typename Kernel::Model MaxConsensus
(
const Kernel &kernel,
const Scorer &scorer,
std::vector<uint32_t> *best_inliers = nullptr,
uint32_t max_iteration = 1024
)
{
const uint32_t min_samples = Kernel::MINIMUM_SAMPLES;
const uint32_t total_samples = kernel.NumSamples();
size_t best_num_inliers = 0;
typename Kernel::Model best_model;
// Test if we have sufficient points to for the kernel.
if (total_samples < min_samples) {
if (best_inliers) {
best_inliers->resize(0);
}
return best_model;
}
// In this robust estimator, the scorer always works on all the data points
// at once. So precompute the list ahead of time.
std::vector<uint32_t> all_samples(total_samples);
std::iota(all_samples.begin(), all_samples.end(), 0);
// Random number generator configuration
std::mt19937 random_generator(std::mt19937::default_seed);
std::vector<uint32_t> sample;
for (uint32_t iteration = 0; iteration < max_iteration; ++iteration) {
UniformSample(min_samples, random_generator, &all_samples, &sample);
std::vector<typename Kernel::Model> models;
kernel.Fit(sample, &models);
// Compute costs for each fit.
for (const auto& model_it : models) {
std::vector<uint32_t> inliers;
scorer.Score(kernel, model_it, all_samples, &inliers);
if (best_num_inliers < inliers.size()) {
best_num_inliers = inliers.size();
best_model = model_it;
if (best_inliers) {
best_inliers->swap(inliers);
}
}
}
}
return best_model;
}
typename Kernel::Model RANSAC(
const Kernel &kernel,
const Scorer &scorer,
std::vector<size_t> *best_inliers = nullptr ,
size_t *best_score = nullptr , // Found number of inliers
double outliers_probability = 1e-2)
{
assert(outliers_probability < 1.0);
assert(outliers_probability > 0.0);
size_t iteration = 0;
const size_t min_samples = Kernel::MINIMUM_SAMPLES;
const size_t total_samples = kernel.NumSamples();
size_t max_iterations = 100;
const size_t really_max_iterations = 4096;
size_t best_num_inliers = 0;
double best_inlier_ratio = 0.0;
typename Kernel::Model best_model;
// Test if we have sufficient points for the kernel.
if (total_samples < min_samples) {
if (best_inliers) {
best_inliers->resize(0);
}
return best_model;
}
// In this robust estimator, the scorer always works on all the data points
// at once. So precompute the list ahead of time [0,..,total_samples].
std::vector<size_t> all_samples(total_samples);
std::iota(all_samples.begin(), all_samples.end(), 0);
std::vector<size_t> sample;
for (iteration = 0;
iteration < max_iterations &&
iteration < really_max_iterations; ++iteration) {
UniformSample(min_samples, &all_samples, &sample);
std::vector<typename Kernel::Model> models;
kernel.Fit(sample, &models);
// Compute the inlier list for each fit.
for (size_t i = 0; i < models.size(); ++i) {
std::vector<size_t> inliers;
scorer.Score(kernel, models[i], all_samples, &inliers);
if (best_num_inliers < inliers.size()) {
best_num_inliers = inliers.size();
best_inlier_ratio = inliers.size() / double(total_samples);
best_model = models[i];
if (best_inliers) {
best_inliers->swap(inliers);
}
}
if (best_inlier_ratio) {
max_iterations = IterationsRequired(min_samples,
outliers_probability,
best_inlier_ratio);
}
}
}
if (best_score)
*best_score = best_num_inliers;
return best_model;
}
double LeastMedianOfSquares(const Kernel &kernel,
typename Kernel::Model * model = NULL,
double* outlierThreshold = NULL,
double outlierRatio=0.5,
double minProba=0.99)
{
const size_t min_samples = Kernel::MINIMUM_SAMPLES;
const size_t total_samples = kernel.NumSamples();
std::vector<double> residuals(total_samples); // Array for storing residuals
std::vector<size_t> vec_sample(min_samples);
double dBestMedian = std::numeric_limits<double>::max();
// Required number of iterations is evaluated from outliers ratio
const size_t N = (min_samples<total_samples)?
getNumSamples(minProba, outlierRatio, min_samples): 0;
for (size_t i=0; i < N; i++) {
// Get Samples indexes
UniformSample(min_samples, total_samples, &vec_sample);
// Estimate parameters: the solutions are stored in a vector
std::vector<typename Kernel::Model> models;
kernel.Fit(vec_sample, &models);
// Now test the solutions on the whole data
for (size_t k = 0; k < models.size(); ++k) {
//Compute Residuals :
for (size_t l = 0; l < total_samples; ++l) {
double error = kernel.Error(l, models[k]);
residuals[l] = error;
}
// Compute median
std::vector<double>::iterator itMedian = residuals.begin() +
std::size_t( total_samples*(1.-outlierRatio) );
std::nth_element(residuals.begin(), itMedian, residuals.end());
double median = *itMedian;
// Store best solution
if(median < dBestMedian) {
dBestMedian = median;
if (model) (*model) = models[k];
}
}
}
// This array of precomputed values corresponds to the inverse
// cumulative function for a normal distribution. For more information
// consult the litterature (Robust Regression for Outlier Detection,
// rouseeuw-leroy). The values are computed for each 5%
static const double ICDF[21] = {
1.4e16, 15.94723940, 7.957896558, 5.287692054,
3.947153876, 3.138344200, 2.595242369, 2.203797543,
1.906939402, 1.672911853, 1.482602218, 1.323775627,
1.188182950, 1.069988721, 0.9648473415, 0.8693011162,
0.7803041458, 0.6946704675, 0.6079568319,0.5102134568,
0.3236002672
};
// Evaluate the outlier threshold
if(outlierThreshold) {
double sigma = ICDF[int((1.-outlierRatio)*20.)] *
(1. + 5. / double(total_samples - min_samples));
*outlierThreshold = (double)(sigma * sigma * dBestMedian * 4.);
if (N==0) *outlierThreshold = std::numeric_limits<double>::max();
}
return dBestMedian;
}
std::pair<double, double> ACRANSAC(const Kernel &kernel,
std::vector<size_t> & vec_inliers,
size_t nIter = 1024,
typename Kernel::Model * model = NULL,
double precision = std::numeric_limits<double>::infinity(),
bool bVerbose = false)
{
vec_inliers.clear();
const size_t sizeSample = Kernel::MINIMUM_SAMPLES;
const size_t nData = kernel.NumSamples();
if(nData <= (size_t)sizeSample)
return std::make_pair(0.0,0.0);
const double maxThreshold = (precision==std::numeric_limits<double>::infinity()) ?
std::numeric_limits<double>::infinity() :
precision * kernel.normalizer2()(0,0) * kernel.normalizer2()(0,0);
std::vector<ErrorIndex> vec_residuals(nData); // [residual,index]
std::vector<double> vec_residuals_(nData);
std::vector<size_t> vec_sample(sizeSample); // Sample indices
// Possible sampling indices (could change in the optimization phase)
std::vector<size_t> vec_index(nData);
for (size_t i = 0; i < nData; ++i)
vec_index[i] = i;
// Precompute log combi
double loge0 = log10((double)Kernel::MAX_MODELS * (nData-sizeSample));
std::vector<float> vec_logc_n, vec_logc_k;
makelogcombi_n(nData, vec_logc_n);
makelogcombi_k(sizeSample, nData, vec_logc_k);
// Output parameters
double minNFA = std::numeric_limits<double>::infinity();
double errorMax = std::numeric_limits<double>::infinity();
// Reserve 10% of iterations for focused sampling
size_t nIterReserve = nIter/10;
nIter -= nIterReserve;
// Main estimation loop.
for (size_t iter=0; iter < nIter; ++iter) {
UniformSample(sizeSample, vec_index, &vec_sample); // Get random sample
std::vector<typename Kernel::Model> vec_models; // Up to max_models solutions
kernel.Fit(vec_sample, &vec_models);
// Evaluate models
bool better = false;
for (size_t k = 0; k < vec_models.size(); ++k) {
// Residuals computation and ordering
kernel.Errors(vec_models[k], vec_residuals_);
for (size_t i = 0; i < nData; ++i) {
const double error = vec_residuals_[i];
vec_residuals[i] = ErrorIndex(error, i);
}
std::sort(vec_residuals.begin(), vec_residuals.end());
// Most meaningful discrimination inliers/outliers
const ErrorIndex best = bestNFA(
sizeSample,
kernel.logalpha0(),
vec_residuals,
loge0,
maxThreshold,
vec_logc_n,
vec_logc_k,
kernel.multError());
if (best.first < minNFA /*&& vec_residuals[best.second-1].first < errorMax*/) {
// A better model was found
better = true;
minNFA = best.first;
vec_inliers.resize(best.second);
for (size_t i=0; i<best.second; ++i)
vec_inliers[i] = vec_residuals[i].second;
errorMax = vec_residuals[best.second-1].first; // Error threshold
if(model) *model = vec_models[k];
if(bVerbose) {
std::cout << " nfa=" << minNFA
<< " inliers=" << best.second
<< " precisionNormalized=" << errorMax
<< " precision=" << kernel.unormalizeError(errorMax)
<< " (iter=" << iter;
std::cout << ",sample=";
std::copy(vec_sample.begin(), vec_sample.end(),
std::ostream_iterator<size_t>(std::cout, ","));
std::cout << ")" <<std::endl;
}
}
}
// ACRANSAC optimization: draw samples among best set of inliers so far
if((better && minNFA<0) || (iter+1==nIter && nIterReserve)) {
if(vec_inliers.empty()) { // No model found at all so far
nIter++; // Continue to look for any model, even not meaningful
nIterReserve--;
} else {
// ACRANSAC optimization: draw samples among best set of inliers so far
vec_index = vec_inliers;
if(nIterReserve) {
nIter = iter+1+nIterReserve;
nIterReserve=0;
}
}
}
}
if(minNFA >= 0)
vec_inliers.clear();
if (!vec_inliers.empty())
{
if (model)
kernel.Unnormalize(model);
errorMax = kernel.unormalizeError(errorMax);
}
return std::make_pair(errorMax, minNFA);
}
typename Kernel::Model RANSAC(
const Kernel &kernel,
const Scorer &scorer,
std::vector<size_t> *best_inliers = NULL,
double *best_score = NULL,
double outliers_probability = 1e-2)
{
assert(outliers_probability < 1.0);
assert(outliers_probability > 0.0);
size_t iteration = 0;
const size_t min_samples = Kernel::MINIMUM_SAMPLES;
const size_t total_samples = kernel.NumSamples();
size_t max_iterations = 100;
const size_t really_max_iterations = 4096;
size_t best_num_inliers = 0;
double best_cost = std::numeric_limits<double>::infinity();
double best_inlier_ratio = 0.0;
typename Kernel::Model best_model;
// Test if we have sufficient points for the kernel.
if (total_samples < min_samples) {
if (best_inliers) {
best_inliers->resize(0);
}
return best_model;
}
// In this robust estimator, the scorer always works on all the data points
// at once. So precompute the list ahead of time.
std::vector<size_t> all_samples;
for (size_t i = 0; i < total_samples; ++i) {
all_samples.push_back(i);
}
std::vector<size_t> sample;
for (iteration = 0;
iteration < max_iterations &&
iteration < really_max_iterations; ++iteration) {
UniformSample(min_samples, total_samples, &sample);
std::vector<typename Kernel::Model> models;
kernel.Fit(sample, &models);
// Compute costs for each fit.
for (size_t i = 0; i < models.size(); ++i) {
std::vector<size_t> inliers;
double cost = scorer.Score(kernel, models[i], all_samples, &inliers);
if (cost < best_cost) {
best_cost = cost;
best_inlier_ratio = inliers.size() / double(total_samples);
best_num_inliers = inliers.size();
best_model = models[i];
if (best_inliers) {
best_inliers->swap(inliers);
}
}
if (best_inlier_ratio) {
max_iterations = IterationsRequired(min_samples,
outliers_probability,
best_inlier_ratio);
}
}
}
if (best_score)
*best_score = best_cost;
return best_model;
}