stnmf.spatial.ellipse

stnmf.spatial.ellipse(image, sigma=2.0)

Fit a two-dimensional Gaussian to an image and return a parameterized ellipse

Parameters:

  • image ((x,y) or (r,x,y) array_like) – Two-dimensional image or stack of r independent two-dimensional images, where x and y are the spatial dimensions

  • sigma (float, optional) – Standard deviations (s.d.) of the mean (Mahalanobis distance) for the ellipse boundary. 2 s.d. are best suited for analysis of receptive fields of retinal ganglion cells [1]. Default is 2.0

Returns:

(mux, muy, r_major, r_minor, rad) (tuple of float, (r,5) np.ndarray) – Parameterized ellipse, where mux and muy are the centroid, r_major and r_minor are the semi-major and semi-minor axes, that is, major and minor radii, and rad is the rotation in radians. Or stack of r parameterized ellipses in an (r, 5) float array

Raises:

Examples

The parameterized ellipse offers a compressed representation of the ellipse. For example, it is useful for calculating the effective diameter of a receptive field.

>>> p = ellipse(spatial_filter)
>>> pixel_size = 30  # Conversion to micrometers
>>> a, b = p[2:4]    # Major and minor axes radii
>>> rf_diameter = 2 * np.sqrt(a*b) * pixel_size

To obtain an outline of the ellipse in data coordinates:

>>> mux, muy, r_major, r_minor, rad = ellipse(spatial_filter)
>>> num_points = 200
>>> ls = np.linspace(0, 2*np.pi, num_points)

>>> rot = [[np.cos(rad), -np.sin(rad)], [np.sin(rad), np.cos(rad)]]
>>> pos = [r_major * np.cos(ls), r_minor * np.sin(ls)]
>>> points = np.dot(rot, pos) + [[mux], [muy]]

References