Write a function to perform a specific matrix operation or image filter for Qualcomm vision models or pre/post-processing.
Implement a zero-padded 3x3 mean filter for a grayscale image represented as a rectangular matrix. For each pixel, average the nine positions in its 3x3 neighborhood, treating out-of-bounds positions as zero. Use floor division and return a new matrix without modifying the input.
Signature: def mean_filter(image):
Example: [[1, 2], [3, 4]] returns [[1, 1], [1, 1]], because every neighborhood sum is 10 and 10 // 9 == 1.
Constraints: The image is non-empty, rectangular, and each intensity is an integer from 0 through 255.
def mean_filter(image):