magnitudeonly

Magnitudeonly, often written as magnitude-only, is a term used to describe representations, measurements, or features that preserve only the magnitude (absolute value) of a quantity while discarding direction, phase, or orientation. The concept appears across mathematics, signal processing, and computer vision as a way to simplify data or focus on amplitude information.

In mathematics and signal processing, magnitude-only data retain the length or size of a quantity. For a complex number z = a + bi, the magnitude is |z| = sqrt(a^2 + b^2). A dataset that stores only |z| sacrifices the argument (phase) information, making exact reconstruction of z impossible without additional data. In Fourier analysis, the magnitude spectrum consists of the magnitudes of frequency components, with phase details omitted; such representations are common for visualization and certain feature extraction tasks, though they limit signal reconstruction.

In imaging and computer vision, magnitude-only features include gradient magnitude maps and other measures that quantify strength of variation while ignoring direction. Such representations are useful for edge detection, texture analysis, or robust pattern recognition when orientation information is irrelevant or too noisy.

Limitations of magnitude-only representations include irreversible information loss and potential ambiguity. They are advantageous when compact, noise-robust summaries are required or when the analysis focuses on amplitude rather than phase or orientation.

See also: magnitude, phase, magnitude spectrum, gradient magnitude, L2 norm.