Centroid Detection for Closed Curves

In image processing and geometric analysis, determining the centroid of closed curves is a fundamental task. MATLAB, with its powerful matrix operations and graphic processing capabilities, is particularly well-suited for such computations through efficient algorithm implementations.

Implementation Approach The program begins by preprocessing input closed curves to ensure continuity. It then calculates centroid coordinates using either polygon approximation or integral methods. For discrete point-based curves, the centroid is approximated by computing the mean of all point coordinates (using mean() function operations). For continuous curves, higher precision is achieved through Green's theorem or area integration methods (implemented via trapz() or integral() functions). Key steps include: - Contour extraction using bwboundaries() for binary images - Coordinate normalization and gap closure algorithms - Vectorized calculations for optimal performance

Key Features - Automatic curve closure handling with manual/auto gap-closing options - Multi-format input support (discrete point sets, binary image contours, etc.) - Visual annotation functionality displaying centroid positions via plot() and scatter() - Computational efficiency optimization suitable for real-time processing through preallocated arrays and parallel computing

Application Scenarios Widely used in industrial part dimension inspection (using regionprops() for comparison), biological cell analysis, motion trajectory tracking, and other fields where centroid data serves as reference points for subsequent morphological analysis or position calibration.