Word Count : 500

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To apply the Prewitt and Sobel operators to the given \( 3 \times 3 \) image matrix: \[ I = \begin{bmatrix} \alpha_1 & \alpha_2 & \alpha_3 \\ \alpha_4 & \alpha_5 & \alpha_6 \\ \alpha_7 & \alpha_8 & \alpha_9 \end{bmatrix} \] we need to convolve it with the respective gradient operators. --- ### 1. Prewitt Operator The Prewitt operator consists of two kernels: #### Prewitt Horizontal (\( G_x \)) \[ G_x = \begin{bmatrix} -1 & 0 & 1 \\ -1 & 0 & 1 _____ _________ __________ ________ __________ _____.
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