imgradient

Gradient magnitude and direction of an image

Syntax

[Gmag,Gdir] = imgradient(I)
[Gmag,Gdir] = imgradient(I,method)
[Gmag,Gdir] = imgradient(Gx,Gy)

Description

[Gmag,Gdir] = imgradient(I) returns the gradient magnitude, Gmag, and the gradient direction, Gdir, of the 2-D grayscale or binary image I.

You optionally can compute the gradient magnitude and direction using a GPU (requires Parallel Computing Toolbox™). For more information, see Image Processing on a GPU.

example

[Gmag,Gdir] = imgradient(I,method) returns the gradient magnitude and direction using the specified method.

example

[Gmag,Gdir] = imgradient(Gx,Gy) returns the gradient magnitude and direction from the directional gradients Gx and Gy in the x and y directions, respectively.

Examples

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Read an image into workspace.

I = imread('coins.png');

Calculate the gradient magnitude and direction, specifying the Prewitt gradient operator.

[Gmag, Gdir] = imgradient(I,'prewitt');

Display the gradient magnitude and direction.

figure
imshowpair(Gmag, Gdir, 'montage');
title('Gradient Magnitude, Gmag (left), and Gradient Direction, Gdir (right), using Prewitt method')

Read an image into workspace.

I = imread('coins.png');

Calculate the x- and y-directional gradients. By default, imgradientxy uses the Sobel gradient operator.

[Gx,Gy] = imgradientxy(I);

Display the directional gradients.

imshowpair(Gx,Gy,'montage')
title('Directional Gradients Gx and Gy, Using Sobel Method')

Calculate the gradient magnitude and direction using the directional gradients.

[Gmag,Gdir] = imgradient(Gx,Gy);

Display the gradient magnitude and direction.

imshowpair(Gmag,Gdir,'montage')
title('Gradient Magnitude (Left) and Gradient Direction (Right)')

Input Arguments

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Input image, specified as a 2-D grayscale or 2-D binary image.

Data Types: single | double | int8 | int32 | uint8 | uint16 | uint32 | logical

Gradient operator, specified as one of the following values.

MethodDescription
'sobel'

Sobel gradient operator. The gradient of a pixel is a weighted sum of pixels in the 3-by-3 neighborhood. For gradients in the vertical (y) direction, the weights are:

[ 1  2  1 
  0  0  0 
 -1 -2 -1 ]
In the x direction, the weights are transposed.

'prewitt'

Prewitt gradient operator. The gradient of a pixel is a weighted sum of pixels in the 3-by-3 neighborhood. For gradients in the vertical (y) direction, the weights are:

[ 1  1  1 
  0  0  0 
 -1 -1 -1 ]
In the x direction, the weights are transposed.

'central'

Central difference gradient. The gradient of a pixel is a weighted difference of neighboring pixels. In the y direction, dI/dy = (I(y+1) - I(y-1))/2.

'intermediate'

Intermediate difference gradient. The gradient of a pixel is the difference between an adjacent pixel and the current pixel. In the y direction, dI/dy = I(y+1) - I(y).

'roberts'

Roberts gradient operator. The gradient of a pixel is the difference between diagonally adjacent pixels. For gradients in one direction, the weights are:

[ 1  0 
  0 -1 ]
In the orthogonal direction, the weights are flipped along the vertical axis.

Data Types: char | string

Horizontal gradient, specified as a numeric matrix. The horizontal (x) axis points in the direction of increasing column subscripts. You can use the imgradientxy function to calculate Gx.

Data Types: single | double | int8 | int32 | uint8 | uint16 | uint32

Vertical gradient, specified as a numeric matrix of the same size as Gx. The vertical (y) axis points in the direction of increasing row subscripts. You can use the imgradientxy function to calculate Gy.

Data Types: single | double | int8 | int32 | uint8 | uint16 | uint32

Output Arguments

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Gradient magnitude, returned as a numeric matrix of the same size as image I or the directional gradients Gx and Gy. Gmag is of class double, unless the input image or directional gradients are of class single, in which case it is of class single.

Data Types: double | single

Gradient direction, returned as a numeric matrix of the same size as gradient magnitude Gmag. Gdir contains angles in degrees within the range [-180, 180] measured counterclockwise from the positive x-axis. (The x-axis points in the direction of increasing column subscripts.) Gdir is of class double, unless the input image I or directional gradients are of class single, in which case it is of class single.

Data Types: double | single

Tips

  • When applying the gradient operator at the boundaries of the image, values outside the bounds of the image are assumed to equal the nearest image border value. This is similar to the 'replicate' boundary option in imfilter.

Algorithms

The algorithmic approach taken in imgradient for each of the listed gradient methods is to first compute directional gradients, Gx and Gy, in the x and y directions, respectively. The horizontal (x) axis points in the direction of increasing column subscripts. The vertical (y) axis points in the direction of increasing row subscripts. The gradient magnitude and direction are then computed from their orthogonal components Gx and Gy.

imgradient does not normalize the gradient output. If the range of the gradient output image has to match the range of the input image, consider normalizing the gradient image, depending on the method argument used. For example, with a Sobel kernel, the normalization factor is 1/8, for Prewitt, it is 1/6, and for Roberts it is 1/2.

Extended Capabilities

Introduced in R2012b