bweuler

Euler number of binary image

Syntax

eul = bweuler(BW,conn)

Description

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.

Examples

Calculate Euler Number for Binary Image

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

BW — Binary image

2-D numeric matrix | 2-D logical matrix

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

conn — Connectivity

8 (default) | 4

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

Data Types: double

Output Arguments

eul — Euler number

numeric scalar

Euler number, returned as a numeric scalar.

Data Types: 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.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• bweuler supports the generation of C code (requires MATLAB^® Coder™). Note that if you choose the generic MATLAB Host Computer target platform, bweuler 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 Types of Code Generation Support in Image Processing Toolbox.

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

Version History

Introduced before R2006a