pyewt.boundaries2d module

pyewt.boundaries2d.UnSymmetrize_Fourier(in_array, extH, extW)

Removes the extension of the spectrum that was introduced to symmetrize the spectrum.

Parameters:

• in_array (ndarray) – Magnitude of the spectrum to unsymmetrize.

• extH (bool or int) – 1 (or True) if there is vertical extension, 0 otherwise.

• extW (bool or int) – 1 (or True) if there is horizontal extension, 0 otherwise.

Returns:

• usym (ndarray) – Spectrum with original size.

• Author (Jerome Gilles)

• Institution (San Diego State University)

• Version (1.0 (07/15/2025))

pyewt.boundaries2d.ewt2d_EmpiricalLaw(histo)

Classifies minima curve lengths into two classes using an empirical law.

Parameters:

• L (1D ndarray) – Set of minima curve lengths.

• ind (2D ndarray) – Original index of each minima (shape: [n_minima, 2]).

Returns:

• bounds (ndarray) – Detected bounds (subset of ind).

• th (float) – Detected scale threshold.

• Author (Jerome Gilles)

• Institution (San Diego State University)

• Version (1.0 (07/15/2025))

pyewt.boundaries2d.ewt2d_HalfNormalLaw(L, Lmax)

Classifies minima curve lengths into two classes using a half-normal law.

Parameters:

• L (1D ndarray) – Set of minima curve lengths.

• ind (2D ndarray) – Original index of each minima (shape: [n_minima, 2]).

• Lmax (float) – Maximum possible length of a minima curve.

Returns:

• bounds (ndarray) – Detected bounds (subset of ind).

• th (float) – Detected scale threshold.

• Author (Jerome Gilles)

• Institution (San Diego State University)

• Version (1.0 (07/15/2025))

pyewt.boundaries2d.ewt2d_OtsuMethod(histo)

Classifies the set of minima curve lengths stored in histo into two classes using Otsu’s method. Returns the boundaries which are supposed to be the meaningful ones.

Parameters:

histo (ndarray) – Set of minima curve lengths (1D array).

Returns:

• bounds (ndarray) – Detected bounds (subset of ind).

• th (int) – Detected scale threshold.

• Author (Jerome Gilles)

• Institution (San Diego State University)

• Version (1.0 (07/05/2025))

pyewt.boundaries2d.ewt2d_fourier_extend(f, n)

Extend image by periodization

Parameters:

• f (-) – image to extend

• n (-)

Returns:

- fe – extended image

Return type:

ndarray

Notes

This function extend the provided image f by periodization on a strip of width n around the image

Author: Jerome Gilles Institution: San Diego State University Version: 1.0 (02/11/2025)

pyewt.boundaries2d.ewt2d_fourier_shrink(f, n)

shrink image

Parameters:

• f (-) – image to extend

• n (-)

Returns:

- fe – shrinked image

Return type:

ndarray

Notes

This function shrinks the provided image f by removing a strip of width n around the image

Author: Jerome Gilles Institution: San Diego State University Version: 1.0 (02/11/2025)

pyewt.boundaries2d.ewt2d_get_maxima(absff, params, extH, extW)

Build a scale-space representation and post-process detected maxima. Discards maxima near the edge and, if needed, the center.

Parameters:

• absff (2D ndarray) – Input image (Fourier spectrum).

• params (dict) – Empirical wavelet parameters (see Notes below).

• extH (int) – 1 if height was extended, 0 otherwise.

• extW (int) – 1 if width was extended, 0 otherwise.

Returns:

• centers (ndarray) – Coordinates of significant maxima.

• plane (ndarray) – Scale-space plane.

Notes

params[“typeDetect”] must be set to the wanted classification

method. The available options are: - “otsu” : uses Otsu’s technique - “halfnormal” : uses a half-normal law to model the problem - “empiricallaw” : uses the data itself to build a model of the problem - “kmeans” : uses kmeans to classify

params[“t”]: is the initial scale for the Gaussian kernel (0.8 is a good default value). params[“kn”]: is the kernel size for the Gaussian kernel (6 is a good default value). params[“niter”]: is the number of iterations through the scales (4 is a good default value). params[“edge”]: is the size (in pixels) of the strip to ignore at the edge of the image (0 is no strip). params[“includeCenter”]: if 1, the center of the image is included in the scale space maxima (0 is not included).

Author: Jerome Gilles Institution: San Diego State University Version: 1.0 (07/15/2025)

pyewt.boundaries2d.ewt2d_gss(f, params)

Build a 2D Gaussian scale space and detect local maxima.

Parameters:

• f (2D ndarray) – Input image (Fourier spectrum).

• params (dict) – Parameters for the scale space and maxima detection (see Notes below).

Returns:

• worm_bound (ndarray) – Coordinates of the detected maxima.

• Th (float) – Threshold for maxima detection.

• plane (ndarray) – Scale-space plane.

Notes

params[“typeDetect”] must be set to the wanted classification

method. The available options are: - “otsu” : uses Otsu’s technique - “halfnormal” : uses a half-normal law to model the problem - “empiricallaw” : uses the data itself to build a model of the problem - “kmeans” : uses kmeans to classify

params[“t”]: is the initial scale for the Gaussian kernel (0.8 is a good default value). params[“kn”]: is the kernel size for the Gaussian kernel (6 is a good default value). params[“niter”]: is the number of iterations through the scales (4 is a good default value).

Author: Jerome Gilles Institution: San Diego State University Version: 1.0 (07/21/2025)

pyewt.boundaries2d.ewt2d_kmeansdetect(L)

Detect meaningful minima using kmeans (for 1D L).

Parameters:

L (1D ndarray) – Vector of the length of the minima curves.

Returns:

• th (float) – Detected scale threshold.

• Author (Jerome Gilles)

• Institution (San Diego State University)

• Version (1.0 (07/15/2025))

pyewt.boundaries2d.ewt2d_localmax(f)

Find local maxmima on a 2D image

Parameters:

f (-) – image on which to perform the detection.

Returns:

• - tag (ndarray) – image with pixels either at 0 or 1 where 1 means a local maximum has been detected.

• Author (Jerome Gilles)

• Institution (San Diego State University)

• Version (1.0 (02/11/2025))

pyewt.boundaries2d.ewt2d_plot_ssplane(plane)

Plot 3D scale-space

Parameters:

• matrix (- plane DOK sparse) – contains the 3D scale-space domain

• Author (Jerome Gilles)

• Institution (San Diego State University)

• Version (1.0 (02/11/2025))

pyewt.boundaries2d.ewt2d_spectrum_regularize(f, params)

2D Spectrum regularization

Parameters:

• f (ndarray) – matrix containing the spectrum

• params (Dictionary) – must have params[“reg”] to be set to one of the methods listed below must have params[“lengthfilter”] to be set for all methods must have params[“sigmafilter”] to be set to the standard deviation for the Gaussian method

Returns:

ff – matrix containing the regularized spectrum

Return type:

ndarray

Notes

This function regularizes f using the selected method set in params[“reg”]. The available methods are: - “none” : does nothing, returns f - “gaussian” : convolve f with a Gaussian of length and standard

deviation given by params[“lengthfilter”] and params[“sigmafilter”], respectively

• “average”: convolve f with a constant filter of length given

  by params[“lengthfilter”]

Author: Jerome Gilles Institution: San Diego State University Version: 1.0 (02/09/2025)

pyewt.boundaries2d.plot_scalespace_maxima(f, maxima, logtag=True, title='Scale-space Maxima', radius=1)

Plot the scale-space maxima on the Fourier spectrum

Parameters:

• f (-) – Input image

• maxima (-) – Arrays that contain the coordinates of the detected maxima in the Fourier domain.

• logtag (-) – Indicate if the logarithm of the spectrum should be used for the background.

• title (-) – Title to be plotted on the figure. The default title is “Scale-space Maxima”.

• radius (-) – Radius of the maxima to be plotted in pixels. The default value is 1 pixel.

Notes

This function plots the position of the detected maxima in the Fourier domain via the scale-space method.

Author: Jerome Gilles Institution: San Diego State University Version: 1.0 (07/15/2025)

pyewt.boundaries2d.symmetrize_fourier(f)

Symmetric extension of the Fourier spectrum

Parameters:

f (ndarray) – input 2D Fourier spectrum

Returns:

• sym (ndarray) – symmetrized Fourier spectrum

• extH (True/False) – indicate a vertical extension

• extW (True/False) – indicate an horizontal extension

Notes

This function returns a symetrized Fourier spectrum by properly extending the expected directions. It returns a new spectrum where each dimension is odd.

Author: Jerome Gilles Institution: San Diego State University Version: 1.0 (02/09/2025)