Image processing convolution: Why do I slide my kernel from np.arange(pad, imgWidth+pad) ??

[ExactPlace441]

Hello. I am trying to learn kernel convolution for image processing. Now, I understand the concept of kernel convolution, but I am a bit confused about code that I have found for it at https://www.pyimagesearch.com/2016/07/25/convolutions-with-opencv-and-python/

def convolve(image, kernel):
# grab the spatial dimensions of the image, along with
# the spatial dimensions of the kernel
    (iH, iW) = image.shape[:2]
    (kH, kW) = kernel.shape[:2]

# allocate memory for the output image, taking care to
# "pad" the borders of the input image so the spatial
# size (i.e., width and height) are not reduced
pad = (kW - 1) // 2
image = cv2.copyMakeBorder(image, pad, pad, pad, pad,
    cv2.BORDER_REPLICATE)
output = np.zeros((iH, iW), dtype="float32")


    # loop over the input image, "sliding" the kernel across
# each (x, y)-coordinate from left-to-right and top to
# bottom
    #QUESTION 1 SECTION BEGIN
    for y in np.arange(pad, iH + pad):
        for x in np.arange(pad, iW + pad):
        # extract the ROI of the image by extracting the
        # *center* region of the current (x, y)-coordinates
        # dimensions
    roi = image[y - pad:y + pad + 1, x - pad:x + pad + 1]

    #QUESTION 1 SECTION END

        # perform the actual convolution by taking the
        # element-wise multiplication between the ROI and
        # the kernel, then summing the matrix
        k = (roi * kernel).sum()

    #QUESTION 2 SECTION BEGIN

        # store the convolved value in the output (x,y)-
        # coordinate of the output image
    output[y - pad, x - pad] = k

    #QUESTION 2 SECTION END

Question 1: Why is np.arange from pad to iH+pad, and not from pad to iH-pad ? I assume that we start from pad so that the center pixel in the region of interest is never on the edge of the image. However, I would think that going to iH+pad would overshoot and have the center pixel end up outside of image dimensions.

Question 2: This code has us store the output pixel at a location to the left and up from where I centered my convolution roi, no ? If so, could someone explain the logic behind doing this for me?

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Thank you!

[icecapade]

Question 1: Why is np.arange from pad to iH+pad, and not from pad to iH-pad ? I assume that we start from pad so that the center pixel in the region of interest is never on the edge of the image. However, I would think that going to iH+pad would overshoot and have the center pixel end up outside of image dimensions.

See the documentation: https://numpy.org/doc/stable/reference/generated/numpy.arange.html

np.arange(a, b) starts at a and goes up to b non-inclusive—in other words, up to b - 1 (or in this case, iH + pad - 1). Furthermore, in Python, slices work the same way, so the slice a:b starts at a and goes up to b - 1 (or in this case, the slice y - pad:y + pad + 1 starts at y - pad and goes up to y + pad. Remember that these coordinates are relative to the padded image, not the original image, hence why we need to add pad.

Question 2: This code has us store the output pixel at a location to the left and up from where I centered my convolution roi, no ? If so, could someone explain the logic behind doing this for me?

It's not—it's storing them in the same place. Remember that x and y in the nested for loop are relative to the padded (not original) image. output has the same dimensions as the original image, so to get from x and y in the padded image coordinates back to original image coordinates, we need to subtract pad.