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imgradient3

Find gradient magnitude and direction of 3-D image

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Syntax

[Gmag,Gazimuth,Gelevation] = imgradient3(I)
[Gmag,Gazimuth,Gelevation] = imgradient3(I,method)
[Gmag,Gazimuth,Gelevation] = imgradient3(Gx,Gy,Gz)

Description

[Gmag,Gazimuth,Gelevation] = imgradient3(I) returns the gradient magnitude, Gmag, gradient direction, Gazimuth, and gradient elevation Gelevation of the 3-D grayscale or binary image I.

example

[Gmag,Gazimuth,Gelevation] = imgradient3(I,method) calculates the gradient magnitude, direction, and elevation using the specified method.

[Gmag,Gazimuth,Gelevation] = imgradient3(Gx,Gy,Gz) calculates the gradient magnitude, direction, and elevation from the directional gradients Gx, Gy, and Gz in the x, y, and z directions, respectively.

Examples

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Open Live Script

Read 3-D data into the workspace and prepare it for processing.

volData = load('mri');
sz = volData.siz;
vol = squeeze(volData.D);

Calculate the gradients.

[Gmag, Gaz, Gelev] = imgradient3(vol);

Visualize the gradient magnitude as a montage.

figure, 
montage(reshape(Gmag,sz(1),sz(2),1,sz(3)),'DisplayRange',[])
title('Gradient magnitude')

Figure contains an axes object. The hidden axes object with title Gradient magnitude contains an object of type image.

Input Arguments

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Input image, specified as a 3-D grayscale image or 3-D binary image.

Gradient operator, specified as one of the following values.

Value

Meaning

"sobel"

Sobel gradient operator. The gradient of a pixel is a weighted sum of pixels in the 3-by-3-by-3 neighborhood. For example, in the depth (z) direction, the weights in the three planes are:

plane z-1plane zplane z+1
[ 1  3  1 
  3  6  3 
  1  3  1 ]    
[ 0  0  0 
  0  0  0 
  0  0  0 ]    
[ -1  -3  -1 
  -3  -6  -3 
  -1  -3  -1 ]

"prewitt"

Prewitt gradient operator. The gradient of a pixel is a weighted sum of pixels in the 3-by-3-by-3 neighborhood. For example, in the depth (z) direction, the weights in the three planes are:

plane z-1plane zplane z+1
[ 1  1  1 
  1  1  1 
  1  1  1 ]    
[ 0  0  0 
  0  0  0 
  0  0  0 ]    
[ -1  -1  -1 
  -1  -1  -1 
  -1  -1  -1 ]

"central"

Central difference gradient. The gradient of a pixel is a weighted difference of neighboring pixels. For example, in the depth (z) direction, dI/dz = (I(z+1) - I(z-1))/2.

"intermediate"

Intermediate difference gradient. The gradient of a pixel is the difference between an adjacent pixel and the current pixel. For example, in the depth (z) direction, dI/dz = I(z+1) - I(z).

When applying the gradient operator at the boundaries of the image, imgradient3 assumes values outside the bounds of the image equal the nearest image border value. This behavior is similar to the "replicate" boundary option in imfilter.

Data Types: char | string

Horizontal gradient, specified as a 3-D numeric array. The horizontal (x) axis points in the direction of increasing column subscripts. You can use the imgradientxyz function to calculate Gx.

Vertical gradient, specified as a 3-D numeric array of the same size as Gx. The vertical (y) axis points in the direction of increasing row subscripts. You can use the imgradientxyz function to calculate Gy.

Depth gradient, specified as a 3-D numeric array of the same size as Gx. The depth (z) axis points in the direction of increasing plane subscripts. You can use the imgradientxyz function to calculate Gz.

Output Arguments

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Magnitude of the gradient vector, returned as a 3-D numeric array of the same size as image I or the directional gradients, Gx, Gy, and Gz.

Gmag is of data type double, unless the input image or any of the directional gradients are of data type single. In this case, Gmag is of data type single.

Azimuthal angle, returned as a 3-D numeric array of the same size as the gradient magnitude, Gmag. Gazimuth contains angles in degrees within the range [-180, 180] measured between positive x-axis and the projection of the point on the x-y plane.

Gazimuth is of data type double, unless the input image or any of the directional gradients are of data type single. In this case, Gmag is of data type single.

Azimuth and Elevation

Geometry of the radial line, the projection of the point in the x-y plane, the azimuthal angle, and the gradient elevation.

Gradient elevation, returned as a 3-D numeric array of the same size as the gradient magnitude, Gmag. Gelevation contains angles in degrees within the range [-90, 90] measured between the radial line and the x-y plane.

Gelevation is of data type double, unless the input image or any of the directional gradients are of data type single. In this case, Gmag is of data type single.

Algorithms

imgradient3 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 1/44 and for Prewitt, the normalization factor is 1/18.

Extended Capabilities

Version History

Introduced in R2016a

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See Also

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