pysdic.Camera.project#

Camera.project(world_points, dx=False, dintrinsic=False, ddistortion=False, dextrinsic=False)[source]#

Project 3D world points to 2D images points using the camera’s intrinsic, extrinsic, and distortion parameters.

Note

The output are the image_points in the image coordinate system \((x, y)\) and not the pixel points (rows, columns).

See also

image_points_to_pixel_points() to convert the image points to pixel points if needed.
See the package pycvcam (Artezaru/pycvcam) for more information on the implementation details.
ProjectionResult for the structure of the output.

Parameters:

world_points (numpy.ndarray) – An array of shape (…, 3) representing \(N_p\) 3D points in the world coordinate system.
dx (bool, optional) – If True, the function will also return the jacobian of the image points with respect to the world points. Default is False.
dintrinsic (bool, optional) – If True, the function will also return the jacobian of the image points with respect to the intrinsic parameters. Default is False.
ddistortion (bool, optional) – If True, the function will also return the jacobian of the image points with respect to the distortion parameters. Default is False.
dextrinsic (bool, optional) – If True, the function will also return the jacobian of the image points with respect to the extrinsic parameters. Default is False.

Returns:

A ProjectionResult object containing the projected image points and optionally the jacobians.

image_points: An array of shape (…, 2) representing the projected images points in the image coordinate system \((x, y)\).
jacobian_dx: (optional) An array of shape (…, 2, 3) representing the jacobian of the normalized points with respect to the world points if dx is True.
jacobian_dintrinsic: (optional) An array of shape (…, 2, \(N_{\text{intrinsic}}\)) representing the jacobian of the pixel points with respect to the intrinsic parameters if dintrinsic is True.
jacobian_ddistortion: (optional) An array of shape (…, 2, \(N_{\text{distortion}}\)) representing the jacobian of the pixel points with respect to the distortion parameters if ddistortion is True.
jacobian_dextrinsic: (optional) An array of shape (…, 2, \(N_{\text{extrinsic}}\)) representing the jacobian of the pixel points with respect to the extrinsic parameters if dextrinsic is True.

Return type:

ProjectionResult

Examples

Lets create a simple camera and project some 3D points:

import numpy
from pysdic import Camera
from pycvcam import Cv2Extrinsic, Cv2Intrinsic

rotation_vector = numpy.array([0.1, 0.2, 0.3])
translation_vector = numpy.array([12.0, 34.0, 56.0])

extrinsic = Cv2Extrinsic.from_rt(rotation_vector, translation_vector)

intrinsic = Cv2Intrinsic.from_matrix(
    numpy.array([[1000, 0, 320],
                [0, 1000, 240],
                [0, 0, 1]])
)

camera = Camera(
    sensor_height=480,
    sensor_width=640,
    intrinsic=intrinsic,
    extrinsic=extrinsic,
)

# Define some 3D world points
world_points = numpy.array([
    [0, 0, 1000],
    [100, 0, 1000],
    [0, 100, 1000],
    [100, 100, 1000]
])

# Project the 3D points to 2D image points
projection_result = camera.project(world_points, dx=True, dintrinsic=True, dextrinsic=True)

Extracting the projected image points and jacobians:

image_points = projection_result.image_points # The projected 2D image points of shape (4, 2)
jacobian_dx = projection_result.jacobian_dx # The jacobian with respect to the world points of shape (4, 2, 3)
jacobian_dintrinsic = projection_result.jacobian_dintrinsic # The jacobian with respect to the intrinsic parameters of shape (4, 2, 4)
jacobian_dextrinsic = projection_result.jacobian_dextrinsic # The jacobian with respect to the extrinsic parameters of shape (4, 2, 6)

pysdic.Camera.project#

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