Contour

A contour is a boundary or edge that defines the shape of an object or the level of a variable. The term is used in several fields to describe lines that connect points sharing a common value or property.

In geography and cartography, contour lines connect points of equal elevation on a map. They depict terrain relief, with the contour interval indicating the vertical distance between lines. Lines generally do not cross, often form closed loops, and may create V shapes where they cross streams. Index contours label elevations, and shading or color helps convey slope steepness.

In mathematics and related areas, a contour is a curve used in analysis. A contour integral traverses a piecewise smooth path in the complex plane to evaluate integrals of complex-valued functions. For real-valued functions of two variables, contour lines are level curves defined by f(x, y) = c.

In visual arts, contour drawing focuses on the outer edges and essential boundaries of a subject. Contours can be extended to internal boundaries (cross-contours) to suggest volume and form, distinguishing edge lines from shading and texture.

In computer vision and imaging, contours are the boundaries detected around objects. Contour detection and tracking support object recognition and shape analysis, with techniques such as active contours (snakes) evolving a curve to fit an object's boundary.