Camera Projection

We can see the camera coordinate frame and a grid of points in the camera coordinate system which will be projected on the sensor. From the coordinates on the sensor we can compute the corresponding pixels.

import numpy as np
import matplotlib.pyplot as plt
from pytransform3d.transformations import plot_transform
from pytransform3d.camera import make_world_grid, cam2sensor, sensor2img


focal_length = 0.2
sensor_size = (0.2, 0.15)
image_size = (640, 480)

plt.figure(figsize=(12, 5))
ax = plt.subplot(121, projection="3d")
ax.set_title("Grid in 3D camera coordinate system")
ax.set_xlim((-1, 1))
ax.set_ylim((-1, 1))
ax.set_zlim((0, 2))
ax.set_xlabel("X")
ax.set_ylabel("Y")
ax.set_zlabel("Z")

cam_grid = make_world_grid(n_points_per_line=11) - np.array([0, 0, -2, 0])
img_grid = cam_grid * focal_length

c = np.arange(len(cam_grid))
ax.scatter(cam_grid[:, 0], cam_grid[:, 1], cam_grid[:, 2], c=c)
ax.scatter(img_grid[:, 0], img_grid[:, 1], img_grid[:, 2], c=c)
plot_transform(ax)

sensor_grid = cam2sensor(cam_grid, focal_length)
img_grid = sensor2img(sensor_grid, sensor_size, image_size)
ax = plt.subplot(122, aspect="equal")
ax.set_title("Grid in 2D image coordinate system")
ax.scatter(img_grid[:, 0], img_grid[:, 1], c=c)
ax.set_xlim((0, image_size[0]))
ax.set_ylim((0, image_size[1]))

plt.show()