Math and statistics » Statistics module

#include "diplib/statistics.h"

dip::uint dip::Count(dip::Image const& in, dip::Image const& mask = {})

Counts the number of non-zero pixels in a scalar image.

in must be scalar, but can have any data type. mask, if forged, must be of the same sizes as in, or be singleton expandable to that size, and must be binary.

dip::UnsignedArray dip::MaximumPixel(dip::Image const& in, dip::Image const& mask = {}, dip::String const& positionFlag = S::FIRST)

Returns the coordinates of the maximum pixel in the image.

The image must be scalar. If in is complex, the modulus of its values are used. If positionFlag is "first", the first maximum is found, in linear index order. If it is "last", the last one is found.

dip::UnsignedArray dip::MinimumPixel(dip::Image const& in, dip::Image const& mask = {}, dip::String const& positionFlag = S::FIRST)

Returns the coordinates of the minimum pixel in the image.

The image must be scalar. If in is complex, the modulus of its values are used. If positionFlag is "first", the first minimum is found, in linear index order. If it is "last", the last one is found.

void dip::CumulativeSum(dip::Image const& in, dip::Image const& mask, dip::Image& out, dip::BooleanArray const& process = {})

Calculates the cumulative sum of the pixel values over all those dimensions which are specified by process.

If process is an empty array, all dimensions are processed. The output is an image of the same size as the input. For tensor images, the output has the same tensor size and shape as the input.

If mask is forged, those pixels not selected by the mask are presumed to be 0.

dip::MinMaxAccumulator dip::MaximumAndMinimum(dip::Image const& in, dip::Image const& mask = {})

Finds the largest and smallest value in the image, within an optional mask.

If mask is not forged, all input pixels are considered. In case of a tensor image, returns the maximum and minimum sample values. In case of a complex samples, treats real and imaginary components as individual samples.

dip::QuartilesResult dip::Quartiles(dip::Image const& in, dip::Image const& mask = {})

Computes the minimum, lower quartile (25th percentile), median (50th percentile), upper quartile (75th percentile), and maximum.

Percentiles are always one of the values in the image. The nearest value to a given partition is used, rather than interpolate as classically done.

If mask is not forged, all input pixels are considered. In case of a tensor image, returns the maximum and minimum sample values. In case of a complex samples, treats real and imaginary components as individual samples.

dip::StatisticsAccumulator dip::SampleStatistics(dip::Image const& in, dip::Image const& mask = {})

Computes the first four central moments of the pixel intensities, within an optional mask.

If mask is not forged, all input pixels are considered. In case of a tensor image, returns the statistics over all sample values. The image must be real-valued.

dip::CovarianceAccumulator dip::Covariance(dip::Image const& in1, dip::Image const& in2, dip::Image const& mask = {})

Computes the covariance and correlation between the two images, within an optional mask.

If mask is not forged, all input pixels are considered. In case of tensor images, returns the covariance over all sample values. The images must be real-valued and have the same number of tensor elements.

To compute the covariance or correlation between two channels in a multi-channel image (a tensor image):

Covariance( in[ 0 ], in[ 1 ], mask );

dip::dfloat dip::SpearmanRankCorrelation(dip::Image const& in1, dip::Image const& in2, dip::Image const& mask = {})

Computes the Spearman rank correlation coefficient.

If mask is not forged, all input pixels are considered. In case of tensor images, returns the Spearman rank correlation coefficient over all sample values. The images must be real-valued and have the same number of tensor elements.

To compute the Spearman rank correlation coefficient between two channels in a multi-channel image (a tensor image):

SpearmanRankCorrelation( in[ 0 ], in[ 1 ], mask );

dip::FloatArray dip::CenterOfMass(dip::Image const& in, dip::Image const& mask = {})

Computes the center of mass (first order moments) of the image in, optionally using only those pixels selected by mask.

If mask is not forged, all input pixels are considered. in must be scalar and real-valued.

dip::MomentAccumulator dip::Moments(dip::Image const& in, dip::Image const& mask = {})

Computes the first order normalized moments and second order normalized central moments of the image in, optionally using only those pixels selected by mask.

If mask is not forged, all input pixels are considered. in must be scalar and real-valued.

Note that the normalization makes the moments invariant to scaling the image intensities, but not to spatial scaling. Divide each element of dip::MomentAccumulator::PlainSecondOrder by dip::MomentAccumulator::Sum to obtain a value that is invariant also to spatial scaling. The first two Hu moments of a 2D image are obtained as follows:

auto moments = dip::Moments( img );
auto m0 = moments.Sum();
auto m2 = moments.PlainSecondOrder();
// scale and translation invariant second order moments:
double nu20 = m2[ 0 ] / m0;
double nu02 = m2[ 1 ] / m0;
double nu11 = m2[ 2 ] / m0;
// scale, translation and rotation-invariant values:
double hu1 = nu20 + nu02;
double hu2 = ( nu20 - nu02 ) * ( nu20 - nu02 ) + 4 * nu11 * nu11;