Fundamental concepts of image processing

1. Algebraic operations Averaging

1.1. Profiles along corresponding lines in the images indicate that the pixel values in each profile fluctuate randomly around the mean gray value, which corresponds to a CT number of zero.

1.2. The profiles are not identical because the fluctuations are random.

1.3. In some imaging systems, it is possible to obtain multiple images of the same object each differing only in the amount of random noise which has been added during the imaging process.

1.3.1. For example, we may have M images in which the essential part of the image is unchanged, but each has a random noise pattern superimposed.

1.4. Most medical images are quantum limited, i.e. the quantum noise component is dominant.

1.4.1. Quantum noise follows Poissonian statistics with a signal-to-noise ratio (SNR) given by the square root of the signal strength

1.4.2. Electronic noise follows Gaussian statistics, resulting in a bell-shaped distribution curve.

2. Algebraic operations Image subtraction

2.1. If an image is contaminated by an uneven background shading pattern, caused by:

2.1.1. Uneven illumination of the scene

2.1.2. Variations in detector sensitivity,

2.1.3. The image can be improved by subtracting the background image from it.

2.2. Subtraction can lead to an underflow, i.e. pixel values less than zero

2.3. To avoid clipping:

2.3.1. a temporary storage matrix with a greater depth (say, 12 or 16 bits per pixel)

2.3.2. the use of signed floating-point numbers (i.e. numbers which are non-integral and can be positive or negative) is needed to store the differences prior to re-scaling to [0, 255].

3. Algebraic operations Multiplication and division

3.1. Subtraction of a background image to correct for uneven illumination rests on the assumption that image features are additively superimposed on the scene background.

3.2. However, in a non-linear system this is not the case, and the intensity associated with a feature is in fact proportional to the background intensity in that part of the image.

3.3. In such cases, division of the image by a scaled version of its background, rather than subtraction, removes the uneven background.

3.4. Division of images is a problem if the divisor image contains a pixel value of zero.

3.5. This is usually avoided by adding a 1 to the entire pixel values of the background image so that they run from 1 to 256, and then re-scaling after division.

3.6. Image division is also used when processing images are collected in different spectral bands;

3.6.1. The ratio of the images is an effective way of generating an image at an intermediate spectral band.

4. Image enhancement in the spatial domain

4.1. Better contrast and visibility of features of interest,

4.2. To enhance their performance in subsequent computer-aided analysis and diagnosis.

5. Algebraic operations

5.1. Algebraic operations produce an output image which is the pixel-by-pixel sum, difference, product or quotient of two or more input images.

5.2. sum

5.3. difference

5.4. product

5.5. quotient

6. Logical (Boolean) operations

6.1. Logical operations also operate on a pixel-by-pixel basis.

6.2. They often use binarized images as their input.

6.3. All logical operations can be implemented from a combination of three basic operations, AND, OR and NOT.

6.4. The effect of each of these is given by a truth table

6.5. Bit “1” is associated with “true” (or “ON”) and bit “0” with “false” (or “OFF”).

6.6. The AND operator produces an output that is 1 (true) if both inputs A and B are 1 (true); otherwise it produces a 0 (false).

6.7. The OR operator produces an output that is 1 (true) if either inputs A or B (or both) are 1 (true); otherwise it produces a 0 (false).

6.8. The NOT operator produces an output that is not equal to the (single) input.

6.9. The operator, XOR (exclusive OR), produces an output that is 1 (true) if either inputs A or B (but not both) are 1 (true); otherwise it produces a 0 (false).