ErosionFiltration

class gtda.images.ErosionFiltration(n_iterations=None, n_jobs=None)

Filtrations of 2D/3D binary images based on the erosion of activated regions.

Binary erosion is a morphological operator commonly used in image processing and relies on the scipy.ndimage module.

This filtration assigns to each pixel in an image a greyscale value calculated as follows. If the minimum Manhattan distance between the pixel and any deactivated pixel in the image is less than or equal to the parameter n_iterations, the assigned value is this distance – in particular, deactivated pixels are assigned a value of 0. Otherwise, the assigned greyscale value is the sum of the lengths along all axes of the image – equivalently, it is the maximum Manhattan distance between any two pixels in the image. The name of this filtration comes from the fact that these values can be computed by iteratively eroding activated regions, shrinking them by a total amount n_iterations.

Parameters

• n_iterations (int or None, optional, default: None) – Number of iterations in the erosion process. None means erosion reaches all activated pixels.

• n_jobs (int or None, optional, default: None) – The number of jobs to use for the computation. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors.

n_iterations_

Effective number of iterations in the erosion process. Set in fit.

Type

int

max_value_

Maximum pixel value among all pixels in all images of the collection. Set in fit.

Type

float

See also

gtda.homology.CubicalPersistence, Binarizer

References

[1] A. Garin and G. Tauzin, “A topological reading lesson: Classification

of MNIST using TDA”; 19th International IEEE Conference on Machine Learning and Applications (ICMLA 2020), 2019; arXiv: 1910.08345.

__init__(n_iterations=None, n_jobs=None)

Initialize self. See help(type(self)) for accurate signature.

fit(X, y=None)

Calculate n_iterations_ and max_value_ from a collection of binary images. Then, return the estimator.

This method is here to implement the usual scikit-learn API and hence work in pipelines.

Parameters

• X (ndarray of shape (n_samples, n_pixels_x, n_pixels_y [, n_pixels_z])) – Input data. Each entry along axis 0 is interpreted as a 2D or 3D binary image.

• y (None) – There is no need of a target in a transformer, yet the pipeline API requires this parameter.

Returns

self

Return type

object

fit_transform(X, y=None, **fit_params)

Fit to data, then transform it.

Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.

Parameters

• X (ndarray of shape (n_samples, n_pixels_x, n_pixels_y [, n_pixels_z])) – Input data. Each entry along axis 0 is interpreted as a 2D or 3D binary image.

• y (None) – There is no need of a target in a transformer, yet the pipeline API requires this parameter.

Returns

Xt – n_pixels_y [, n_pixels_z]) Transformed collection of images. Each entry along axis 0 is a 2D or 3D greyscale image.

Return type

ndarray of shape (n_samples, n_pixels_x,

fit_transform_plot(X, y=None, sample=0, **plot_params)

Fit to data, then apply transform_plot.

Parameters

• X (ndarray of shape (n_samples, ..)) – Input data.

• y (ndarray of shape (n_samples,) or None) – Target values for supervised problems.

• sample (int) – Sample to be plotted.

• **plot_params – Optional plotting parameters.

Returns

Xt – Transformed one-sample slice from the input.

Return type

ndarray of shape (1, ..)

get_params(deep=True)

Get parameters for this estimator.

Parameters

deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns

params – Parameter names mapped to their values.

Return type

mapping of string to any

static plot(Xt, sample=0, colorscale='greys', origin='upper')

Plot a sample from a collection of 2D greyscale images.

Parameters

• Xt (ndarray of shape (n_samples, n_pixels_x, n_pixels_y)) – Collection of 2D greyscale images, such as returned by transform.

• sample (int, optional, default: 0) – Index of the sample in Xt to be plotted.

• colorscale (str, optional, default: 'greys') – Color scale to be used in the heat map. Can be anything allowed by plotly.graph_objects.Heatmap.

• origin ('upper' | 'lower', optional, default: 'upper') – Position of the [0, 0] pixel of data, in the upper left or lower left corner. The convention 'upper' is typically used for matrices and images.

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters

**params (dict) – Estimator parameters.

Returns

self – Estimator instance.

Return type

object

transform(X, y=None)

For each binary image in the collection X, calculate a corresponding greyscale image based on the distance of its pixels to their closest activated neighboring pixel. Return the collection of greyscale images.

Parameters

• X (ndarray of shape (n_samples, n_pixels_x, n_pixels_y [, n_pixels_z])) – Input data. Each entry along axis 0 is interpreted as a 2D or 3D binary image.

• y (None) – There is no need of a target in a transformer, yet the pipeline API requires this parameter.

Returns

Xt – n_pixels_y [, n_pixels_z]) Transformed collection of images. Each entry along axis 0 is a 2D or 3D greyscale image.

Return type

ndarray of shape (n_samples, n_pixels_x,

transform_plot(X, sample=0, **plot_params)

Take a one-sample slice from the input collection and transform it. Before returning the transformed object, plot the transformed sample.

Parameters

• X (ndarray of shape (n_samples, ..)) – Input data.

• sample (int) – Sample to be plotted.

• plot_params (dict) – Optional plotting parameters.

Returns

Xt – Transformed one-sample slice from the input.

Return type

ndarray of shape (1, ..)