Sobel Edge Detection

Apply the Sobel operator in the X direction to a 2D grayscale image (matrix).

The Sobel $G_x$ kernel is: $G_x = \begin{bmatrix} -1 & 0 & 1 \\ -2 & 0 & 2 \\ -1 & 0 & 1 \end{bmatrix}$

Perform valid convolution (no padding) by sliding the kernel over the image. For each position, compute the sum of element-wise products between the kernel and the overlapping image region. Return the absolute value of each result, rounded to 4 decimal places.

The output matrix will have dimensions $(H-2) \times (W-2)$ where $H$ and $W$ are the input dimensions.

Example:

Input:

image = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]

Output:

[[8]]

Reasoning:

The input image is a 3x3 matrix: [[1, 2, 3], [4, 5, 6], [7, 8, 9]].
We apply the Sobel $G_x$ kernel to the image using valid convolution. Since the kernel is 3x3, the output will be a 1x1 matrix (because the input dimensions are 3x3, so $(3-2) \times (3-2) = 1 \times 1$ ).
We calculate the sum of element-wise products between the kernel and the overlapping image region: $(-1 \cdot 1) + (0 \cdot 2) + (1 \cdot 3) + (-2 \cdot 4) + (0 \cdot 5) + (2 \cdot 6) + (-1 \cdot 7) + (0 \cdot 8) + (1 \cdot 9) = -1 + 0 + 3 -8 + 0 + 12 - 7 + 0 + 9 = 8$ .
The final output is the absolute value of the result, which is already positive, rounded to 4 decimal places: $[[8.0000]]$ , but since the problem doesn't specify to keep trailing zeros, it is [[8]].

Constraints:

Input image is a 2D list of numbers (at least 3x3)
Return a 2D list of absolute gradient values
Round each value to 4 decimal places

Example:

Constraints:

Test Results