Comparative Analysis of Gradient-Based Edge Detection Methods

This document implements and compares various gradient-based edge detection methodologies. The evaluated techniques include Basic Gradient, Robert, Sobel, Prewitt, Laplace, LoG (Laplacian of Gaussian), and Canny operators. Through comparative analysis, we gain insights into their respective advantages and limitations in edge detection applications. The Basic Gradient method employs simple pixel intensity variations for edge detection, typically implemented through horizontal and vertical difference calculations. The Robert operator utilizes diagonal differences with 2x2 convolution kernels ([1, 0; 0, -1] and [0, 1; -1, 0]) to capture edges at 45-degree orientations. Sobel operator enhances noise resistance through 3x3 gradient convolution kernels that weight central pixels higher, computing both magnitude and direction for improved edge localization. Prewitt operator employs similar 3x3 kernels but with uniform weighting, making it more sensitive to horizontal and vertical edges. Laplace operator leverages second-order derivatives through Laplacian kernels (e.g., [0,1,0; 1,-4,1; 0,1,0]) to detect fine edges but requires careful noise handling. The LoG method combines Gaussian smoothing (using σ parameter for scale control) with Laplacian operation to achieve scale-space edge detection. Finally, the Canny algorithm implements a multi-stage process including Gaussian filtering, gradient computation, non-maximum suppression, and double thresholding with hysteresis to produce high-quality edge maps. This comprehensive comparison enables optimal method selection based on specific application requirements regarding noise tolerance, edge connectivity, and computational efficiency.