| OIV.ImageViz.Engines.ArithmeticAndLogic.LogicalOperations Namespace |
The Logical Operations category contains logical operations between two images or between an image and a constant as union, intersection, complementary.
Classes| Class | Description | |
|---|---|---|
 | SoBitShiftProcessing | |
| SoInvertImageProcessing | OIV.ImageViz.Engines.ArithmeticAndLogic.LogicalOperations.SoInvertImageProcessing engine calculates the reverse of an image. |
| SoLogicalImageProcessing | OIV.ImageViz.Engines.ArithmeticAndLogic.LogicalOperations.SoLogicalImageProcessing engine performs logical operations between two image. |
| SoLogicalNotProcessing | |
| SoLogicalValueProcessing |
Enumerations| Enumeration | Description | |
|---|---|---|
 | SoBitShiftProcessingShiftDirections | |
| SoLogicalImageProcessingLogicalOperators | |
| SoLogicalValueProcessingLogicalOperators |
RemarksLogical 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.
Grayscale Images
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.
Masking and Bit-Plane Combination
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:
remains unchanged if 
- turns to 0 if
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.
Color Images
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:
,
and
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:
