Calculating Perimeter of Binary Images Using Morphological Methods

Morphological methods can be employed to calculate multiple metrics for binary images, including perimeter, area, circularity, rectangularity, and elongation. Morphology is an image processing technique used for analyzing and measuring geometric features in images. Through morphological operations on binary images, contour information can be extracted to calculate perimeter and area. The perimeter calculation typically involves applying edge detection operators (like Sobel or Canny) or using morphological gradient operations (dilation minus erosion) to identify boundary pixels. Area computation can be implemented through pixel counting or region filling algorithms.

Furthermore, shape characteristics can be evaluated by calculating circularity (4π·area/perimeter²) and rectangularity (area/(width·height)) metrics. Circularity measurement often utilizes the regionprops function in MATLAB or OpenCV's contour analysis to assess how closely an object resembles a perfect circle. Rectangularity calculation may involve minimum bounding rectangle detection using rotating calipers algorithm or oriented bounding box estimation.

Elongation assessment (major axis length/minor axis length) helps quantify the stretching degree of objects, commonly implemented through principal component analysis (PCA) on coordinate points or ellipse fitting techniques. Morphological methods therefore serve as powerful tools for comprehensive binary image analysis and measurement, with practical implementations available in libraries like OpenCV (morphologyEx function) and MATLAB (bwmorph, regionprops functions).