This Python script implements the eight-point algorithm for estimating the essential matrix from corresponding points in two images, using the power of PyTorch for efficient numerical computations both in CPU and GPU. The essential matrix is a fundamental component in computer vision, used for tasks such as stereo vision, structure from motion, and camera calibration.

• Introduction
• Requirements
• Usage

The eight-point algorithm is a widely used method for estimating the essential matrix, which encodes the geometric relationship between two camera views of a scene. Given corresponding points in two images and camera matrices, the algorithm computes the essential matrix that describes the relative pose between the two camera views.

This algorithm is implemented in Python using the PyTorch library for efficient numerical computations, enabling seamless execution on both GPUs and CPUs.

This figure provides an illustration of epipolar lines being computed across two images for a given collection of matching points:

This graph depicts the relationship between time and the quantity of points, showcasing the PyTorch implementation on both CPU and GPU, alongside the OpenCV cv.findEssentialMat using the method=cv.LMEDS. The exclusion of OpenCV cv.findEssentialMat with method=cv.RANSAC is due to its partial utilization of points.

Evidently, the PyTorch implementations on both CPU and GPU exhibit swifter performance compared to the OpenCV cv.findEssentialMat when employing the method=cv.LMEDS. Notably, as the number of points escalates, the execution time on CPU experiences a significant surge, whereas the GPU execution time remains relatively stable. It is noteworthy that the GPU implementation aligns with the CPU counterpart after approximately 1000 sets of corresponding points.

To run this script, you need:

• Python 3.x
• PyTorch
• Numpy

To use the eight_point_essential_matrix function, follow these steps:

1. Copy the eight_point_essential_matrix function from the provided script.

2. Call the function with appropriate inputs:

   img1_points = ...  # Corresponding points in image 1 (N x 2)
   img2_points = ...  # Corresponding points in image 2 (N x 2)
   camera_1_matrix = ...  # Camera matrix for image 1 (3 x 3)
   camera_2_matrix = ...  # Camera matrix for image 2 (3 x 3)
   
   device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
   result = eight_point_essential_matrix(img1_points, img2_points, camera_1_matrix, camera_2_matrix, device=device)

3. The result will be a dictionary containing the estimated essential matrix and normalized epipoles for both images.

4. For a practical demonstration of invoking this function and subsequently computing as well as visualizing epipolar lines, please refer to the run.py script.