A weighted center can move when sample values change even if their coordinates stay fixed. Its weighting rule belongs beside the coordinate.
Specify what supplies the weights
An array-value center of mass weights positions by the selected sample values. A binary-support center instead gives equal weight to each included foreground position. Both need a defined support and nonzero total weight before the resulting coordinate can be interpreted as a center of something specific. Primary reference: SciPy array-value center of mass.
For an original worksheet, retain the coordinate convention, support mask and weight array. Do not equate an intensity-weighted result with the midpoint of an enclosing rectangle. The coordinate is a summary of the selected weighting, not evidence that the physical object moved.
Compare fictional fixed positions
Use sample-center coordinates x = 0 and x = 2 with positive values 10 and 30. Equal binary weights give the center (0 + 2)/2 = 1. Value weighting gives (0 × 10 + 2 × 30)/(10 + 30) = 1.5. The coordinate positions are unchanged.
The midpoint of their coordinate span is also 1, while the weighted center is displaced toward the larger value. This invented one-dimensional calculation assumes positive weights and a nonzero total. It does not prescribe handling of negative values or establish an actual object's mass distribution.
Review changes in center estimates
Prepare an original trial showing positions and weights separately. If a reported center changes, first compare the support and the values used as weights. Retain the calculation domain rather than describing every numerical movement as a measured displacement of the package or a mechanical alignment change.
This guide supplies no localization accuracy or HM camera claim. Its decision is whether the reported center summarizes equal foreground membership or intensity contribution. Those definitions must remain distinguishable before a coordinate is used in a later geometry or tracking question.
Customer Questions
What is the fictional equal-weight center?
One in the stated coordinate unit.
What is the value-weighted center?
One point five.
Did either sample position move?
No. The weighting rule 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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