Add line estimation model

skimage/measure/fit.py

@@ -0,0 +1,125 @@
+import numpy as np
+
+
+class BaseModel(object):
+
+    def __init__(self):
+        self._params = None
+
+
+class LineModel(BaseModel):
+
+    '''Total least squares estimator for 2D lines.
+
+    Lines are parameterized using polar coordinates:
+
+        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`.
+
+    '''
+
+    def estimate(self, data):
+        '''Estimate line model from data using total least squares.
+
+        Parameters
+        ----------
+        data : (N, 2) array
+            N points with `(x, y)` coordinates, respectively.
+
+        '''
+
+        X0 = data.mean(axis=0)
+
+        if data.shape[0] == 2: # well determined
+            theta = np.arctan2(data[1,1] - data[0,1], data[1,0] - data[0,0])
+        elif data.shape[0] > 2: # over-determined
+            data = data - X0
+            # first principal component
+            _, _, v = np.linalg.svd(data)
+            theta = np.arctan2(v[0, 1], v[0, 0])
+        else: # under-determined
+            raise ValueError('At least 2 input points needed.')
+
+        # angle perpendicular to line angle
+        theta = (theta + np.pi / 2) % np.pi
+        # line always passes through mean
+        dist = X0[0] * np.cos(theta) + X0[1] * np.sin(theta)
+
+        self._params = np.array([dist, theta])
+
+    def residuals(self, data):
+        '''Determine residuals of data to model.
+
+        For each point the shortest distance to the line is returned.
+
+        Parameters
+        ----------
+        data : (N, 2) array
+            N points with `(x, y)` coordinates, respectively.
+
+        Returns
+        -------
+        residuals : (N, ) array
+            Residual for each data point.
+
+        '''
+
+        dist, theta = self._params
+        data_dists = (data[:, 0] * np.cos(theta) + data[:, 1] * np.sin(theta))
+        return np.abs(dist - data_dists)
+
+    @classmethod
+    def is_degenerate(cls, data):
+        '''Check whether set of points is degenerate.
+
+        Parameters
+        ----------
+        data : (N, 2) array
+            N points with `(x, y)` coordinates, respectively.
+
+        Returns
+        -------
+        flag : bool
+            Flag indicating if data is degenerate.
+
+        '''
+
+        return data.shape[0] < 2
+
+    def predict_x(self, y):
+        '''Predict x-coordinates using the estimated model.
+
+        Parameters
+        ----------
+        y : array
+            y-coordinates.
+
+        Returns
+        -------
+        x : array
+            Predicted x-coordinates.
+
+        '''
+
+        dist, theta = self._params
+        return (dist - y * np.cos(theta)) / np.cos(theta)
+
+    def predict_y(self, x):
+        '''Predict y-coordinates using the estimated model.
+
+        Parameters
+        ----------
+        x : array
+            x-coordinates.
+
+        Returns
+        -------
+        y : array
+            Predicted y-coordinates.
+
+        '''
+
+        dist, theta = self._params
+        return (dist - x * np.cos(theta)) / np.sin(theta)