Add missing double colons for equations

This commit is contained in:
Johannes Schönberger
2013-05-06 11:36:38 +02:00
parent 5656feb61b
commit 9e7fb07d67
+10 -10
View File
@@ -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