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#include "precomp.hpp"
namespace cv
{
namespace ml
{
const double minEigenValue = DBL_EPSILON;
class CV_EXPORTS EMImpl : public EM
{
public:
int nclusters;
int covMatType;
TermCriteria termCrit;
CV_IMPL_PROPERTY_S(TermCriteria, TermCriteria, termCrit)
void setClustersNumber(int val)
{
nclusters = val;
CV_Assert(nclusters > 1);
}
int getClustersNumber() const
{
return nclusters;
}
void setCovarianceMatrixType(int val)
{
covMatType = val;
CV_Assert(covMatType == COV_MAT_SPHERICAL ||
covMatType == COV_MAT_DIAGONAL ||
covMatType == COV_MAT_GENERIC);
}
int getCovarianceMatrixType() const
{
return covMatType;
}
EMImpl()
{
nclusters = DEFAULT_NCLUSTERS;
covMatType=EM::COV_MAT_DIAGONAL;
termCrit = TermCriteria(TermCriteria::COUNT+TermCriteria::EPS, EM::DEFAULT_MAX_ITERS, 1e-6);
}
virtual ~EMImpl() {}
void clear()
{
trainSamples.release();
trainProbs.release();
trainLogLikelihoods.release();
trainLabels.release();
weights.release();
means.release();
covs.clear();
covsEigenValues.clear();
invCovsEigenValues.clear();
covsRotateMats.clear();
logWeightDivDet.release();
}
bool train(const Ptr<TrainData>& data, int)
{
Mat samples = data->getTrainSamples(), labels;
return trainEM(samples, labels, noArray(), noArray());
}
bool trainEM(InputArray samples,
OutputArray logLikelihoods,
OutputArray labels,
OutputArray probs)
{
Mat samplesMat = samples.getMat();
setTrainData(START_AUTO_STEP, samplesMat, 0, 0, 0, 0);
return doTrain(START_AUTO_STEP, logLikelihoods, labels, probs);
}
bool trainE(InputArray samples,
InputArray _means0,
InputArray _covs0,
InputArray _weights0,
OutputArray logLikelihoods,
OutputArray labels,
OutputArray probs)
{
Mat samplesMat = samples.getMat();
std::vector<Mat> covs0;
_covs0.getMatVector(covs0);
Mat means0 = _means0.getMat(), weights0 = _weights0.getMat();
setTrainData(START_E_STEP, samplesMat, 0, !_means0.empty() ? &means0 : 0,
!_covs0.empty() ? &covs0 : 0, !_weights0.empty() ? &weights0 : 0);
return doTrain(START_E_STEP, logLikelihoods, labels, probs);
}
bool trainM(InputArray samples,
InputArray _probs0,
OutputArray logLikelihoods,
OutputArray labels,
OutputArray probs)
{
Mat samplesMat = samples.getMat();
Mat probs0 = _probs0.getMat();
setTrainData(START_M_STEP, samplesMat, !_probs0.empty() ? &probs0 : 0, 0, 0, 0);
return doTrain(START_M_STEP, logLikelihoods, labels, probs);
}
float predict(InputArray _inputs, OutputArray _outputs, int) const
{
bool needprobs = _outputs.needed();
Mat samples = _inputs.getMat(), probs, probsrow;
int ptype = CV_32F;
float firstres = 0.f;
int i, nsamples = samples.rows;
if( needprobs )
{
if( _outputs.fixedType() )
ptype = _outputs.type();
_outputs.create(samples.rows, nclusters, ptype);
}
else
nsamples = std::min(nsamples, 1);
for( i = 0; i < nsamples; i++ )
{
if( needprobs )
probsrow = probs.row(i);
Vec2d res = computeProbabilities(samples.row(i), needprobs ? &probsrow : 0, ptype);
if( i == 0 )
firstres = (float)res[1];
}
return firstres;
}
Vec2d predict2(InputArray _sample, OutputArray _probs) const
{
int ptype = CV_32F;
Mat sample = _sample.getMat();
CV_Assert(isTrained());
CV_Assert(!sample.empty());
if(sample.type() != CV_64FC1)
{
Mat tmp;
sample.convertTo(tmp, CV_64FC1);
sample = tmp;
}
sample.reshape(1, 1);
Mat probs;
if( _probs.needed() )
{
if( _probs.fixedType() )
ptype = _probs.type();
_probs.create(1, nclusters, ptype);
probs = _probs.getMat();
}
return computeProbabilities(sample, !probs.empty() ? &probs : 0, ptype);
}
bool isTrained() const
{
return !means.empty();
}
bool isClassifier() const
{
return true;
}
int getVarCount() const
{
return means.cols;
}
String getDefaultName() const
{
return "opencv_ml_em";
}
static void checkTrainData(int startStep, const Mat& samples,
int nclusters, int covMatType, const Mat* probs, const Mat* means,
const std::vector<Mat>* covs, const Mat* weights)
{
// Check samples.
CV_Assert(!samples.empty());
CV_Assert(samples.channels() == 1);
int nsamples = samples.rows;
int dim = samples.cols;
// Check training params.
CV_Assert(nclusters > 0);
CV_Assert(nclusters <= nsamples);
CV_Assert(startStep == START_AUTO_STEP ||
startStep == START_E_STEP ||
startStep == START_M_STEP);
CV_Assert(covMatType == COV_MAT_GENERIC ||
covMatType == COV_MAT_DIAGONAL ||
covMatType == COV_MAT_SPHERICAL);
CV_Assert(!probs ||
(!probs->empty() &&
probs->rows == nsamples && probs->cols == nclusters &&
(probs->type() == CV_32FC1 || probs->type() == CV_64FC1)));
CV_Assert(!weights ||
(!weights->empty() &&
(weights->cols == 1 || weights->rows == 1) && static_cast<int>(weights->total()) == nclusters &&
(weights->type() == CV_32FC1 || weights->type() == CV_64FC1)));
CV_Assert(!means ||
(!means->empty() &&
means->rows == nclusters && means->cols == dim &&
means->channels() == 1));
CV_Assert(!covs ||
(!covs->empty() &&
static_cast<int>(covs->size()) == nclusters));
if(covs)
{
const Size covSize(dim, dim);
for(size_t i = 0; i < covs->size(); i++)
{
const Mat& m = (*covs)[i];
CV_Assert(!m.empty() && m.size() == covSize && (m.channels() == 1));
}
}
if(startStep == START_E_STEP)
{
CV_Assert(means);
}
else if(startStep == START_M_STEP)
{
CV_Assert(probs);
}
}
static void preprocessSampleData(const Mat& src, Mat& dst, int dstType, bool isAlwaysClone)
{
if(src.type() == dstType && !isAlwaysClone)
dst = src;
else
src.convertTo(dst, dstType);
}
static void preprocessProbability(Mat& probs)
{
max(probs, 0., probs);
const double uniformProbability = (double)(1./probs.cols);
for(int y = 0; y < probs.rows; y++)
{
Mat sampleProbs = probs.row(y);
double maxVal = 0;
minMaxLoc(sampleProbs, 0, &maxVal);
if(maxVal < FLT_EPSILON)
sampleProbs.setTo(uniformProbability);
else
normalize(sampleProbs, sampleProbs, 1, 0, NORM_L1);
}
}
void setTrainData(int startStep, const Mat& samples,
const Mat* probs0,
const Mat* means0,
const std::vector<Mat>* covs0,
const Mat* weights0)
{
clear();
checkTrainData(startStep, samples, nclusters, covMatType, probs0, means0, covs0, weights0);
bool isKMeansInit = (startStep == START_AUTO_STEP) || (startStep == START_E_STEP && (covs0 == 0 || weights0 == 0));
// Set checked data
preprocessSampleData(samples, trainSamples, isKMeansInit ? CV_32FC1 : CV_64FC1, false);
// set probs
if(probs0 && startStep == START_M_STEP)
{
preprocessSampleData(*probs0, trainProbs, CV_64FC1, true);
preprocessProbability(trainProbs);
}
// set weights
if(weights0 && (startStep == START_E_STEP && covs0))
{
weights0->convertTo(weights, CV_64FC1);
weights.reshape(1,1);
preprocessProbability(weights);
}
// set means
if(means0 && (startStep == START_E_STEP/* || startStep == START_AUTO_STEP*/))
means0->convertTo(means, isKMeansInit ? CV_32FC1 : CV_64FC1);
// set covs
if(covs0 && (startStep == START_E_STEP && weights0))
{
covs.resize(nclusters);
for(size_t i = 0; i < covs0->size(); i++)
(*covs0)[i].convertTo(covs[i], CV_64FC1);
}
}
void decomposeCovs()
{
CV_Assert(!covs.empty());
covsEigenValues.resize(nclusters);
if(covMatType == COV_MAT_GENERIC)
covsRotateMats.resize(nclusters);
invCovsEigenValues.resize(nclusters);
for(int clusterIndex = 0; clusterIndex < nclusters; clusterIndex++)
{
CV_Assert(!covs[clusterIndex].empty());
SVD svd(covs[clusterIndex], SVD::MODIFY_A + SVD::FULL_UV);
if(covMatType == COV_MAT_SPHERICAL)
{
double maxSingularVal = svd.w.at<double>(0);
covsEigenValues[clusterIndex] = Mat(1, 1, CV_64FC1, Scalar(maxSingularVal));
}
else if(covMatType == COV_MAT_DIAGONAL)
{
covsEigenValues[clusterIndex] = svd.w;
}
else //COV_MAT_GENERIC
{
covsEigenValues[clusterIndex] = svd.w;
covsRotateMats[clusterIndex] = svd.u;
}
max(covsEigenValues[clusterIndex], minEigenValue, covsEigenValues[clusterIndex]);
invCovsEigenValues[clusterIndex] = 1./covsEigenValues[clusterIndex];
}
}
void clusterTrainSamples()
{
int nsamples = trainSamples.rows;
// Cluster samples, compute/update means
// Convert samples and means to 32F, because kmeans requires this type.
Mat trainSamplesFlt, meansFlt;
if(trainSamples.type() != CV_32FC1)
trainSamples.convertTo(trainSamplesFlt, CV_32FC1);
else
trainSamplesFlt = trainSamples;
if(!means.empty())
{
if(means.type() != CV_32FC1)
means.convertTo(meansFlt, CV_32FC1);
else
meansFlt = means;
}
Mat labels;
kmeans(trainSamplesFlt, nclusters, labels,
TermCriteria(TermCriteria::COUNT, means.empty() ? 10 : 1, 0.5),
10, KMEANS_PP_CENTERS, meansFlt);
// Convert samples and means back to 64F.
CV_Assert(meansFlt.type() == CV_32FC1);
if(trainSamples.type() != CV_64FC1)
{
Mat trainSamplesBuffer;
trainSamplesFlt.convertTo(trainSamplesBuffer, CV_64FC1);
trainSamples = trainSamplesBuffer;
}
meansFlt.convertTo(means, CV_64FC1);
// Compute weights and covs
weights = Mat(1, nclusters, CV_64FC1, Scalar(0));
covs.resize(nclusters);
for(int clusterIndex = 0; clusterIndex < nclusters; clusterIndex++)
{
Mat clusterSamples;
for(int sampleIndex = 0; sampleIndex < nsamples; sampleIndex++)
{
if(labels.at<int>(sampleIndex) == clusterIndex)
{
const Mat sample = trainSamples.row(sampleIndex);
clusterSamples.push_back(sample);
}
}
CV_Assert(!clusterSamples.empty());
calcCovarMatrix(clusterSamples, covs[clusterIndex], means.row(clusterIndex),
CV_COVAR_NORMAL + CV_COVAR_ROWS + CV_COVAR_USE_AVG + CV_COVAR_SCALE, CV_64FC1);
weights.at<double>(clusterIndex) = static_cast<double>(clusterSamples.rows)/static_cast<double>(nsamples);
}
decomposeCovs();
}
void computeLogWeightDivDet()
{
CV_Assert(!covsEigenValues.empty());
Mat logWeights;
cv::max(weights, DBL_MIN, weights);
log(weights, logWeights);
logWeightDivDet.create(1, nclusters, CV_64FC1);
// note: logWeightDivDet = log(weight_k) - 0.5 * log(|det(cov_k)|)
for(int clusterIndex = 0; clusterIndex < nclusters; clusterIndex++)
{
double logDetCov = 0.;
const int evalCount = static_cast<int>(covsEigenValues[clusterIndex].total());
for(int di = 0; di < evalCount; di++)
logDetCov += std::log(covsEigenValues[clusterIndex].at<double>(covMatType != COV_MAT_SPHERICAL ? di : 0));
logWeightDivDet.at<double>(clusterIndex) = logWeights.at<double>(clusterIndex) - 0.5 * logDetCov;
}
}
bool doTrain(int startStep, OutputArray logLikelihoods, OutputArray labels, OutputArray probs)
{
int dim = trainSamples.cols;
// Precompute the empty initial train data in the cases of START_E_STEP and START_AUTO_STEP
if(startStep != START_M_STEP)
{
if(covs.empty())
{
CV_Assert(weights.empty());
clusterTrainSamples();
}
}
if(!covs.empty() && covsEigenValues.empty() )
{
CV_Assert(invCovsEigenValues.empty());
decomposeCovs();
}
if(startStep == START_M_STEP)
mStep();
double trainLogLikelihood, prevTrainLogLikelihood = 0.;
int maxIters = (termCrit.type & TermCriteria::MAX_ITER) ?
termCrit.maxCount : DEFAULT_MAX_ITERS;
double epsilon = (termCrit.type & TermCriteria::EPS) ? termCrit.epsilon : 0.;
for(int iter = 0; ; iter++)
{
eStep();
trainLogLikelihood = sum(trainLogLikelihoods)[0];
if(iter >= maxIters - 1)
break;
double trainLogLikelihoodDelta = trainLogLikelihood - prevTrainLogLikelihood;
if( iter != 0 &&
(trainLogLikelihoodDelta < -DBL_EPSILON ||
trainLogLikelihoodDelta < epsilon * std::fabs(trainLogLikelihood)))
break;
mStep();
prevTrainLogLikelihood = trainLogLikelihood;
}
if( trainLogLikelihood <= -DBL_MAX/10000. )
{
clear();
return false;
}
// postprocess covs
covs.resize(nclusters);
for(int clusterIndex = 0; clusterIndex < nclusters; clusterIndex++)
{
if(covMatType == COV_MAT_SPHERICAL)
{
covs[clusterIndex].create(dim, dim, CV_64FC1);
setIdentity(covs[clusterIndex], Scalar(covsEigenValues[clusterIndex].at<double>(0)));
}
else if(covMatType == COV_MAT_DIAGONAL)
{
covs[clusterIndex] = Mat::diag(covsEigenValues[clusterIndex]);
}
}
if(labels.needed())
trainLabels.copyTo(labels);
if(probs.needed())
trainProbs.copyTo(probs);
if(logLikelihoods.needed())
trainLogLikelihoods.copyTo(logLikelihoods);
trainSamples.release();
trainProbs.release();
trainLabels.release();
trainLogLikelihoods.release();
return true;
}
Vec2d computeProbabilities(const Mat& sample, Mat* probs, int ptype) const
{
// L_ik = log(weight_k) - 0.5 * log(|det(cov_k)|) - 0.5 *(x_i - mean_k)' cov_k^(-1) (x_i - mean_k)]
// q = arg(max_k(L_ik))
// probs_ik = exp(L_ik - L_iq) / (1 + sum_j!=q (exp(L_ij - L_iq))
// see Alex Smola's blog http://blog.smola.org/page/2 for
// details on the log-sum-exp trick
int stype = sample.type();
CV_Assert(!means.empty());
CV_Assert((stype == CV_32F || stype == CV_64F) && (ptype == CV_32F || ptype == CV_64F));
CV_Assert(sample.size() == Size(means.cols, 1));
int dim = sample.cols;
Mat L(1, nclusters, CV_64FC1), centeredSample(1, dim, CV_64F);
int i, label = 0;
for(int clusterIndex = 0; clusterIndex < nclusters; clusterIndex++)
{
const double* mptr = means.ptr<double>(clusterIndex);
double* dptr = centeredSample.ptr<double>();
if( stype == CV_32F )
{
const float* sptr = sample.ptr<float>();
for( i = 0; i < dim; i++ )
dptr[i] = sptr[i] - mptr[i];
}
else
{
const double* sptr = sample.ptr<double>();
for( i = 0; i < dim; i++ )
dptr[i] = sptr[i] - mptr[i];
}
Mat rotatedCenteredSample = covMatType != COV_MAT_GENERIC ?
centeredSample : centeredSample * covsRotateMats[clusterIndex];
double Lval = 0;
for(int di = 0; di < dim; di++)
{
double w = invCovsEigenValues[clusterIndex].at<double>(covMatType != COV_MAT_SPHERICAL ? di : 0);
double val = rotatedCenteredSample.at<double>(di);
Lval += w * val * val;
}
CV_DbgAssert(!logWeightDivDet.empty());
L.at<double>(clusterIndex) = logWeightDivDet.at<double>(clusterIndex) - 0.5 * Lval;
if(L.at<double>(clusterIndex) > L.at<double>(label))
label = clusterIndex;
}
double maxLVal = L.at<double>(label);
double expDiffSum = 0;
for( i = 0; i < L.cols; i++ )
{
double v = std::exp(L.at<double>(i) - maxLVal);
L.at<double>(i) = v;
expDiffSum += v; // sum_j(exp(L_ij - L_iq))
}
if(probs)
L.convertTo(*probs, ptype, 1./expDiffSum);
Vec2d res;
res[0] = std::log(expDiffSum) + maxLVal - 0.5 * dim * CV_LOG2PI;
res[1] = label;
return res;
}
void eStep()
{
// Compute probs_ik from means_k, covs_k and weights_k.
trainProbs.create(trainSamples.rows, nclusters, CV_64FC1);
trainLabels.create(trainSamples.rows, 1, CV_32SC1);
trainLogLikelihoods.create(trainSamples.rows, 1, CV_64FC1);
computeLogWeightDivDet();
CV_DbgAssert(trainSamples.type() == CV_64FC1);
CV_DbgAssert(means.type() == CV_64FC1);
for(int sampleIndex = 0; sampleIndex < trainSamples.rows; sampleIndex++)
{
Mat sampleProbs = trainProbs.row(sampleIndex);
Vec2d res = computeProbabilities(trainSamples.row(sampleIndex), &sampleProbs, CV_64F);
trainLogLikelihoods.at<double>(sampleIndex) = res[0];
trainLabels.at<int>(sampleIndex) = static_cast<int>(res[1]);
}
}
void mStep()
{
// Update means_k, covs_k and weights_k from probs_ik
int dim = trainSamples.cols;
// Update weights
// not normalized first
reduce(trainProbs, weights, 0, CV_REDUCE_SUM);
// Update means
means.create(nclusters, dim, CV_64FC1);
means = Scalar(0);
const double minPosWeight = trainSamples.rows * DBL_EPSILON;
double minWeight = DBL_MAX;
int minWeightClusterIndex = -1;
for(int clusterIndex = 0; clusterIndex < nclusters; clusterIndex++)
{
if(weights.at<double>(clusterIndex) <= minPosWeight)
continue;
if(weights.at<double>(clusterIndex) < minWeight)
{
minWeight = weights.at<double>(clusterIndex);
minWeightClusterIndex = clusterIndex;
}
Mat clusterMean = means.row(clusterIndex);
for(int sampleIndex = 0; sampleIndex < trainSamples.rows; sampleIndex++)
clusterMean += trainProbs.at<double>(sampleIndex, clusterIndex) * trainSamples.row(sampleIndex);
clusterMean /= weights.at<double>(clusterIndex);
}
// Update covsEigenValues and invCovsEigenValues
covs.resize(nclusters);
covsEigenValues.resize(nclusters);
if(covMatType == COV_MAT_GENERIC)
covsRotateMats.resize(nclusters);
invCovsEigenValues.resize(nclusters);
for(int clusterIndex = 0; clusterIndex < nclusters; clusterIndex++)
{
if(weights.at<double>(clusterIndex) <= minPosWeight)
continue;
if(covMatType != COV_MAT_SPHERICAL)
covsEigenValues[clusterIndex].create(1, dim, CV_64FC1);
else
covsEigenValues[clusterIndex].create(1, 1, CV_64FC1);
if(covMatType == COV_MAT_GENERIC)
covs[clusterIndex].create(dim, dim, CV_64FC1);
Mat clusterCov = covMatType != COV_MAT_GENERIC ?
covsEigenValues[clusterIndex] : covs[clusterIndex];
clusterCov = Scalar(0);
Mat centeredSample;
for(int sampleIndex = 0; sampleIndex < trainSamples.rows; sampleIndex++)
{
centeredSample = trainSamples.row(sampleIndex) - means.row(clusterIndex);
if(covMatType == COV_MAT_GENERIC)
clusterCov += trainProbs.at<double>(sampleIndex, clusterIndex) * centeredSample.t() * centeredSample;
else
{
double p = trainProbs.at<double>(sampleIndex, clusterIndex);
for(int di = 0; di < dim; di++ )
{
double val = centeredSample.at<double>(di);
clusterCov.at<double>(covMatType != COV_MAT_SPHERICAL ? di : 0) += p*val*val;
}
}
}
if(covMatType == COV_MAT_SPHERICAL)
clusterCov /= dim;
clusterCov /= weights.at<double>(clusterIndex);
// Update covsRotateMats for COV_MAT_GENERIC only
if(covMatType == COV_MAT_GENERIC)
{
SVD svd(covs[clusterIndex], SVD::MODIFY_A + SVD::FULL_UV);
covsEigenValues[clusterIndex] = svd.w;
covsRotateMats[clusterIndex] = svd.u;
}
max(covsEigenValues[clusterIndex], minEigenValue, covsEigenValues[clusterIndex]);
// update invCovsEigenValues
invCovsEigenValues[clusterIndex] = 1./covsEigenValues[clusterIndex];
}
for(int clusterIndex = 0; clusterIndex < nclusters; clusterIndex++)
{
if(weights.at<double>(clusterIndex) <= minPosWeight)
{
Mat clusterMean = means.row(clusterIndex);
means.row(minWeightClusterIndex).copyTo(clusterMean);
covs[minWeightClusterIndex].copyTo(covs[clusterIndex]);
covsEigenValues[minWeightClusterIndex].copyTo(covsEigenValues[clusterIndex]);
if(covMatType == COV_MAT_GENERIC)
covsRotateMats[minWeightClusterIndex].copyTo(covsRotateMats[clusterIndex]);
invCovsEigenValues[minWeightClusterIndex].copyTo(invCovsEigenValues[clusterIndex]);
}
}
// Normalize weights
weights /= trainSamples.rows;
}
void write_params(FileStorage& fs) const
{
fs << "nclusters" << nclusters;
fs << "cov_mat_type" << (covMatType == COV_MAT_SPHERICAL ? String("spherical") :
covMatType == COV_MAT_DIAGONAL ? String("diagonal") :
covMatType == COV_MAT_GENERIC ? String("generic") :
format("unknown_%d", covMatType));
writeTermCrit(fs, termCrit);
}
void write(FileStorage& fs) const
{
fs << "training_params" << "{";
write_params(fs);
fs << "}";
fs << "weights" << weights;
fs << "means" << means;
size_t i, n = covs.size();
fs << "covs" << "[";
for( i = 0; i < n; i++ )
fs << covs[i];
fs << "]";
}
void read_params(const FileNode& fn)
{
nclusters = (int)fn["nclusters"];
String s = (String)fn["cov_mat_type"];
covMatType = s == "spherical" ? COV_MAT_SPHERICAL :
s == "diagonal" ? COV_MAT_DIAGONAL :
s == "generic" ? COV_MAT_GENERIC : -1;
CV_Assert(covMatType >= 0);
termCrit = readTermCrit(fn);
}
void read(const FileNode& fn)
{
clear();
read_params(fn["training_params"]);
fn["weights"] >> weights;
fn["means"] >> means;
FileNode cfn = fn["covs"];
FileNodeIterator cfn_it = cfn.begin();
int i, n = (int)cfn.size();
covs.resize(n);
for( i = 0; i < n; i++, ++cfn_it )
(*cfn_it) >> covs[i];
decomposeCovs();
computeLogWeightDivDet();
}
Mat getWeights() const { return weights; }
Mat getMeans() const { return means; }
void getCovs(std::vector<Mat>& _covs) const
{
_covs.resize(covs.size());
std::copy(covs.begin(), covs.end(), _covs.begin());
}
// all inner matrices have type CV_64FC1
Mat trainSamples;
Mat trainProbs;
Mat trainLogLikelihoods;
Mat trainLabels;
Mat weights;
Mat means;
std::vector<Mat> covs;
std::vector<Mat> covsEigenValues;
std::vector<Mat> covsRotateMats;
std::vector<Mat> invCovsEigenValues;
Mat logWeightDivDet;
};
Ptr<EM> EM::create()
{
return makePtr<EMImpl>();
}
}
} // namespace cv
/* End of file. */