centrumgewogen

Centrumgewogen is a term used in statistics and signal processing to describe a weighting scheme in which weights are largest at the center of a data window and decline with distance from the center. The aim is to give more influence to observations near the middle while still incorporating surrounding values. This contrasts with uniform weighting, where all points contribute equally, and with weightings that emphasize edges.

In time-series smoothing, a center-weighted moving average (CWMA) uses symmetric weights around the central point. For example, a five-point window might use weights such as [1, 2, 3, 2, 1] or [1, 4, 6, 4, 1], normalized to the sum of the weights. In image processing, center-weighted kernels assign a higher weight to the central pixel, producing smoothing that preserves central detail more than a simple average.

Mathematically, the center-weighted average of a set of values x around index i is (sum_j w_j x_{i+j}) / (sum_j w_j), where w_j are symmetric and peak at the center. Weights may follow simple linear, triangular, Gaussian-like, or other symmetric profiles. Use of centrumgewogen can reduce the influence of distant observations, but at the cost of potentially blurring sharp features and introducing window- or parameter-dependent bias. The term is common in Dutch-language texts; in English-language literature it is usually described as center-weighted or center-weighted averaging.