ellipse

A parametrized dataset of pictures of ellipses, for Neural Network experimentation.

from ellipse import *
import matplotlib.pyplot as plt
%matplotlib inline

This example reminds us how the plots are oriented, which is not the usual math way.

A = np.array([[1,2],[3,4]])
print(A)
plt.imshow(A, cmap='Blues')
plt.colorbar()
plt.show()

[[1 2]
 [3 4]]

Basic options

Let's see the basic parameters

plt.imshow(get_ellipse())
plt.show()

Change the position

plt.imshow(get_ellipse(row=40, col=10))
plt.show()

Change the radii

plt.imshow(get_ellipse(a=20, b=5))
plt.show()

Change the angle. Note that the image row,col coordinate system is still right-handed, so rotation turns anticlockwise as normal.

plt.imshow(get_ellipse(a=20, b=5, theta=np.pi/12))
plt.show()

We can combine all the options

plt.imshow(get_ellipse(row=48, col=16, a=16, b=2, theta=np.pi/6))
plt.show()

Advanced Options

We can adjust the downsampling to make a smoother or coarser edge. The default is 4. For illustration, here is the edge effect of the downsampling

fig,ax = plt.subplots(1,3, figsize=(6,18),dpi=100)
ax[0].imshow(get_ellipse(a=20, downsample_factor=1))
ax[0].set_title("factor 1")
ax[0].set_aspect(1.0)
ax[1].imshow(get_ellipse(a=20, downsample_factor=10))
ax[1].set_title("factor 10")
ax[1].set_aspect(1.0)
ax[2].imshow(get_ellipse(a=20, downsample_factor=10) - get_ellipse(a=20, downsample_factor=1))
ax[2].set_title("difference")
ax[2].set_aspect(1.0)
fig.tight_layout()
plt.show()

The coordinate system wraps around, so the ellipse is really drawn on a torus.

plt.imshow(get_ellipse(img_size=64, row=56, col=16, a=16, b=2, theta=np.pi/6, downsample_factor=4))
plt.show()

We can change the canvas size, but note that you will want to adjust the centers and radii, which chosen to reasonable values for a 64x64 canvas

plt.imshow(get_ellipse(img_size=8, row=5, col=3, a=3, b=1, theta=np.pi/6, downsample_factor=1))
plt.show()

plt.imshow(get_ellipse(img_size=256, row=160, col=96, a=96, b=32, theta=np.pi/6, downsample_factor=1))
plt.show()

Sometimes, we do not want to allow that wrap-around. The check_bounds function is used by allow_wrap=False. See the check_bounds.ipynb notebook for more use of boundschecking.

check_bounds(img_size=64, row=56, col=16, a=16, b=2, theta=np.pi/6, downsample_factor=4)

False

check_bounds(img_size=64, row=47, col=16, a=16, b=2, theta=np.pi/6, downsample_factor=4)

True

Generating Random Examples

We can generate random examples and feed their parameters to get_ellipse

p = generate(64, row_range=(0,64), col_range=(0,64), area_range=(8*np.pi,16*np.pi), logar_range=(1,2), theta_range=(0,np.pi))
plt.imshow(get_ellipse(**p))
plt.title(f"bounds? {check_bounds(**p)}")
plt.show()

fig,axs = plt.subplots(1,8, figsize=(4*8,4))
for i in range(8):
    p = generate(64, row_range=(0,64), col_range=(0,64), area_range=(8*np.pi,16*np.pi), logar_range=(1,2), theta_range=(0,np.pi))
    E = get_ellipse(**p, downsample_factor=3)
    axs[i].imshow(E)
plt.show()

Pre-defined datasets

Some datasets are particularly useful for our experiements. We have hard-coded their parameterizations.

from ellipse.datasets import torus
X = torus(n=100,return_arrays=True)

fig,ax = plt.subplots(10,10, figsize=(20,20))
for i in range(100):
    ax[i//10,i%10].imshow(X[i])
plt.show()

import ellipse

help(ellipse.get_ellipse)

Help on function get_ellipse in module ellipse:

get_ellipse(img_size: int = 64, row: int = 32, col: int = 32, a: float = 16, b: float = 16, theta: float = 0.0, downsample_factor: int = 4, allow_wrap=True)
    Make a single ellipse with the given geometry.
    NOTE! We use the "upper-left" origin convention, so that plt.imgshow( ) and print( )
    give the same orientation of the image/matrix.
    
    :param img_size: Output image resolution. For example, 64 gives a 64x64 image.
    :param r: row-position of ellipse center.  Relative to upper-left of image.
    :param c: col-position of ellipse center.  Relative to upper-left of image.
    :param a: Length of semi-major axis.
    :param b: Length of semi-minor axis.
    :param theta: Angle in radians of the semi-major axis versus the row-axis, in range [0,pi]
    :param downsample_factor: Oversampling factor for downscaling image. Default=4.
    :param allow_wrap: If False, raise an exception if the ellipse wraps around the image.
    :return: numpy array of shape (img_size,img_size) suitable for `matplotlib.pyplot.imshow`