piekvolumes

Piekvolumes is a term used in data analysis and computational topology to denote the measure of regions around local maxima (peaks) of a scalar field, reflecting how large a peak's influence is within the domain.

Definition: For a scalar field f on a domain D with finite measure, a peak p is a local maximum. The piekvolume V(p) is the measure of the basin of p, defined as the set of points in D from which a monotone ascent leads to p without crossing a higher peak.

Computation: Piekvolumes can be estimated by segmentation methods that assign each point to a peak, such as watershed or regional-growing algorithms, often using thresholds on f or on gradient magnitude to control basin boundaries. In practice, the choice of threshold or scale parameter affects the resulting volumes.

Applications: They are used in terrain analysis to quantify dominance of peaks, in image processing to summarize the extent of bright spots, and in signal processing to compare peak prominence across datasets. The concept also supports comparative studies of how peak structure changes with scale, noise, or filtering.

Notes: The concept is not universally standardized; definitions of basins, thresholds, and scale influence results. The term is primarily used in technical contexts and may be described differently in various disciplines. In practice, a clear specification of the field, the basin criteria, and the chosen measurement method is essential for reproducibility. See also local maxima, watershed segmentation, regional maxima.