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5 changed files with 10 additions and 155 deletions

1
.gitignore vendored
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build

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#!/bin/bash
# Check if the argument is provided
if [ -z "$1" ]; then
echo "No C++ file provided."
exit 1
fi
# Extract the filename without extension
filename=$(basename -- "$1")
filename="${filename%.*}"
mkdir -p "build/$filename"
# Compile the C++ file
g++ -o "build/$filename/$filename" "$1"
# Check if the compilation was successful
if [ $? -eq 0 ]; then
echo "Compilation successful. Executable is located at build/$filename/$filename"
else
echo "Compilation failed."
exit 1
fi
echo "Running: $filename"
build/$filename/$filename

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@ -170,15 +170,16 @@ def main():
print("e1: " , e1)
print("e2: " , e2)
if True:
t = D[:3, 3]
t_2d = apply_intrinsics(K, t)
# can we find e1's epipol by projecting p2 into p1 (which is effectively projecting t into p1)
print("t: ", t)
print("t_2d: ", t_2d)
print("e1: ", e1)
print("F.T @ t_2d: ", F.T @ t_2d)
return
# if True:
# this is wrong
# t = D[:3, 3]
# t_2d = apply_intrinsics(K, t)
# # can we find e1's epipol by projecting p2 into p1 (which is effectively projecting t into p1)
# print("t: ", t)
# print("t_2d: ", t_2d)
# print("e1: ", e1)
# print("F.T @ t_2d: ", F.T @ t_2d)
# return
img1_with_lines, img2_with_lines = draw_epipolar_lines(img1, img2, pts1, pts2, F)

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#include <iostream>
#include <Eigen/Dense>
#include <iostream>
using std::cout;
using std::endl;
int main() {
// Generate 20 random 2D points (source points)
Eigen::MatrixXd src_points(2, 20);
src_points = Eigen::MatrixXd::Random(2, 20);
// Define a known rotation matrix R and translation vector t
double theta = M_PI / 4; // 45 degrees rotation
Eigen::Matrix2d R;
R << std::cos(theta), -std::sin(theta),
std::sin(theta), std::cos(theta);
Eigen::Vector2d t(1.0, 2.0);
// Apply the transformation to generate the destination points
Eigen::MatrixXd dst_points = (R * src_points).colwise() + t;
// Use Eigen's Umeyama function to estimate the transformation
Eigen::Matrix3d T = Eigen::umeyama(src_points, dst_points, true);
// Print the estimated transformation matrix
std::cout << "Estimated transformation matrix:\n" << T << std::endl;
// Apply the resulting transformation to the source points
Eigen::MatrixXd src_points_hom(3, 20);
src_points_hom.topRows(2) = src_points;
src_points_hom.row(2) = Eigen::RowVectorXd::Ones(20);
Eigen::MatrixXd aligned_points = (T * src_points_hom).topRows(2);
// Print the original, transformed, and recovered points
std::cout << "Original Source Points:\n" << src_points << std::endl;
std::cout << "Transformed Destination Points:\n" << dst_points << std::endl;
std::cout << "Recovered Aligned Points:\n" << aligned_points << std::endl;
// Calculate the difference between the destination points and the aligned points
double difference = (dst_points - aligned_points).norm();
std::cout << "\nDifference between destination and aligned points: " << difference << std::endl;
return 0;
}

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import numpy as np
def umeyama(src, dst, estimate_scale=True):
"""Umeyama algorithm to estimate similarity transformation."""
assert src.shape == dst.shape
# Compute the mean of the source and destination points
src_mean = np.mean(src, axis=0)
dst_mean = np.mean(dst, axis=0)
# Subtract the means from the points
src_centered = src - src_mean
dst_centered = dst - dst_mean
# Compute the covariance matrix
cov_matrix = np.dot(dst_centered.T, src_centered) / src.shape[0]
# Singular Value Decomposition
U, D, Vt = np.linalg.svd(cov_matrix)
# Compute the rotation matrix
R = np.dot(U, Vt)
if np.linalg.det(R) < 0:
Vt[-1, :] *= -1
R = np.dot(U, Vt)
# Compute the scale factor
if estimate_scale:
var_src = np.var(src_centered, axis=0).sum()
scale = 1.0 / var_src * np.sum(D)
else:
scale = 1.0
# Compute the translation vector
t = dst_mean - scale * np.dot(R, src_mean)
# Create the transformation matrix
T = np.identity(3)
T[:2, :2] = scale * R
T[:2, 2] = t
return T
# Generate 20 random 2D points
np.random.seed(42) # For reproducibility
src_points = np.random.rand(20, 2)
# Define a known rotation matrix R and translation vector t
theta = np.pi / 4 # 45 degrees rotation
R = np.array([
[np.cos(theta), -np.sin(theta)],
[np.sin(theta), np.cos(theta)]
])
t = np.array([1.0, 2.0])
# Apply the transformation to generate the destination points
dst_points = np.dot(src_points, R.T) + t
# Perform Umeyama to estimate the transformation
T = umeyama(src_points, dst_points)
# Apply the resulting transformation to the source points
src_points_hom = np.hstack((src_points, np.ones((src_points.shape[0], 1))))
aligned_points = np.dot(T, src_points_hom.T).T[:, :2]
# Calculate the difference between the destination points and the aligned points
difference = np.linalg.norm(dst_points - aligned_points)
print("Original Source Points:\n", src_points)
print("Transformed Destination Points:\n", dst_points)
print("Recovered Aligned Points:\n", aligned_points)
print("\nDifference between destination and aligned points:", difference)