imgradientxy

Find directional gradients of 2-D image

Syntax

[Gx,Gy] = imgradientxy(I)

[Gx,Gy] = imgradientxy(I,method)

Description

[Gx,Gy] = imgradientxy(I) returns the directional gradients, Gx and Gy of the grayscale or binary image I.

[Gx,Gy] = imgradientxy(I,method) returns the directional gradients using the specified method.

Examples

Calculate Directional Gradients Using Prewitt Method

Read an image into workspace.

I = imread('coins.png');

Calculate the x- and y-directional gradients using the Prewitt gradient operator.

[Gx, Gy] = imgradientxy(I,'prewitt');

Display the directional gradients.

figure
imshowpair(Gx, Gy, 'montage');
title('Directional Gradients: x-direction, Gx (left), y-direction, Gy (right), using Prewitt method')

Calculate Gradient Magnitude and Direction Using Directional Gradients

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

I — Input image

2-D grayscale image | 2-D binary image

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

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

method — Gradient operator

'sobel' (default) | 'prewitt' | 'central' | 'intermediate'

Gradient operator, specified as one of the following values.

Method	Description
'sobel'	Sobel gradient operator. The gradient of a pixel is a weighted sum of pixels in the 3-by-3 neighborhood. 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. 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).

Data Types: char | string

Output Arguments

Gx — Horizontal gradient

numeric matrix

Horizontal gradient, returned as a numeric matrix of the same size as image I. The horizontal (x) axis points in the direction of increasing column subscripts. Gx is of data type double, unless the input image I is of data type single, in which case Gx is of data type single.

Data Types: single | double

Gy — Vertical gradient

numeric matrix

Vertical gradient, returned as a numeric matrix of the same size as image I. The vertical (y) axis points in the direction of increasing row subscripts. Gy is of data type double, unless the input image I is of data type single, in which case Gy is of data type single.

Data Types: single | double

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.

Algorithms

The algorithmic approach is to compute directional gradients with respect to the x-axis and y-axis. The x-axis is defined along the columns going right and the y-axis is defined along the rows going down.

imgradientxy 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, and for Prewitt, it is 1/6.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• imgradientxy supports the generation of C code (requires MATLAB^® Coder™). Note that if you choose the generic MATLAB Host Computer target platform, imgradientxy generates code that uses a precompiled, platform-specific shared library. Use of a shared library preserves performance optimizations but limits the target platforms for which code can be generated. For more information, see Types of Code Generation Support in Image Processing Toolbox.

• The value of method must be a compile time constant.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Image Processing on a GPU.

Version History

Introduced in R2012b