Computing the Minimum Bounding Rectangle for a Closed Region

This MATLAB code demonstrates how to compute the minimum bounding rectangle for a closed region. The minimum bounding rectangle refers to the smallest-area rectangle that can exactly enclose the given region. This algorithm is widely used in computer vision and image processing applications for object localization and shape analysis. The implementation consists of several key steps: First, the region data is loaded from a text file containing coordinate points: data = load('region_data.txt'); The core computation uses the minboundrect function, which implements a rotating calipers algorithm to find the optimal rectangle orientation by calculating convex hull properties and testing different rotation angles: rect = minboundrect(data); Visualization is achieved by plotting both the original region points and the computed rectangle boundary: plot(data(:,1), data(:,2), 'b.'); hold on; plot(rect(:,1), rect(:,2), 'r-', 'LineWidth', 2); hold off; legend('Original Region', 'Minimum Bounding Rectangle'); Finally, the rectangle coordinates and area are calculated using polyarea function, which implements the shoelace formula for polygon area computation: area = polyarea(rect(:,1), rect(:,2)); disp('Minimum bounding rectangle coordinates:'); disp(rect); disp(['Minimum bounding rectangle area: ', num2str(area)]); This MATLAB implementation can calculate minimum bounding rectangles for any closed region by simply modifying the input filename. The algorithm handles arbitrary 2D shapes by first computing their convex hull and then determining the optimal rectangle orientation that minimizes area while fully containing all points.