Image gradient

In graphics software for digital image editing, the term gradient or color gradient is also used for a gradual blend of color which can be considered as an even gradation from low to high values, and seen from black to white in the images to the right.

Mathematically, the gradient of a two-variable function (here the image intensity function) at each image point is a 2D vector with the components given by the derivatives in the horizontal and vertical directions.

At each image point, the gradient vector points in the direction of largest possible intensity increase, and the length of the gradient vector corresponds to the rate of change in that direction.

Approximations of these derivative functions can be defined at varying degrees of accuracy.

Image gradients are often utilized in maps and other visual representations of data in order to convey additional information.

GIS tools use color progressions to indicate elevation and population density, among others.

Image gradients can also be used for robust feature and texture matching.

These gradients are less susceptible to lighting and camera changes, so matching errors are reduced.

Two types of gradients, with blue arrows to indicate the direction of the gradient. Light areas indicate higher pixel values
A blue and green color gradient .
Left: Black and white picture of a cat. Center: The same cat, displayed in a gradient image in the x direction. Appears similar to an embossed image. Right: The same cat, displayed in a gradient image in the y direction. Appears similar to an embossed image.
On the left, an intensity image of a cat. In the center, a gradient image in the x direction measuring horizontal change in intensity. On the right, a gradient image in the y direction measuring vertical change in intensity. Gray pixels have a small gradient; black or white pixels have a large gradient.