Ytroughness

Ytroughness is a metric used in the analysis of two-dimensional scalar fields to quantify trough-like features that run predominantly along the vertical axis (the y-direction). The term is not widely standardized and appears mainly in discussions of pattern analysis, terrain morphology, and texture characterization. It captures vertical valley structures rather than isotropic or horizontal features.

Computation. Given a grid f(x,y), compute vertical profiles p_x(y) = f(x, y) at each horizontal position x. For each profile, identify local minima along y and measure their prominence, defined as the depth of a trough relative to adjacent maxima. Aggregate prominences across x by taking an average or summing the most pronounced troughs. Normalize by a reference scale such as the overall range or standard deviation to yield a unitless score.

Normalizations and variants. Ytroughness can be reported as a single global score or as a spatial map using moving windows. A higher value indicates more pronounced vertical valleys or more frequent troughs. The measure is sensitive to sampling resolution along y and to noise, so smoothing or multiscale analysis is common.

Applications. In geoscience, ytroughness helps describe valley-oriented terrain features; in image analysis, it characterizes textures with vertical troughs; in materials science and manufacturing, it can quantify vertical channeling or patterning. It is typically defined within a study and compared with related metrics such as trough depth or ridge strength.

Origin and relation. The name derives from valleys (troughs) and the preference for vertical orientation. Ytroughness is a niche or emerging concept and does not have a universally accepted definition, with variants tailored to specific datasets. See also: trough depth, profile analysis, anisotropic texture measures.