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...

Detailed Description

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.

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 $I_1$ and $I_2$ , and perform a logical AND operation.

Suppose that for pixel (n,m), intensities $I_1$ and $I_2$ are respectively equal to $I_1(n,m) = 5$ and $I_2(n,m) = 12$ . What will be the value of the result $O(n,m)$ ? 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.

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 $I_1$ and $I_2$ have grayscale values in the range 0 to 15 (4-bit images), one has to shift the image $I_2$ by 4 bits on the left. A logical OR between image $I_1$ and image $I_2$ shifted by 4 bits ( $I_1 \vee ( I_2 << 4)$ ) gives an 8-bit image made of the two images.

Color Images

Let us consider the two color images $I_1$ and $I_2$ . Suppose we want to perform $O={I_1}\otimes{I_2}$ where $\otimes$ 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:

$\left\{\begin{array}{c} R_O(i,j)={R_1(i,j)}\otimes{R_2(i,j)}\\ G_O(i,j)={G_1(i,j)}\otimes{G_2(i,j)}\\ B_O(i,j)={B_1(i,j)}\otimes{B_2(i,j)}\\ A_O(i,j)={A_1(i,j)}\otimes{A_2(i,j)} \end{array}\right.$

For example, let us suppose that $I_1(i,j)=(255;0;255;255)$ (opaque magenta) and $I_2=(127;127;255;255)$ (opaque light blue) performing an AND operation, then we should get :

$\left\{\begin{array}{l} R_O(i,j)={255}\wedge{127}=127\\ G_O(i,j)={0}\wedge{127}=0\\ B_O(i,j)={255}\wedge{255}=255\\ A_O(i,j)={255}\wedge{255}=255 \end{array}\right.$

When performing a logical operation between an image and a fixed value: $O(i,j)={I_1(i,j)}\otimes{C}$ , the following formulas apply:

$O(i,j)=\left[\begin{array}{c} R_O(i,j)\\ G_O(i,j)\\ B_O(i,j)\\ A_O(i,j) \end{array}\right]=\left[\begin{array}{c} {R_1(i,j)}\otimes{C}\\ {G_1(i,j)}\otimes{C}\\ {B_1(i,j)}\otimes{C}\\ {A_1(i,j)}\otimes{C} \end{array}\right].$

For example, let us suppose that $I_1(i,j)=(255;0;255;255)$ (opaque magenta) and $C=7$ performing a XOR operation then we should get:

$O(i,j)=\left[\begin{array}{c} R_O(i,j)\\ G_O(i,j)\\ B_O(i,j)\\ A_O(i,j) \end{array}\right]=\left[\begin{array}{c} {255}\otimes{7}\\ {0}\otimes{7}\\ {255}\otimes{7}\\ {255}\otimes{7} \end{array}\right]=\left[\begin{array}{c} {248}\\ {7}\\ {248}\\ {248} \end{array}\right].$

Open Inventor Release 2023.2.3

Classes

Detailed Description

Grayscale Images

Masking and Bit-Plane Combination

Color Images