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imgradient3

Find 3-D gradient magnitude and direction of images

Syntax

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

Description

example

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

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

[Gmag,Gazimuth,Gelevation] = imgradient3(Gx,Gy,Gz) calculates the gradient magnitude and direction from the directional gradients along the x-axis, Gx, y-axis, Gy and z-axis, Gz.

Examples

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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')

Input Arguments

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Input image, specified as a nonsparse, numeric or logical, 3-D matrix

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical

Gradient operator, specified as one of the following values.

Value

Meaning

'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)

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

Directional gradient along x-axis (horizontal), specified as a nonsparse, numeric or logical, 3-D matrix. The x-axis points in the direction of increasing column subscripts. The matrix must be equal in size to Gy and Gz.imgradientxyz returns Gx.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Directional gradient along y-axis (vertical), specified as a nonsparse, numeric or logical, 3-D matrix. The y-axis points in the direction of increasing row subscripts. The matrix must be equal in size to Gx and Gz.imgradientxyz returns Gy.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Directional gradient along z-axis, specified as a nonsparse, numeric or logical, 3-D matrix. The matrix must be equal in size to Gx and Gy. imgradientxyz returns Gz.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Output Arguments

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Magnitude of the gradient vector, returned as a nonsparse matrix the same size as image I.

Gmag is of class double, unless the input image I or any of the directional gradients Gx, Gy, or Gz are of class single. In this case, Gmag is of class single.

Azimuthal angle, returned as a nonsparse matrix the same size as image I. 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 class double, unless the input image I or any of the directional gradients Gx, Gy, or Gz are of class single. In this case, Gazimuth is of class single.

Gazimuth and Gelevation

Gradient elevation, returned as a nonsparse matrix the same size as image I. Gelevation contains angles in degrees within the range [-90 90] measured between the radial line and the x-y plane.

Gelevation is of class double, unless the input image I or any of the directional gradients Gx, Gy, or Gz are of class single. In this case, Gelevation is of class 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

Introduced in R2016a

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