imgradient3

Find gradient magnitude and direction of 3-D image

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.

[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

Compute 3-D Gradient Magnitude and Direction Using Sobel Method

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

I — Input image

3-D grayscale image | 3-D binary image

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

method — Gradient operator

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

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-1 plane z plane 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-1 plane z plane 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

Gx — Horizontal gradient

3-D numeric array

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.

Gy — Vertical gradient

3-D numeric array

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.

Gz — Depth gradient

3-D numeric array

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

Gmag — Magnitude of the gradient vector

3-D numeric array

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.

Gazimuth — Azimuthal angle

3-D numeric array

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

Gelevation — Gradient elevation

3-D numeric array

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

C/C++ Code Generation

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

Usage notes and limitations:

• imgradient3 supports the generation of C and C++ code (requires MATLAB^® Coder™). For more information, see Code Generation for Image Processing.

• When generating code, the input argument method must be a compile-time constant.

GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Usage notes and limitations:

• When generating code, the input argument method must be a compile-time constant.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

Version History

Introduced in R2016a

R2022b: Support for thread-based environments

imgradient3 now supports thread-based environments.