diff --git a/skimage/measure/fit.py b/skimage/measure/fit.py index 9b9d4526..cd739316 100644 --- a/skimage/measure/fit.py +++ b/skimage/measure/fit.py @@ -18,18 +18,18 @@ class LineModel(BaseModel): """Total least squares estimator for 2D lines. - Lines are parameterized using polar coordinates as functional model: + Lines are parameterized using polar coordinates as functional model:: dist = x * cos(theta) + y * sin(theta) This parameterization is able to model vertical lines in contrast to the standard line model `y = a*x + b`. - This estimator minimizes the squared distances from all points to the line: + This estimator minimizes the squared distances from all points to the line:: min{ sum((dist - x_i * cos(theta) + y_i * sin(theta))**2) } - The `_params` attribute contains the parameters in the following order: + The `_params` attribute contains the parameters in the following order:: dist, theta @@ -143,16 +143,16 @@ class CircleModel(BaseModel): """Total least squares estimator for 2D circles. - The functional model of the circle is: + The functional model of the circle is:: r**2 = (x - xc)**2 + (y - yc)**2 This estimator minimizes the squared distances from all points to the - circle: + circle:: min{ sum((r - sqrt((x_i - xc)**2 + (y_i - yc)**2))**2) } - The `_params` attribute contains the parameters in the following order: + The `_params` attribute contains the parameters in the following order:: xc, yc, r @@ -260,7 +260,7 @@ class EllipseModel(BaseModel): """Total least squares estimator for 2D ellipses. - The functional model of the ellipse is: + The functional model of the ellipse is:: xt = xc + a*cos(theta)*cos(t) - b*sin(theta)*sin(t) yt = yc + a*sin(theta)*cos(t) + b*cos(theta)*sin(t) @@ -270,14 +270,14 @@ class EllipseModel(BaseModel): shortest distance from the point to the ellipse. This estimator minimizes the squared distances from all points to the - ellipse: + ellipse:: min{ sum(d_i**2) } = min{ sum((x_i - xt)**2 + (y_i - yt)**2) } Thus you have `2 * N` equations (x_i, y_i) for `N + 5` unknowns (t_i, xc, yc, a, b, theta), which gives you an effective redundancy of `N - 5`. - The `_params` attribute contains the parameters in the following order: + The `_params` attribute contains the parameters in the following order:: xc, yc, a, b, theta @@ -513,7 +513,7 @@ def ransac(data, model_class, min_samples, residual_threshold, ------- model : object Best model with largest consensus set. - inliers : (N,) array + inliers : (N, ) array Indices of inliers. References