Lecture Notes

Images can be represented as:

  1. Surface in a 3D space
  2. Visual Intensity Array
  3. 2D Numerical Array

Representing Digital Images: Consider a continuous image with a function $f(s, t)$ Through sampling and quantization, the digital image will then be $f(x, y)$

Formula to get the coordinates of the center of the image: $(x_c, y_c) = (floor(M/2), floor(N/2))$

Two types of different image resolutions:

  1. Spatial Resolution (1920 x 1080) - is determined how fine/coarse the image is (ex: low spatial resolution would result in jagged lines; think of pixelated alphabets/sharp images). It is sensitive to shape variation.

  2. Intensity Resolution (Bit depth): 8-bit, 16-bit, 24-bit - refers to the number of intensity levels used to represent an image (depends on the number of bits). Greater the sensitivity, the finer the level of detail that can be distinguished in the image.

Saturation - the intensity level of an image.

Noise - It is a variation of brightness

Picking the resolution of an image depends on 5 factors:

  1. Intended Use
  2. Viewing Conditions
  3. Display/Output Device Capabilities
  4. File Size and Storage
  5. Image Content

Relationship Between Pixels:

Neighbors of a Pixel: The 4-neighborhood of pixel p(x,y) is the set: {(x-1, y), (x+1, y), (x, y-1), (x, y+1)}

The two pixels p and q are 4-adjacent (or connected) if q is in $N_4(p)$ or p is in $N_4(q)$

The 8-neighborhood of pixel p(x,y) is the set:

Distance Measures

The use of distance measures are used to measure the distance between pixel coordinates in an image.

Three common distance measures:

  1. Euclidean - straight line distance $ D(p,q) = \sqrt((x-u)^2 + (y-v)^2 )$
  2. City-Block (Manhattan Distance) - creates a diamond-shape distance measure. $ D(p, q) = |x - u| + |y - v|$
  3. Chessboard - creates a squared-shape distance measure. $ D(p, q) = max(|x-u|, |y-v|)$

Readings

Summary

Formula to get center of image: $(x_c, y_c) = (floor(M/2), floor(N/2))$

Two Types of image resolutions:

  1. Spatial Resolution - Depends on the number of samples; is sensitive to shape variation.
  2. Intensity Resolution - Depends on the number of bits; is sensitive to lighting variations. The greater the intensity levels, the finer the image is.

NOTE: Intensity level is determined 2^{num of bits}

Saturation describes the intensity level of an image.

Noise is the variation of brightness or color in images. Produces grainy texture.

You must consider 5 factors when picking a resolution of an image:

  1. Intended Use
  2. Viewing Conditions
  3. Display/Output Device Capabilities
  4. File Size and Storage
  5. Image Content

The Neighbors of a Pixel is useful for edge detection and other applications. There are three adjacency types:

  1. 4-adjacency - A pixel $p$ at coordinates $(x,y)$ that has two horizontal and two vertical neighbors w/ coordinates $(x+1, y), (x-1, y), (x, y+1), (x, y-1)$
  2. 8-adjacency - A pixel $p$ at coordinates $(x, y)$ that has four neighbors + the other 4 neighbors in the 4-adjacency neighbors $(x+1, y+1), (x+1, y-1), (x-1, y+1), (x-1, y-1)$
  3. m-adjacency (mixed adjacency) -

NOTE: first two are the main important ones.

Distance Measures are used to measure the distance between pixel coordinates in an image. There are three distance measured used for image processing:

  1. Euclidean - Straight Line $D(p, q) = \sqrt{(x-u)^2 + (y-v)^2}$ where p and q represent a pixel.
  2. City-Block - Diamond-centered shape $D(p, q) = |x - u| + |y - v|$
  3. ChessBoard - Square-centered shape $D(p, q) = max(|x-u|, |y-v|)$

NOTE: picking the appropriate distance is important since the distance could affect the outcome of image processing algorithms.