Lecture
NOTE: QUIZ ON MONDAY FEB 5
Spatial Operations
Set of operations include:
- Single-pixel
- Neighborhood
- Geometric
Difference between intensity transformation and spatial filtering
- Intensity Transformation - it is point-based–affects each pixel independently.
- Spatial Filtering - neighborhood-based–considers the surrounding pixels.
Intensity transformations
It is also known as point processing The purpose of intensity transformations is to modify pixels values to enhance the image.
The transformation is independent of locations–determined only by the intensity values.
Intensity transformation can be denoted by the formula: $s = T(r)$ where: s is the transformed; r is the original pixel
In terms of thresholding in intensity transformations, if a pixel’s value is at a certain range, then it is assigned to a certain value. For example: if a pixel is less than 127, then automatically assign it to 0; otherwise assign it with a value of 255.
Log transformations: $s = clog(1+r)$ Log transformations are useful for enhancing (stretching) dark areas.
Reading
Two principal categories of spatial processing:
- intensity transformations - operate on singel pixels of an image (ex: contrast manipulation and image thresholding)
- spatial filtering - performs operations on the neighborhood of every pixel in an image (image smothing and sharpening).
Frequency domain - operations performed on the Fourier transform of an image, rather than the image itself.
The spatial domain processes are based on the expression: $ g(x, y) = T[f(x,y)]$ where $f(x,y)$ is an input image and $g(x,y)$ is the output image, and T is an operator of $f$ defined over a neighborhood of point $(x,y)$
Enhancement - process of manipulating an image so that the result is more suitable than the original for a specific application.
Negative Images
It has intensity levels in the range $[0, L-1]$ Negative transformation is in the form: $s = L - 1 - r$ Is useful for enhacing white/gray detail that is embedded in dark regions of an image.
Log Transformations
Has the general form $s = clog(1+r)$ where $c$ is a constant and $r \geq 0$ It maps a narrow range of low intensity values in the input into a wider range of output levels.
Basically high values of input levels are mapped to narrower range in output; lower values of input levels are mapped to wider range in output
Log transformations are useful to expand values of dark pixels in an image while compressing high-level values.
Log functions have an important characteristic that it compresses the dynamic range of pixel values.
Summary
Set Operations
A grayscale image is represented as: $A^c = {(x, y, K-z) | (x, y, z) \in A}$ where K is the maximum intensity values in an image.
EXAMPLE: In an 8-bit image, K would be K = 255
Spatial Operations
The use of spatial operations are performed directly on the pixels of an image. Spatial Operations are branched into 3 categories:
- Single-pixel (Intensity transformation) - Also known as point processing, is the most simplest operation. Alters intensity of individual pixels using a transformation function $T$ in the form: $s = T(z)$ where z is the intensity of a pixel in the original image and s is the mapped intensity of the corresponding pixel in the processed image.
NOTE: Intensity transformation uses a Look-Up Table to define the transformation function T(*) for specific intensity adjustments. Ex: if a pixel’s value is at a certain range, then it is assigned to a certain value.
- Neighborhood (Spatial Filtering) - Generates a corresponding pixel by analyzing each pixel by considering the values of nearby pixels.
- Geometric - Modifies the spatial arrangement of pixels in an image.
Log Transformations
It is a non-linear (line curves), transformation function that is in the formula: $S = clog(1+r)$ where c is the scaling parameter.
NOTE: Log transformations are useful in the sense that it enhances (stretches) the dark areas.