A kernel’s coefficient array needs an anchor linking it to an output coordinate. Changing that anchor changes which input neighborhood is sampled there.
Specify the reference index
An image-filter anchor specifies the reference position within a kernel relative to the output coordinate. In a correlation formulation, input sample locations include the kernel index minus that anchor. Coefficients alone therefore do not fully define neighborhood alignment at a reported pixel. Primary reference: OpenCV filter2D anchor and sample-coordinate formula.
For an original worksheet, use explicit zero-based coordinates and label the anchor index. Keep this alignment choice separate from flipping the coefficient array for convolution. Both can alter a response, but they are different operations and require different evidence.
Calculate fictional alignment changes
Suppose an invented row has values [10,20,30,40,50] at indices 0 through 4, with a three-sample correlation kernel [1,2,4]. At output index 2 and anchor 1, sampled values are 20,30,40, giving 20 +2 ×30 +4 ×40 =240.
With anchor 0, that same output index instead uses 30,40,50 and gives 30 +2 ×40 +4 ×50 =310. Both windows remain inside the row. The unnormalized floating sums differ because the reference changed, not because the physical object moved.
Review coordinates and boundary behavior
Prepare a trial record of output location, anchor, input coordinates and each weighted term. Verify the anchor lies within the selected kernel and retain the software convention used. If a window extends outside the image, add its border rule rather than silently dropping samples.
This calculation is not a machine-position calibration or an HM inspection setting. It isolates a filter-reference choice and excludes output clipping. The reader decision is whether an apparent response displacement follows the intended neighborhood alignment before it is attributed to scene motion.
Customer Questions
Do coefficients alone define the sampled neighborhood?
No. The anchor and output coordinate also matter.
What is the anchor 1 sum in the example?
240 under the stated correlation convention.
Did the input row move when the anchor changed?
No. The sampling reference changed.
Primary References
These references support the technical principles discussed in this guide. The worked examples and review questions are educational.
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