Basic medical image processing and analysis

• Each PIXEL contains a series of 1's & 0's defining the grayscale or shade of that particular point on a digital image
• Computers then operate on the simplest number system of all, called the BINARY SYSTEM.
• • The binary number system has only two digits. (0&1) 
• • Power of 2 notation is used in radiologic imaging to describe image size, image dynamic range (shades of gray) & image storage capacity. -THUS, THE SIZE OF IMAGE IS DESCRIBED IN BINARY NUMBER SYSTEM BY POWER OF 2 EQUIVALENTS. 
• In computer language a single binary digit, 0 or 1, is called a BIT
• Bits are often grouped into bunches of eight called BYTE
• Computer capacity is expressed by the number of BYTES that can be accommodated
• Computers in radiology departments usually have capacities measured in GIGABYTES.
• 1 kilobyte (KB) is equal to 1024 bytes (or 2^10)
• • 1 Gigabyte (GB) = 1024 megabytes
• Information entropy: quantitative information of an image

  • Refers to the actual amount of information included in the image that can be computed.
• ENTROPY: AKA Shannon’s Entropy (1948), or Information Entropy
• Information entropy describes how much randomness (or uncertainty) there is in a signal or an image; in other words, how much information is provided by the signal or image.
• Fixed-length coding: Use of the same number of bits to represent all pixels
• In fixed-length coding, when a program reads an image file it knows that the first 12-bits represent the value of the first pixel, the next 12-bits represent the second pixel, and so on, with no need for any special symbol to represent the end of each pixel’s data.
• variable-length coding uses a variable number of bits to represent pixel values.
• Variable-length coding provides short code-words for frequent characters and long code-words for infrequent characters.
• Variability is primarily dependent on frequency of occurrence of data.
• Coding redundancy: The use of more bits that are needed to convey a given amount of information
• Redundant code has a number of consequences including bloated source code, reduced reliability and reduced maintainability
• Two major methods of variable-length encoding to reduce

  coding redundancy:

  1. Huffman coding (Huffman, 1952)
  2. Arithmetic coding (Abramson, 1963)
• ENCODED: Compressed image
• DECODED: Compressed image that had been

  RECONSTRUCTED.
• Huffman coding is an entropy encoding algorithm used for

  lossless data compression.
• Huffman coding guarantees the uniqueness of the decoding

  process so that a set of codes can only represent one set of

  image values.
• Huffman coding replaces each pixel value of an image with a special code on a one-to-one basis.
• Arithmetic coding replaces each pixel value of an image with a one code
• The main idea behind Arithmetic coding is to assign each

  symbol an interval
• Arithmetic coding consists of a few arithmetic operations due to its complexity is less. In terms of complexity, arithmetic coding is asymptotically better than Huffman coding.
• Huffman coding is a statistical method while arithmetic coding is NOT
• Arithmetic coding yields an optimum result while Huffman coding DOES NOT
• There is one-to-one correspondence between source symbol and code word in Huffman coding while arithmetic coding has none
• Transformations: manipulation of images
• The Fourier and the inverse transform enable the transformation of a two-dimensional image from the spatial domain to the frequency domain, and vice versa.
• The two functions f (x, y) and F(u, v) are called the Fourier transform pair.
• Fourier transform provides a frequency spectrum of a signal.
• For medical images utilizing multi-modalities: In the transformation model, three categories can be identified according to the associated degrees of freedom: rigid, affine, and nonlinear.
• RIGID REGISTRATION: the transformation involves only reflection,

  translations and rotations. This suffices to register images of rigid objects (like bones).
• AFFINE TRANSFORMATION: preserves the parallelism of lines, but neither their lengths nor their mutual angles. It extends the degrees of freedom of the rigid transformation with scaling and shearing in each image dimension. It is an appropriate transformation model when the image has been skewed during acquisition.
• NONLINEAR TRANSFORMATION: allow the mapping of straight

  lines to curves. The similarity measure can be calculated globally, on the entire image, or locally, on a sub-image.