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Calculate Image Moments of an Ellipse

Image moments can be used to determine the center of gravity or average pixel location of a binary object as well as the orientation of an object according to its axes of variation.

The interactive plot below demonstrates how to calculate the image moments of an ellipse-defined mask.

import itk
import matplotlib.pyplot as plt
import numpy as np
from ipywidgets import interact

output_size = [100, 100]  # size of binary image containing the ellipse


@interact(
    tx=(0, output_size[0], 1),
    ty=(0, output_size[1], 1),
    a=(5, 50, 1),
    b=(5, 50, 1),
    theta=(0, 2 * np.pi, 0.1),
)
def foo(tx=30, ty=50, a=5, b=10, theta=np.pi / 4.0):
    """
    Creates a binary image of an ellipse and calculates the image moments.  Major (purple) and minor (green)
    principal axes are displayed.

    Parameters
    ==========
    tx, ty : translation x and y
    a, b : ellipse horizontal and vertical widths before rotation
    theta : angle of rotation (radians)
    """

    # ellipse starts as unit circle, use world transform to define final ellipse
    ellipse = itk.EllipseSpatialObject[2].New()
    ellipse_transform = itk.AffineTransform[itk.D, 2].New()
    ellipse_transform.Scale([a, b])
    ellipse_transform.Rotate2D(theta)
    ellipse_transform.Translate([tx, ty])
    ellipse.SetObjectToWorldTransform(ellipse_transform)

    ellipse_img = itk.spatial_object_to_image_filter(
        input=ellipse, inside_value=1, outside_value=0, size=output_size
    )

    momentor = itk.ImageMomentsCalculator.New(Image=ellipse_img)
    momentor.Compute()

    centroid = momentor.GetCenterOfGravity()
    prin_axes = itk.array_from_matrix(momentor.GetPrincipalAxes())
    minor_axes = prin_axes[0]
    major_axes = prin_axes[1]

    fig, ax = plt.subplots(figsize=[8, 8])
    plt.imshow(ellipse_img, cmap="gray")
    plt.scatter(centroid[0], centroid[1])

    minor_pt = centroid + minor_axes * 5
    plt.plot([centroid[0], minor_pt[0]], [centroid[1], minor_pt[1]], color="green")

    major_pt = centroid + major_axes * 5
    plt.plot([centroid[0], major_pt[0]], [centroid[1], major_pt[1]], color="purple")

    print(momentor)