# edge

Find edges in 2-D grayscale image

## Syntax

``BW = edge(I)``
``BW = edge(I,method)``
``BW = edge(I,method,threshold)``
``BW = edge(I,method,threshold,direction)``
``BW = edge(___,"nothinning")``
``BW = edge(I,method,threshold,sigma)``
``BW = edge(I,method,threshold,h)``
``````[BW,threshOut] = edge(___)``````
``````[BW,threshOut,Gx,Gy] = edge(___)``````

## Description

````BW = edge(I)` returns a binary image `BW` containing `1`s where the function finds edges in the grayscale or binary image `I` and `0`s elsewhere. By default, `edge` uses the Sobel edge detection method. TipTo find edges in a 3-D grayscale or binary image, use the `edge3` function. ```

example

````BW = edge(I,method)` detects edges in image `I` using the edge-detection algorithm specified by `method`.```
````BW = edge(I,method,threshold)` returns all edges that are stronger than `threshold`.```
````BW = edge(I,method,threshold,direction)` specifies the orientation of edges to detect. The Sobel and Prewitt methods can detect edges in the vertical direction, horizontal direction, or both. The Roberts method can detect edges at angles of 45° from horizontal, 135° from horizontal, or both. This syntax is valid only when `method` is `"Sobel"`, `"Prewitt"`, or `"Roberts"`.```
````BW = edge(___,"nothinning")` skips the edge-thinning stage, which can improve performance. This syntax is valid only when `method` is `"Sobel"`, `"Prewitt"`, or `"Roberts"`.```
````BW = edge(I,method,threshold,sigma)` specifies `sigma`, the standard deviation of the filter. This syntax is valid only when `method` is `"log"` or `"Canny"`.```
````BW = edge(I,method,threshold,h)` detects edges using the `"zerocross"` method with a filter, `h`, that you specify. This syntax is valid only when `method` is `"zerocross"`.```
``````[BW,threshOut] = edge(___)``` also returns the threshold value.```
``````[BW,threshOut,Gx,Gy] = edge(___)``` also returns the directional gradients. For the Sobel and Prewitt methods, `Gx` and `Gy` correspond to the horizontal and vertical gradients, respectively. For the Roberts methods, `Gx` and `Gy` correspond to the gradient at angles of 135° and 45° from horizontal, respectively. This syntax is valid only when `method` is `"Sobel"`, `"Prewitt"`, or `"Roberts"`.```

## Examples

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Read a grayscale image into the workspace and display it.

```I = imread('circuit.tif'); imshow(I)```

Find edges using the Canny method.

`BW1 = edge(I,'Canny');`

Find edges using the Prewitt method.

`BW2 = edge(I,'Prewitt');`

Display both results side-by-side.

`imshowpair(BW1,BW2,'montage')`

## Input Arguments

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Input image, specified as a 2-D grayscale image or 2-D binary image.

For the `"approxcanny"` method, images of data type `single` or `double` must be normalized to the range [0, 1]. If `I` has values outside the range [0, 1], then you can use the `rescale` function to rescale values to the expected range.

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

Edge detection method, specified as one of the following.

MethodDescription
`"Sobel"`

Finds edges at those points where the gradient of the image `I` is maximum, using the Sobel approximation to the derivative.

`"Prewitt"`

Finds edges at those points where the gradient of `I` is maximum, using the Prewitt approximation to the derivative.

`"Roberts"`Finds edges at those points where the gradient of `I` is maximum, using the Roberts approximation to the derivative.
`"log"`Finds edges by looking for zero-crossings after filtering `I` with a Laplacian of Gaussian (LoG) filter.
`"zerocross"`Finds edges by looking for zero-crossings after filtering `I` with a filter that you specify, `h`.
`"Canny"`

Finds edges by looking for local maxima of the gradient of `I`. The `edge` function calculates the gradient using the derivative of a Gaussian filter. This method uses two thresholds to detect strong and weak edges, including weak edges in the output if they are connected to strong edges. By using two thresholds, the Canny method is less likely than the other methods to be fooled by noise, and more likely to detect true weak edges.

`"approxcanny"`

Finds edges using an approximate version of the Canny edge detection algorithm that provides faster execution time at the expense of less precise detection. Floating point images are expected to be normalized to the range [0, 1].

Sensitivity threshold, specified as a numeric scalar for any `method`, or a 2-element vector for the `"Canny"` and `"approxcanny"` methods. `edge` ignores all edges that are not stronger than `threshold`. For more information about this parameter, see Algorithm.

• If you do not specify `threshold`, or if you specify an empty array (`[]`), then `edge` chooses the value or values automatically.

• For the `"log"` and `"zerocross"` methods, if you specify the threshold value `0`, then the output image has closed contours because it includes all the zero-crossings in the input image.

• The `"Canny"` and `"approxcanny"` methods use two thresholds. `edge` disregards all edges with edge strength below the lower threshold, and preserves all edges with edge strength above the higher threshold. You can specify `threshold` as a 2-element vector of the form `[low high]` with `low` and `high` values in the range [0, 1]. You can also specify `threshold` as a numeric scalar, which `edge` assigns to the higher threshold. In this case, `edge` uses `threshold*0.4` as the lower threshold.

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

Direction of edges to detect, specified as `"horizontal"`, `"vertical"`, or `"both"`. The `direction` argument is only valid when the `method` is `"Sobel"`, `"Prewitt"`, or `"Roberts"`.

Note

If you select the Roberts `method`, then the `"horizontal"` direction detects edges at an angle of 135° from horizontal, and the `"vertical"` direction detects edges at an angle of 45° from horizontal.

Data Types: `char` | `string`

Filter, specified as a numeric matrix. The `h` argument is supported by the `"zerocross"` method only.

Data Types: `double`

Standard deviation of the filter, specified as a numeric scalar. The `sigma` argument is supported by the `"Canny"` and `"log"` methods only.

MethodDescription
`"Canny"`

Scalar value that specifies the standard deviation of the Gaussian filter. The default is `sqrt(2)`. `edge` chooses the size of the filter automatically, based on `sigma`.

`"log"` (Laplacian of Gaussian)

Scalar value that specifies the standard deviation of the Laplacian of Gaussian filter. The default is `2`. The size of the filter is `n`-by-`n`, where `n=ceil(sigma*3)*2+1`.

Data Types: `double`

## Output Arguments

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Output binary image, returned as a logical array of the same size as `I`, with `1`s where the function finds edges in `I` and `0`s elsewhere.

Calculated threshold value used in the computation, returned as a 2-element vector for the `"Canny"` `method`, an empty vector (`[]`) for the `"approxcanny"` method, or a numeric scalar for all other edge detection methods.

Horizontal gradient, returned as a numeric array of the same size as `I`. A large horizontal gradient magnitude indicates a strong vertical edge.

Note

If you select the Roberts `method`, then `edge` returns the gradient calculated at an angle of 135° from horizontal.

Vertical gradient, returned as a numeric array of the same size as `I`. A large vertical gradient magnitude indicates a strong horizontal edge.

Note

If you select the Roberts `method`, then `edge` returns the gradient calculated at an angle of 45° from horizontal.

## Algorithms

• For the gradient-magnitude edge detection methods (Sobel, Prewitt, and Roberts), `edge` uses `threshold` to threshold the calculated gradient magnitude.

• For the zero-crossing methods, including Laplacian of Gaussian, `edge` uses `threshold` as a threshold for the zero-crossings. In other words, a large jump across zero is an edge, while a small jump is not.

• The Canny method applies two thresholds to the gradient: a high threshold for low edge sensitivity and a low threshold for high edge sensitivity. `edge` starts with the low sensitivity result and then grows it to include connected edge pixels from the high sensitivity result. This helps fill in gaps in the detected edges.

• In all cases, `edge` chooses the default threshold heuristically, depending on the input data. The best way to vary the threshold is to run `edge` once, capturing the calculated threshold as the second output argument. Then, starting from the value calculated by `edge`, adjust the threshold higher to detect fewer edge pixels, or lower to detect more edge pixels.

## References

[1] Canny, John, "A Computational Approach to Edge Detection," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI-8, No. 6, 1986, pp. 679-698.

[2] Lim, Jae S., Two-Dimensional Signal and Image Processing, Englewood Cliffs, NJ, Prentice Hall, 1990, pp. 478-488.

[3] Parker, James R., Algorithms for Image Processing and Computer Vision, New York, John Wiley & Sons, Inc., 1997, pp. 23-29.

## Version History

Introduced before R2006a

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