Epipolar Line Visualization

Implement a function to compute and draw epipolar lines given a fundamental matrix. The fundamental matrix is a key concept in Epipolar Geometry, which describes the relationship between two images of the same scene taken from different viewpoints. This relationship is crucial in Depth Estimation tasks, as it allows us to infer the 3D structure of the scene from 2D images.

To find the epipolar line in image 2 corresponding to a point in image 1, we can use the following process:

Represent the point in image 1 as a vector $x$ .
Multiply the fundamental matrix $F$ by the point $x$ to obtain the coefficients of the epipolar line $l$ in image 2.

l = F \cdot x

This technique is widely used in computer vision applications, such as stereo vision and structure from motion.

Example:

Input:

Point and F matrix

Output:

Epipolar line coefficients

Reasoning:

l = F @ [x, y, 1]

Constraints:

Input parameters: point (1D numpy array of shape (3,) with dtype float64), F (2D numpy array of shape (3, 3) with dtype float64)
Valid ranges: point coordinates in [0, 1000], F matrix elements in [-1000, 1000]
Output format: return epipolar line coefficients as 1D numpy array of shape (3,) with dtype float64, representing ax + by + c = 0
Special conditions: assume point is in homogeneous coordinates (x, y, 1) and F is a valid fundamental matrix with rank 2

Example:

Constraints:

Test Results