[Arithmetic And Logic]

The Logical Operations category contains logical operations between two images or between an image and a constant as union, intersection, complementary. More...

## Classes | |

class | SoBitShiftProcessing |

SoBitShiftProcessing engine More... | |

class | SoInvertImageProcessing |

SoInvertImageProcessing engine calculates the reverse of an image. More... | |

class | SoLogicalImageProcessing |

SoLogicalImageProcessing engine performs logical operations between two image. More... | |

class | SoLogicalNotProcessing |

SoLogicalNotProcessing engine More... | |

class | SoLogicalValueProcessing |

SoLogicalValueProcessing engine More... |

The Logical Operations category contains logical operations between two images or between an image and a constant as union, intersection, complementary.

Logical operations are usually performed on binary images, but may also be applied to grayscale images. In a binary image, a pixel/voxel with value 1 has the value true and a pixel/voxel with value 0 a value false. Each logical operation is linked to a boolean operation. In a binary image I, all pixels/voxels with value 1 belong to the set A, and all 0-value pixels to the complement set of A or the background.

When a logical operation is applied to a grayscale image, the logical operations for binary images are applied to each bit plane. Let us consider the two images and , and perform a logical AND operation.

Suppose that for pixel (n,m), intensities and are respectively equal to and . What will be the value of the result ? If we consider the binary coding of the two numbers and apply the operator to each of the eight bits as shown on the Figure 1.

**Figure 1**

The result of this logical AND may appear rather strange and for this reason logical operations applied to grayscale images have to be handled with care.

- remains unchanged if
- turns to 0 if

The two main applications of logical operations on grayscale images are for masking and for combining bit planes.

To mask an image, a logical AND is performed between images I and M where every pixel with value 1 is coded with 1 (short value) and every pixel with value 0 is coded with 0 (short value). In masking a grayscale image I with a binary image M:

To combine bit planes, if two images and have grayscale values in the range 0 to 15 (4-bit images), one has to shift the image by 4 bits on the left. A logical OR between image and image shifted by 4 bits ( ) gives an 8-bit image made of the two images.

- ,
- and

Let us consider the two color images and . Suppose we want to perform where is a boolean operator.

When a logical operation is applied to color image, it operates on each color channel. A color image pixel/voxel is a quadruplet of values coded on one unsigned byte each:

then we will have the following relations:

For example, let us suppose that (opaque magenta) and (opaque light blue) performing an AND operation, then we should get :

When performing a logical operation between an image and a fixed value: , the following formulas apply:

For example, let us suppose that (opaque magenta) and performing a XOR operation then we should get:

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