel.ScalarUnormalize(*bestRMS);
}
kernel.Unnormalize(bestModel);
if (t == t_max) {
return eProsacReturnCodeMaxIterationsParamReached ;
}
if (t == T_N) {
return eProsacReturnCodeMaxIterationsFromProportionParamReached;
}
if (I_N_best == m) {
return eProsacReturnCodeInliersIsMinSamples;
}
return eProsacReturnCodeFoundModel;
} // prosac