# imgradient3

Find gradient magnitude and direction of 3-D image

## Syntax

## Description

`[`

returns the gradient magnitude, `Gmag`

,`Gazimuth`

,`Gelevation`

]
= imgradient3(`I`

)`Gmag`

, gradient
direction, `Gazimuth`

, and gradient elevation
`Gelevation`

of the 3-D grayscale or
binary image `I`

.

`[`

calculates the gradient magnitude, direction, and elevation using
the specified `Gmag`

,`Gazimuth`

,`Gelevation`

]
= imgradient3(`I`

,`method`

)`method`

.

## 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 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 (
| ||||||

| 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 (
| ||||||

`"central" ` | Central difference gradient. The gradient of a pixel is a weighted difference of
neighboring pixels. For example, in the depth
( | ||||||

`"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 ( |

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

`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 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.

## See Also

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