Symmetry Detection and Analysis Algorithm (Algorithm 1)

--Output Using Algorithm 1 This algorithm efficiently identifies and analyzes symmetry in images through a series of methodical steps:

1. Finding the Line of Symmetry

SIFT Feature Matching:
- Utilizes SIFT (Scale-Invariant Feature Transform) to extract keypoints and descriptors from both the original image and its horizontally flipped version.
- Matches these features using a brute-force matcher (BFMatcher), selecting the most accurate matches.
Hexbin Analysis:
- Analyzes matched points by calculating the angle and distance (r, theta) relative to the X-axis.
- Generates a hexbin plot to visualize the distribution of these (r, θ) pairs.
Vote Sorting:
- Examines the hexbin plot to identify the most prominent bin, indicating the most likely line of symmetry.

Corner Detection:
- Applies Harris corner detection to identify points with significant intensity changes, often corresponding to corners.
Thresholding and Sorting:
- Filters detected corners using a threshold and selects the top 15 based on their corner response values (corner strength).
Code Implementation:
- The detect_harris_corners function processes the image, converting it to grayscale, applying the Harris corner detector, and selecting the top 15 corners.

Symmetry Line Equation:
- Determines the line of symmetry (given by r and theta), and calculates each detected corner's symmetric counterpart using geometric properties of the line.
Opposite Point Calculation:
- Computes the corresponding point for each corner on the opposite side of the symmetry line by reflecting the point across the line.

Spline Drawing:
- Draws a B-spline curve connecting each original corner and its symmetric counterpart.
- The draw_b_spline_curve function interpolates between these points to create smooth connecting curves.

The final image displays the original Harris corners, their symmetric counterparts, the symmetry line, and the B-spline curves connecting each pair of points.

This approach combines feature matching, symmetry detection, corner detection, and curve interpolation to analyze and visualize symmetry in images.