Euler number of binary image




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.

This function supports code generation (see Tips).


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Calculate Euler Number for Binary Image

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 =


Input Arguments

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BW — Input binary imagelogical or numeric matrix that must be 2-D, real, and nonsparse

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

n — Connectivity8 (default) | 4

Connectivity, specified as either the value 4 or 8.

44-connected objects
88-connected objects

Example: BW2 = bweuler(BW,4);

Data Types: double

Output Arguments

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eul — Euler numbernumeric scalar value

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

More About

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  • This function supports the generation of C code using MATLAB® Coder™. Note that if you choose the generic MATLAB Host Computer target platform, the function generates code that uses a precompiled, platform-specific shared library. Use of a shared library preserves performance optimizations but limits the target platforms for which code can be generated. For more information, see Understanding Code Generation with Image Processing Toolbox.


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.

See Also


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