Method:

• Extracted four lines: l₁, l₂, l₃, and l₄ from the given points.
• Computed intersections: l_∞1 = l₁ × l₂ and l_∞2 = l₃ × l₄.
• Found line at infinity: l_∞ = l_∞1 × l_∞2.
• Normalized l_∞ and embedded it in the third row of matrix H.
• Applied matrix H to rectify the image, ensuring that the parallel lines are restored.

Cosines:

Method:

• Constructed matrix A using constraints from the lines:
  • Row: [l₁₀l₂₀, (l₁₀l₂₁ + l₁₁l₂₀) / 2, l₁₁l₂₁]
• Used SVD on A to get V^T and extracted x from the last row: x = V^T[-1] / V^T[-1][-1].
• Formed matrix C_∞ = [[x₀, x₁ / 2], [x₁ / 2, 1]].
• Performed SVD on C_∞ to obtain D for rectification matrix H_metric = diag([√(1/D[0]), √(1/D[1]), 1]) @ U^T.
• Applied matrix H to metric rectify the image, ensuring that the perpendicular lines are restored.

Cosines:

Method

• Constructed matrix A in computeH(x1, x2): Each pair of corresponding points (x, y) from x1 and (u, v) from x2 contributed two equations to the matrix:
  • [u, v, 1, 0, 0, 0, -x * u, -x * v, -x]
  • [0, 0, 0, u, v, 1, -y * u, -y * v, -y]
• Applied SVD: Extracted the last row of V^T to compute the homography matrix H.
• Normalized coordinates: Scaled input points by np.max(points).
• Denormalized H: Adjusted H back to the original coordinate system using the equation:

  Hdenormalized = T-1 H T

  where T is the normalization transformation matrix.
• Composite image: Combined the warped image with the original using a binary mask to create a seamless result.