Centerweighted

Centerweighted is a descriptive term used in statistics, image processing, and photography to describe a weighting scheme that favors data points nearer the center of a specified region. It is often written center-weighted in some sources.

In photography, centerweighted metering measures light for exposure by giving greater emphasis to the central portion of the frame, with weights tapering toward the edges. Most cameras allocate a large share of the exposure decision to the center while still considering peripheral areas. This approach works well when the main subject is near the frame’s center but can mischaracterize scenes with off-center subjects.

In image processing, centerweighted kernels or filters assign larger weights to the center pixel when computing averages or convolutions. A common 3x3 centerweighted kernel is [1 2 1; 2 4 2; 1 2 1], which sums to 16 and provides a Gaussian-like smoothing effect. Larger kernels follow the same principle, with the center weight dominating the others to emphasize central information.

In statistics and data analysis, centerweighted schemes assign weights that decline with distance from a central point, producing a mean or moving average that is more responsive to central observations than to distant ones. The exact weights can be chosen to reflect a desired decay, often resembling a radial or Gaussian profile.

Advantages include enhanced emphasis on central features and reduced influence from peripheral noise or outliers; drawbacks include potential bias when important information lies away from the center or when the region of interest is not well defined. The choice of weighting depends on the task and data.

Related concepts include center-weighted averaging, Gaussian weighting, and weighted moving averages.