Detection » Circle detectors module

#include "diplib/detection.h"

struct dip::RadonCircleParameters

Stores the parameters for one hypersphere (circle, sphere).

void dip::HoughTransformCircleCenters(dip::Image const& in, dip::Image const& gv, dip::Image& out, dip::UnsignedArray const& range = {})

Hough transform for circles in 2D binary images.

Computes the Hough parameter space for circles in 2D images, with the radius dimension collapsed. The parameter space out has the same sizes as the binary input image in. gv is a vector image of the same sizes as in, with the gradient vector for each pixel of in.

range must be empty, or have exactly two elements representing the minimum and maximum radius to be considered. If empty, the minimum radius is 0, and the maximum is the length of the image diagonal.

dip::CoordinateArray dip::FindHoughMaxima(dip::Image const& in, dip::dfloat distance = 10.0, dip::dfloat fraction = 0.1)

Find local maxima in Hough parameter space.

Finds the local maxima (using dip::WatershedMaxima) in the given Hough parameter space. Maxima distance pixels away from a higher maximum are filtered out. Maxima lower than fraction times the highest maximum are ignored. fraction should be lower than 1.

dip::Distribution dip::PointDistanceDistribution(dip::Image const& in, dip::CoordinateArray const& points, dip::UnsignedArray range = {})

Compute distance distribution for a set of points.

Computes the distance distributions from points to all ‘on’ pixels in the binary image in. The returned (multi-valued) distribution indicates, for every integer distance, how many ‘on’ pixels are found at that distance for that point.

range must be empty, or have exactly two elements representing the minimum and maximum distance to be considered. If empty, the minimum distance is 0, and the maximum is the length of the image diagonal.

dip::FloatCoordinateArray dip::FindHoughCircles(dip::Image const& in, dip::Image const& gv, dip::UnsignedArray const& range = {}, dip::dfloat distance = 10.0, dip::dfloat fraction = 0.1)

Find circles in 2D binary images.

Finds circles in 2D binary images using the 2-1 Hough transform. First, circle centers are computed using dip::HoughTransformCircleCenters, and then a radius is calculated for each center. Note that only a single radius is returned per center coordinates.

gv is a vector image of the same sizes as in, with the gradient vector for each pixel of in.

range must be empty, or have exactly two elements representing the minimum and maximum radius to be considered. If empty, the minimum radius is 0, and the maximum is the length of the image diagonal.

distance is the minimum distance between centers, used to suppress noisy results. fraction is the minimum height of a peak in the Hough transform, with respect to the largest peak, that should be considered, again to suppress noisy results.

dip::RadonCircleParametersArray dip::RadonTransformCircles(dip::Image const& in, dip::Image& out, dip::Range radii = {10,30}, dip::dfloat sigma = 1.0, dip::dfloat threshold = 1.0, dip::String const& mode = S::FULL, dip::StringSet const& options = {S::NORMALIZE,S::CORRECT})

Detects hyperspheres (circles, spheres) using the generalized Radon transform.

This function can obtain highly precise values for the origin and the radius of the circles/spheres, in any number of dimensions. Note the distinction between a circle and a disk (or a sphere and a ball): this function works to detect the former, a hollow version of the latter. If presented with an image containing disks or balls, the results will likely not be useful. Apply dip::GradientMagnitude to the image to convert disks or balls into circles or spheres.

radii determines the radii for the template, and thus also the size of the parameter space. Note that it is not possible to find locations of maxima with sub-pixel precision at the boundary of an image, so the first radius to be probed should be strictly smaller than the smallest circle/sphere to be detected, and the last radius should be strictly larger.

sigma specifies the parameter to the Gaussian regularization used when creating the templates. This parameter is linked to the step size of radii. For example, if sigma is set to 2, then the step size can be 2 also, reducing the size of the parameter space.

threshold is used to distinguish relevant peaks in the parameter space: Peaks must be at least threshold above the surrounding valley to be counted. dip::WatershedMaxima is used to find peaks, threshold sets the maxDepth parameter there.

The Radon transform parameter space can be computed in three different ways, determined by the value for mode:

• "full": out is the full parameter space, an image of the size of in with an additional dimension for the r axis. This is the default.
• "projection": out is of the size of in, with two tensor components (channels). out[ 0 ] is the max projection of the parameter space over the r axis, out[ 1 ] is the argmax projection.
• "subpixel projection": Idem, but the argmax is computed with sub-pixel precision. It computes 3 slices along r at the time, and looks for local maxima along the r axis by fitting a parabola to the the 3 samples.

The parameter options can contain the following values:

• "normalize": Normalizes the integral over the template for each r, so that larger circles don’t have a larger maximum. This prevents a bias towards larger circles.
• "correct": If normalized, the size of the template is corrected to reduce bias in the radius estimate.
• "hollow": Adds a negative ring just inside the positive ring of the template. This forces the algorithm to look for rings, not disks.
• "filled": Fills the positive ring with negative values. This forces the algorithm to look for rings without anything in them.
• "no maxima detection": The dip::RadonCircleParametersArray output is an empty array.
• "no parameter space": The out image is not used.

By default, options contains "normalize" and "correct".

in must be scalar and non-complex, and have at least one dimension. out will be of type dip::DT_SFLOAT.