# Documentation

### This is machine translation

Translated by
Mouseover text to see original. Click the button below to return to the English version of the page.

# bweuler

Euler number of binary image

## Syntax

``eul = bweuler(BW,n)``

## Description

example

````eul = bweuler(BW,n)` returns the Euler number for the binary image `BW`. The Euler number is the total number of objects in the image minus the total number of holes in those objects. `n` specifies the connectivity. Objects are connected sets of `on` pixels, that is, pixels having a value of 1.```

## Examples

collapse all

Read binary image into workspace, and display it.

```BW = imread('circles.png'); imshow(BW)```

Calculate the Euler number. In this example, all the circles touch so they create one object. The object contains four "holes", which are the black areas created by the touching circles. Thus the Euler number is 1 minus 4, or -3.

`bweuler(BW)`
```ans = -3 ```

## Input Arguments

collapse all

Input binary image, specified as a logical or numeric matrix that must be 2-D, real, and nonsparse.

Example: `BW = imread('circles.png');eul = bweuler(BW,4);`

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

Connectivity, specified as either the value `4` or `8`.

ValueDescription
`4`4-connected objects
`8`8-connected objects

Example: `BW2 = bweuler(BW,4);`

Data Types: `double`

## Output Arguments

collapse all

Euler number, returned as a numeric scalar value of class `double`.

## Algorithms

`bweuler` computes the Euler number by considering patterns of convexity and concavity in local 2-by-2 neighborhoods. See [2] for a discussion of the algorithm used.

## References

[1] Horn, Berthold P. K., Robot Vision, New York, McGraw-Hill, 1986, pp. 73-77.

[2] Pratt, William K., Digital Image Processing, New York, John Wiley & Sons, Inc., 1991, p. 633.