Minimum Bounding Rectangle Fitting for Convex Hull Boundaries

Minimum bounding rectangle fitting for convex hull boundaries is a fundamental computational geometry problem with broad applications in object detection, bounding box computation, and image processing. The core objective is to find the smallest possible rectangle that completely encloses a convex hull.

### Implementation Approach Convex Hull Calculation: The process begins by extracting boundary points of the target object and computing its convex hull. The convex hull represents the smallest convex polygon containing all boundary points, effectively eliminating interference from redundant points. Rotating Calipers Method: This algorithm systematically explores all possible orientations of the convex hull by rotating the coordinate system. For each orientation, it calculates the corresponding minimum bounding rectangle, ensuring tight fitting around the hull geometry. Rectangle Parameter Optimization: At each rotation angle, the method identifies extreme points (leftmost, rightmost, topmost, bottommost) of the projected convex hull to determine rectangle dimensions and position. The final solution selects the rectangle with the smallest area among all orientations.

### MATLAB Implementation Key Points Convex Hull Extraction: Use the built-in `convhull` function to efficiently compute convex hull vertices. Extreme Point Calculation: During rotation, determine extreme points through coordinate projections to establish rectangle width and height. Angle Optimization: Typically rotate the coordinate system in fixed increments (e.g., 1-degree steps) to balance computational efficiency with global optimality approximation.

This method not only fits regular shapes effectively but also handles complex contour bounding box calculations, demonstrating high practical utility in engineering applications.