DenseMatrix project(RandomAccessIterator begin, RandomAccessIterator end, FeatureVectorCallback callback,
IndexType dimension, const IndexType max_iter, const ScalarType epsilon,
const IndexType target_dimension, const DenseVector& mean_vector)
{
timed_context context("Data projection");
// The number of data points
const IndexType n = end-begin;
// Dense representation of the data points
DenseVector current_vector(dimension);
DenseMatrix X = DenseMatrix::Zero(dimension,n);
for (RandomAccessIterator iter=begin; iter!=end; ++iter)
{
callback.vector(*iter,current_vector);
X.col(iter-begin) = current_vector - mean_vector;
}
// Initialize FA model
// Initial variances
DenseMatrix sig = DenseMatrix::Identity(dimension,dimension);
// Initial linear mapping
DenseMatrix A = DenseMatrix::Random(dimension, target_dimension).cwiseAbs();
// Main loop
IndexType iter = 0;
DenseMatrix invC,M,SC;
ScalarType ll = 0, newll = 0;
while (iter < max_iter)
{
++iter;
// Perform E-step
// Compute the inverse of the covariance matrix
invC = (A*A.transpose() + sig).inverse();
M = A.transpose()*invC*X;
SC = n*(DenseMatrix::Identity(target_dimension,target_dimension) - A.transpose()*invC*A) + M*M.transpose();
// Perform M-step
A = (X*M.transpose())*SC.inverse();
sig = DenseMatrix(((X*X.transpose() - A*M*X.transpose()).diagonal()/n).asDiagonal()).array() + epsilon;
// Compute log-likelihood of FA model
newll = 0.5*(log(invC.determinant()) - (invC*X).cwiseProduct(X).sum()/n);
// Check for convergence
if ((iter > 1) && (fabs(newll - ll) < epsilon))
break;
ll = newll;
}
return X.transpose()*A;
}
DenseVector compute_mean(RandomAccessIterator begin, RandomAccessIterator end,
FeatureVectorCallback callback, IndexType dimension)
{
DenseVector mean = DenseVector::Zero(dimension);
DenseVector current_vector(dimension);
for (RandomAccessIterator iter=begin; iter!=end; ++iter)
{
callback(*iter,current_vector);
mean += current_vector;
}
mean.array() /= (end-begin);
return mean;
}
DenseSymmetricMatrix compute_covariance_matrix(RandomAccessIterator begin, RandomAccessIterator end,
const DenseVector& mean, FeatureVectorCallback callback, IndexType dimension)
{
timed_context context("Constructing PCA covariance matrix");
DenseSymmetricMatrix covariance_matrix = DenseSymmetricMatrix::Zero(dimension,dimension);
DenseVector current_vector(dimension);
for (RandomAccessIterator iter=begin; iter!=end; ++iter)
{
callback(*iter,current_vector);
covariance_matrix.selfadjointView<Eigen::Upper>().rankUpdate(current_vector,1.0);
}
covariance_matrix.selfadjointView<Eigen::Upper>().rankUpdate(mean,-1.0);
return covariance_matrix;
}
EmbeddingResult project(const ProjectionResult& projection_result, RandomAccessIterator begin,
RandomAccessIterator end, FeatureVectorCallback callback, unsigned int dimension)
{
timed_context context("Data projection");
DenseVector current_vector(dimension);
const DenseSymmetricMatrix& projection_matrix = projection_result.first;
DenseMatrix embedding = DenseMatrix::Zero((end-begin),projection_matrix.cols());
for (RandomAccessIterator iter=begin; iter!=end; ++iter)
{
callback(*iter,current_vector);
embedding.row(iter-begin) = projection_matrix.transpose()*current_vector;
}
return EmbeddingResult(embedding,DenseVector());
}
DenseMatrix project(const DenseMatrix& projection_matrix, const DenseVector& mean_vector,
RandomAccessIterator begin, RandomAccessIterator end,
FeatureVectorCallback callback, IndexType dimension)
{
timed_context context("Data projection");
DenseVector current_vector(dimension);
DenseVector current_vector_subtracted_mean(dimension);
DenseMatrix embedding = DenseMatrix::Zero((end-begin),projection_matrix.cols());
for (RandomAccessIterator iter=begin; iter!=end; ++iter)
{
callback(*iter,current_vector);
current_vector_subtracted_mean = current_vector - mean_vector;
embedding.row(iter-begin) = projection_matrix.transpose()*current_vector_subtracted_mean;
}
return embedding;
}
ImageRAII match( IplImage * image1, IplImage * image2, std::pair< CvMat *, CvMat * > image1_keys, std::pair< CvMat *, CvMat * > image2_keys )
{
ImageRAII appended_images = appendimages( image1, image2 );
ImageRAII rgb_appended_images( cvCreateImage( cvGetSize( appended_images.image ), appended_images.image->depth, 3 ) );
cvCvtColor( appended_images.image, rgb_appended_images.image, CV_GRAY2RGB );
CvScalar red;
red.val[2] = 255;
std::vector< std::pair< int, int > > points;
// check for matches with the vectors in image1 and image2
for( int i = 0; i < image1_keys.first->height; i++ )
{
double magnitude1 = 0;
MatrixRAII current_vector( cvCreateMat( 1, image1_keys.first->cols, CV_32FC1 ) );
// keeps track of minimum row found b/t image1 and image2 vectors
MatrixRAII min( cvCreateMat( 1, image2_keys.first->cols, CV_32FC1 ) );
cvGetRow( image1_keys.first, current_vector.matrix, i );
CvPoint point1 = cvPoint( ( int )cvmGet( current_vector.matrix, 0, 1 ), ( int )cvmGet( current_vector.matrix, 0, 0 ) );
std::map< float, int > angles;
for( int k = 0; k < image1_keys.second->width; k++ )
magnitude1 += pow( cvmGet( image1_keys.second, i, k ), 2 );
magnitude1 = cvSqrt( magnitude1 );
// compare a vector in image1 to every vector in image2 by calculating the cosine simularity
for( int j = 0; j < image2_keys.first->height; j++ )
{
MatrixRAII descriptor1( cvCreateMat( 1, image1_keys.second->cols, CV_32FC1 ) );
MatrixRAII descriptor2( cvCreateMat( 1, image2_keys.second->cols, CV_32FC1 ) );
cvGetRow( image1_keys.second, descriptor1.matrix, i );
cvGetRow( image2_keys.second, descriptor2.matrix, j );
double dot_product = cvDotProduct( descriptor1.matrix, descriptor2.matrix );
double magnitude2 = 0;
for( int k = 0; k < image2_keys.second->width; k++ )
magnitude2 += pow( cvmGet( descriptor1.matrix, 0, k ), 2 );
magnitude2 = cvSqrt( magnitude2 );
angles.insert( std::pair< float, int >( acos( dot_product / ( magnitude1 * magnitude2 ) ), j ) );
}
std::map< float, int >::iterator it = angles.begin();
int index = it->second;
float angle = it->first;
it++;
if( angle < THRESHOLD * it->first )
{
points.push_back( std::make_pair( i, index ) );
}
}
std::vector< std::pair< int, int > >::iterator it;
for( it = points.begin(); it < points.end(); it++ )
{
CvPoint point1 = cvPoint( ( int )cvmGet( image1_keys.first, it->first, 1 ), ( int )cvmGet( image1_keys.first, it->first, 0 ) );
CvPoint point2 = cvPoint( ( int )cvmGet( image2_keys.first, it->second, 1 ) + image1->width, ( int )cvmGet( image2_keys.first, it->second, 0 ) );
cvLine( rgb_appended_images.image, point1, point2, red );
}
return rgb_appended_images;
}