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imgradientxy

Directional gradients of an image

Syntax

[Gx,Gy] = imgradientxy(I)
[Gx,Gy] = imgradientxy(I,method)
[gpuarrayGx,gpuarrayGy] = imgradientxy(gpuarrayI,___)

Description

example

[Gx,Gy] = imgradientxy(I) returns the directional gradients, Gx and Gy, the same size as the input image I.

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.

example

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

example

[gpuarrayGx,gpuarrayGy] = imgradientxy(gpuarrayI,___) performs the operation on a GPU. The input image and the return values are gpuArrays. This syntax requires the Parallel Computing Toolbox™

Examples

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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')

Read image into a gpuArray.

I = gpuArray(imread('coins.png'));
imshow(I)

Calculate gradient magnitude and gradient direction using Prewitt’s gradient operator and display images.

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

figure, imshow(Gx, []), title('Directional gradient: X axis')
figure, imshow(Gy, []), title('Directional gradient: Y axis')

Read an image into workspace.

I = imread('coins.png');

Calculate x- and y-directional gradients, using the Sobel gradient operator by default.

[Gx, Gy] = imgradientxy(I);

Display the directional gradients.

figure
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.

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

Read image and return directional gradients, Gx and Gx, as well as gradient magnitude and direction, Gmag and Gdir, utilizing default Sobel gradient operator.

Read image into a gpuArray.

I = gpuArray(imread('coins.png'));
imshow(I)

Calculate gradient and display images.

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

figure, imshow(Gmag, []), title('Gradient magnitude')
figure, imshow(Gdir, []), title('Gradient direction')
figure, imshow(Gx, []), title('Directional gradient: X axis')
figure, imshow(Gy, []), title('Directional gradient: Y axis')

Input Arguments

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Input image, specified as a grayscale or binary image, that is, a numeric or logical 2-D matrix that must be nonsparse, or a gpuArray.

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

Input image, specified as a 2-D grayscale or binary gpuArray 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 (default)
'prewitt'Prewitt gradient operator
'central'

Central difference gradient: dI/dx = (I(x+1)- I(x-1))/2

'intermediate'

Intermediate difference gradient: dI/dx = I(x+1) - I(x)

Data Types: char

Output Arguments

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Directional gradient along the x-axis, returned as non-sparse matrix equal in size to image I. The x-axis points in the direction of increasing column subscripts. The output matrices are of class double, unless the input image is of class single, in which case they are of class single.

Data Types: single | double

Directional gradient along the x-axis, returned as non-sparse gpuArray equal in size to image I. The x-axis points in the direction of increasing column subscripts. The output matrices are of class double, unless the input image is of class single, in which case they are of class single.

Data Types: single | double

Directional gradients along the y-axis, returned as non-sparse matrix equal in size to image I. The y-axis points in the direction of increasing row subscripts. The output matrices are of class double, unless the input image is of class single, in which case they are of class single.

Data Types: single | double

Directional gradients along the y-axis, returned as non-sparse gpuArray equal in size to image I. The y-axis points in the direction of increasing row subscripts. The output matrices are of class double, unless the input image is of class single, in which case they are of class 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.

Introduced in R2012b

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