ktch.outline.EllipticFourierAnalysis#

class ktch.outline.EllipticFourierAnalysis(n_harmonics=20, n_dim=2, reflect=False, metric='', impute=False)[source]#

Elliptic Fourier Analysis (EFA)

Parameters:
n_harmonics: int, default=20

harmonics

n_dim: int, default=2

dimension

reflect: bool, default=False

reflect

metric: str

metric

impute: bool, False

impute

Notes

EFA is widely applied for outline shape analysis in two-dimensional space [Kuhl_Giardina_1982].

\[\begin{split}\begin{align} x(l) &= \frac{a_0}{2} + \sum_{i=1}^{n} \left[ a_i \cos\left(\frac{2\pi i t}{T}\right) + b_i \sin\left(\frac{2\pi i t}{T}\right) \right]\\ y(l) &= \frac{c_0}{2} + \sum_{i=1}^{n} \left[ c_i \cos\left(\frac{2\pi i t}{T}\right) + d_i \sin\left(\frac{2\pi i t}{T}\right) \right]\\ \end{align}\end{split}\]

EFA is also applied for a closed curve in the three-dimensional space (e.g., [Lestrel_1997], [Lestrel_et_al_1997], and [Godefroy_et_al_2012]).

References

[Kuhl_Giardina_1982]

Kuhl, F.P., Giardina, C.R. (1982) Elliptic Fourier features of a closed contour. Comput. Graph. Image Process. 18: 236–258. https://doi.org/10.1016/0146-664X(82)90034-X

[Lestrel_1997]

Lestrel, P.E., 1997. Introduction and overview of Fourier descriptors, in: Fourier Descriptors and Their Applications in Biology. Cambridge University Press, pp. 22–44. https://doi.org/10.1017/cbo9780511529870.003

[Lestrel_et_al_1997]

Lestrel, P.E., Read, D.W., Wolfe, C., 1997. Size and shape of the rabbit orbit: 3-D Fourier descriptors, in: Lestrel, P.E. (Ed.), Fourier Descriptors and Their Applications in Biology. Cambridge University Press, pp. 359–378. https://doi.org/10.1017/cbo9780511529870.017

[Godefroy_et_al_2012]

Godefroy, J.E., Bornert, F., Gros, C.I., Constantinesco, A., 2012. Elliptical Fourier descriptors for contours in three dimensions: A new tool for morphometrical analysis in biology. C. R. Biol. 335, 205–213. https://doi.org/10.1016/j.crvi.2011.12.004

Methods

fit_transform(X[, t, norm])

Fit to data, then transform it.

get_feature_names_out([input_features])

Get output feature names.

get_metadata_routing()

Get metadata routing of this object.

get_params([deep])

Get parameters for this estimator.

inverse_transform(X_transformed[, t_num, ...])

Inverse analysis of elliptic Fourier analysis.

set_inverse_transform_request(*[, ...])

Request metadata passed to the inverse_transform method.

set_output(*[, transform])

Set output container.

set_params(**params)

Set the parameters of this estimator.

set_transform_request(*[, norm, t])

Request metadata passed to the transform method.

transform(X[, t, norm])

EFA.
fit_transform(X, t=None, norm=True)[source]#

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:
Xarray-like of shape (n_samples, n_features)

Input samples.

yarray-like of shape (n_samples,) or (n_samples, n_outputs), default=None

Target values (None for unsupervised transformations).

**fit_paramsdict

Additional fit parameters.

Returns:
X_newndarray array of shape (n_samples, n_features_new)

Transformed array.

get_feature_names_out(input_features: None | npt.ArrayLike = None) → np.ndarray[source]#

Get output feature names.

Parameters:
input_featuresNone | npt.ArrayLike, optional

Input feature names, by default None

Returns:
feature_names_outndarray of str objects

Transformed feature names.

get_metadata_routing()#

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:
routingMetadataRequest

A MetadataRequest encapsulating routing information.

get_params(deep=True)#

Get parameters for this estimator.

Parameters:
deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:
paramsdict

Parameter names mapped to their values.

inverse_transform(X_transformed, t_num=100, as_frame=False)[source]#

Inverse analysis of elliptic Fourier analysis.

Parameters:
X_transformedarray-like of shape (n_samples, n_features)

Elliptic Fourier coefficients.

t_numint, default = 100

Number of coordinate values.

as_framebool, default = False

If True, return pd.DataFrame.

Returns:
X_coordsarray-like of shape (n_samples, t_num, 2) or pd.DataFrame

Coordinate values reconstructed from the elliptic Fourier coefficients.

set_inverse_transform_request(*, X_transformed: bool | None | str = '$UNCHANGED$', as_frame: bool | None | str = '$UNCHANGED$', t_num: bool | None | str = '$UNCHANGED$') → EllipticFourierAnalysis#

Request metadata passed to the inverse_transform method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

  • True: metadata is requested, and passed to inverse_transform if provided. The request is ignored if metadata is not provided.

  • False: metadata is not requested and the meta-estimator will not pass it to inverse_transform.

  • None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

  • str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:
X_transformedstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for X_transformed parameter in inverse_transform.

as_framestr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for as_frame parameter in inverse_transform.

t_numstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for t_num parameter in inverse_transform.

Returns:
selfobject

The updated object.

set_output(*, transform=None)#

Set output container.

See Introducing the set_output API for an example on how to use the API.

Parameters:
transform{“default”, “pandas”}, default=None

Configure output of transform and fit_transform.

  • “default”: Default output format of a transformer

  • “pandas”: DataFrame output

  • “polars”: Polars output

  • None: Transform configuration is unchanged

Added in version 1.4: “polars” option was added.

Returns:
selfestimator instance

Estimator instance.

set_params(**params)#

Set the parameters of this estimator.

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

Parameters:
**paramsdict

Estimator parameters.

Returns:
selfestimator instance

Estimator instance.

set_transform_request(*, norm: bool | None | str = '$UNCHANGED$', t: bool | None | str = '$UNCHANGED$') → EllipticFourierAnalysis#

Request metadata passed to the transform method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

  • True: metadata is requested, and passed to transform if provided. The request is ignored if metadata is not provided.

  • False: metadata is not requested and the meta-estimator will not pass it to transform.

  • None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

  • str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:
normstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for norm parameter in transform.

tstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for t parameter in transform.

Returns:
selfobject

The updated object.

transform(X: list(npt.ArrayLike) | npt.ArrayLike, t: npt.ArrayLike = None, norm: bool = True) → npt.ArrayLike[source]#

EFA.

Parameters:
X: {list of array-like, array-like} of shape (n_samples, n_coords, dim)

Coordinate values of n_samples. The i-th array-like of shape (n_coords_i, 2) represents 2D coordinate values of the i-th sample.

t: array-like of shape (n_samples, n_coords), optional

Parameters indicating the position on the outline of n_samples. The i-th ndarray of shape (n_coords_i, ) corresponds to each coordinate value in the i-th element of X. If t=None, then t is calculated based on the coordinate values with the linear interpolation.

norm: bool, default=True

Normalize the elliptic Fourier coefficients by the major axis of the 1st ellipse.

Returns:
X_transformed: array-like of shape (n_samples, (1+2*n_harmonics)*n_dim)

Returns the array-like of coefficients. (a_0, a_1, …, a_n, b_0, b_1, …, b_n, , c_0, c_1, …, c_n, d_0, d_1, …, d_n)

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