skimage2.measure.LineModelND#

class skimage2.measure.LineModelND(origin, direction)[source]#

Bases: _BaseModel

Total least squares estimator for N-dimensional lines.

In contrast to ordinary least squares line estimation, this estimator minimizes the orthogonal distances of points to the estimated line.

Lines are defined by a point (origin) and a unit vector (direction) according to the following vector equation:

X = origin + lambda * direction

Parameters:

originarray-like, shape (N,): Coordinates of line origin in N dimensions.
directionarray-like, shape (N,): Vector giving line direction.

Raises:

ValueError: If length of origin and direction differ.

Examples

>>> x = np.linspace(1, 2, 25)
>>> y = 1.5 * x + 3
>>> lm = LineModelND.from_estimate(np.stack([x, y], axis=-1))
>>> lm.origin
array([1.5 , 5.25])
>>> lm.direction
array([0.5547 , 0.83205])
>>> res = lm.residuals(np.stack([x, y], axis=-1))
>>> np.abs(np.round(res, 9))
array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
       0., 0., 0., 0., 0., 0., 0., 0.])
>>> np.round(lm.predict_y(x[:5]), 3)
array([4.5  , 4.562, 4.625, 4.688, 4.75 ])
>>> np.round(lm.predict_x(y[:5]), 3)
array([1.   , 1.042, 1.083, 1.125, 1.167])

__init__(origin, direction)[source]#

estimate(data)[source]#

Estimate line model from data.

Deprecated since version 0.26: estimate is deprecated since version 0.26 and will be removed in version 2.2. Please use LineModelND.from_estimate class constructor instead.

This minimizes the sum of shortest (orthogonal) distances from the given data points to the estimated line.

Parameters:

data(N, dim) array: N points in a space of dimensionality dim >= 2.

Returns:

successbool: True, if model estimation succeeds.

classmethod from_estimate(data)[source]#

Estimate line model from data.

This minimizes the sum of shortest (orthogonal) distances from the given data points to the estimated line.

Parameters:

data(N, dim) array: N points in a space of dimensionality dim >= 2.

Returns:

modelSelf or FailedEstimation

An instance of the line model if the estimation succeeded. Otherwise, we return a special FailedEstimation object to signal a failed estimation. Testing the truth value of the failed estimation object will return False. E.g.

model = LineModelND.from_estimate(...)
if not model:
    raise RuntimeError(f"Failed estimation: {model}")

property params#: Return model attributes as origin, direction tuple.

Deprecated since version 0.26: params is deprecated since version 0.26 and will be removed in version 2.2. params attribute deprecated; use origin, direction attributes instead.

predict(x, axis=0, params=<DEPRECATED>)[source]#

Predict intersection of line model with orthogonal hyperplane.

Parameters:

xndarray of shape (n, 1): Coordinates along an axis.
axisint: Axis orthogonal to the hyperplane intersecting the line.

Returns:

datandarray of shape (n, m): Predicted coordinates.

Other Parameters:

paramsDEPRECATED, optional: Optional custom parameter set in the form (origin, direction).

Deprecated since version 0.26.

Raises:

ValueError: If the line is parallel to the given axis.

predict_x(y, params=<DEPRECATED>)[source]#

Predict x-coordinates for 2D lines using the estimated model.

Alias for:

predict(y, axis=1)[:, 0]

Parameters:

yarray: y-coordinates.

Returns:

xarray: Predicted x-coordinates.

Other Parameters:

paramsDEPRECATED, optional: Optional custom parameter set in the form (origin, direction).

Deprecated since version 0.26.

predict_y(x, params=<DEPRECATED>)[source]#

Predict y-coordinates for 2D lines using the estimated model.

Alias for:

predict(x, axis=0)[:, 1]

Parameters:

xarray: x-coordinates.

Returns:

yarray: Predicted y-coordinates.

Other Parameters:

paramsDEPRECATED, optional: Optional custom parameter set in the form (origin, direction).

Deprecated since version 0.26.

residuals(data, params=<DEPRECATED>)[source]#

Determine residuals of data to model.

For each point, the shortest (orthogonal) distance to the line is returned. It is obtained by projecting the data onto the line.

Parameters:

data(N, dim) array: N points in a space of dimension dim.

Returns:

residuals(N,) array: Residual for each data point.

Other Parameters:

paramsDEPRECATED, optional: Optional custom parameter set in the form (origin, direction).

Deprecated since version 0.26.