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Euler number of binary image



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


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Read binary image into workspace, and display it.

BW = imread('circles.png');

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.

ans = -3

Input Arguments

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Binary image, specified as a 2-D numeric matrix or 2-D logical matrix. For numeric input, any nonzero pixels are considered to be on.

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

Connectivity, specified as the values 4 for 4-connected objects or 8 for 8-connected objects.

Data Types: double

Output Arguments

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Euler number, returned as a numeric scalar.

Data Types: double


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.


[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.

Extended Capabilities

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

Version History

Introduced before R2006a

See Also