Camera position in world coordinate from cv::solvePnP

The term "camera-position-in-world-coordinate-from-cv-solvepnp" refers to the use of the solvePnP function in computer vision libraries, such as OpenCV, to determine the position and orientation of a camera in world coordinates based on known object points and their corresponding image points.

What is solvePnP?

solvePnP stands for "solve Perspective-n-Point." It is a function used in computer vision, specifically in the OpenCV library, to estimate the pose of a 3D object when given a set of 3D points on the object and their corresponding 2D projections in an image. The "pose" here refers to the position and orientation (rotation) of the object (or camera) relative to some coordinate system.

How Does It Work?

The function works under the perspective projection model where a few known points on an object (n>=4 non-coplanar points) are related to their positions in a camera's image. Here's the basic outline:

1. Object Points: These are the coordinates of points in the world (3D space). In the context of camera position estimation, these are often predefined markers or features whose world coordinates are known.
2. Image Points: These are the coordinates of the same points on the object as seen by the camera (2D space).
3. Camera Matrix: Also known as the intrinsic matrix, it includes information like the focal lengths (fx, fy) and the optical center (cx, cy), usually obtained from camera calibration.
4. Distortion Coefficients: These parameters account for lens distortion that affects the camera's image.

Using these inputs, solvePnP computes the rotation vector and the translation vector, which together describe the camera's pose relative to the world coordinates:

• Rotation Vector: This vector can be converted to a rotation matrix that describes how much the camera is rotated concerning the world coordinate system.
• Translation Vector: This describes the position of the camera's origin in world coordinates.

Why is it Useful?

Knowing the camera's position and orientation in a global space is critical for various applications:

• Augmented Reality (AR): Placing virtual objects in real-world scenes accurately.
• Robotics: Navigation and interaction with objects.
• 3D Reconstruction: Building a 3D model of the world from different camera viewpoints.
• Computer Graphics: Integrating CGI accurately with filmed footage.

Practical Example

If you use OpenCV, the solvePnP function might be used as follows:

import cv2
import numpy as np

# Extended to 6 known 3D coordinates of object points
object_points = np.array([
    [0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1], [1, 1, 0], [1, 0, 1]
], dtype=float)

# Corresponding 2D coordinates on the camera image
image_points = np.array([
    [320, 240], [420, 240], [320, 340], [320, 240], [420, 340], [420, 240]
], dtype=float)

# Camera matrix (ensure you replace with your camera's calibration data)
camera_matrix = np.array([
    [800, 0, 320],
    [0, 800, 240],
    [0, 0, 1]
])

# Assuming no lens distortion
dist_coeffs = np.zeros(4)

# Solve for pose using SOLVEPNP_ITERATIVE
success, rotation_vector, translation_vector = cv2.solvePnP(
    object_points, image_points, camera_matrix, dist_coeffs, flags=cv2.SOLVEPNP_ITERATIVE
)

# Check if solvePnP was successful
if success:
    print("Rotation Vector:\n", rotation_vector)
    print("Translation Vector:\n", translation_vector)
else:
    print("solvePnP failed to find a solution.")

Output:

Rotation Vector:
 [[0.09769877]
 [0.03272385]
 [3.13898061]]
Translation Vector:
 [[-0.01693165]
 [-0.01949978]
 [-8.32753168]]

Here, the rotation_vector and translation_vector together give the position of the camera in world coordinates, assuming the object points are fixed in the world. This helps in understanding where the camera is in space relative to these known points.