Spatial Domain Methods

Question 1

Define Spatial Domain Methods

Answer 1

Image manipulation methods based on the direct manipulation of pixels in a digital image

Question 2

Name the three main types of image operations in the Spacial Domain

Answer 2

Point operations –> where the outputted pixel depends solely on the input value of the same coordinate

Local Operations –> where the outputted value depends on the neighbouring pixels of the input value of the same coordinate

Global Operations –> Where the output pixel depends on all of the pixel values in the input image

Question 3

Point Operations

Answer 3

Changes a pixel’s intensity values based on some function f.

New outputted pixel value depends on:
Value of input pixel
Mapping Function

Examples of point operations:
Histogram Equalization
Gamma Correction / Power Law Transformation

Question 4

Gamma Correction / Power Law Transformatin

Answer 4

A Point operation, this operation adjusts the brightness of an image using gamma correction:

O = 255 x (I / 255)^G

O = outputted pixel [0, 255]
I = input pixel value [0, 255]
G = Gamma (controls brighness of image)

If G > 1, Brighter input values are mapped to darker output values
If G < 1, Darker input values are mapped to brighter output values

Question 5

Histogram equalization

Answer 5

Point operation used to improve contrast in an image.

The result displayed image displayed on a histogram would show a more widely spread range of intensity values, creating a more broad uniform shape

Question 6

Contrast stretching

Answer 6

A general case of image normalization with a piece wise linear transformation function

Question 7

What is Piece wise transformation

Answer 7

A spatial domain method used for enhancing a group of pixels that fall in a defined range

Question 8

Local Operations

Answer 8

Local operations are image manipulation operations where the the value of the outputted pixel depends on the values of the neighboring pixels of the inputted pixel.

Question 9

What are the two categories of local operations?

Answer 9

Linear Filters
Non-linear Filters

Question 10

Linear Filters

Answer 10

Filters used in local operations of an image where the outputted pixel is the weighted sum of the neighboring values of the input pixel. The weights are defined in the kernal

Used to smooth the image and preserve edges

Question 11

What are some examples of Linear Filters

Answer 11

Gaussian Filter
Box Filter

Question 12

Kernal

Answer 12

A matrix of values used in the convolution process to modify an image

Question 13

Non-Linear Filters

Answer 13

Use a more complex function than a simple weighted sum of pixel values.
Generally, instead of using the kernal for a convolution process, they use it to obtain the neighbouring pixel values, then use ordering mechanisms to produce the output pixel

Used for edge-detection and noise-reduction

Question 14

What are the differences of Linear and Non-Linear filters?

Answer 14

Linear and Non-Linear filters are both examples of filters used in local operations of an image, but they operate differently and have different effects on the output of the image. linear filters use a kernal, (a small matrix of numerical coefficients), and use matrix multiplication to multiply this with the neighborhood of the inputted pixel to produce a weighted sum of the values of the neighboring pixels of the inputted pixel, which is then the outputted pixel value. This process is called convolution. Linear filters are called linear because they perform a linear operation on the neighborhood of the inputted pixel values to produce the outputted pixel. Non-linear filters, on the other hand, use a variety of different techniques to combine the values of the neighboring pixels of the inputted pixel, depending on the type of non-linear filter you are using. Generally, however, Non-Linear filters use the kernel to find the values of the neighboring pixels of the inputted pixel and then use some ordering mechanisms to produce the outputted image. Linear filters are used for edge-preserving and smoothing of an image while Non-Linear filters are used for edge-detection and noise-reduction of an image

Question 15

Box Filter

Answer 15

A type of Linear Filter

involves averaging the pixel values of the neighboring pixels in a KxK window

Question 16

Gaussian Filter

Answer 16

A type of Linear Filter

Uses a Gaussian kernel for the convolution (square matrix of numerical coefficients where each value corresponds to values on the Gaussian curve)

Question 17

What are some examples of Non-Linear Filters?

Answer 17

Median Filter
Bilateral Filter

Question 18

Median Filter

Answer 18

Sorts the pixels in a given neighborhood in icnreasing order. The median of these values is then used as the value of the outputted pixel

Question 19

Bilateral Filter

Answer 19

Uses two Gaussian functions to determine the weights of the neighboring pixels of the inputted value:
The first Gaussian function acts the same as the one used in the Gaussian filter (considers the distance between the pixels)

The second Gaussian Function takes into account the difference in pixel values between the neighboring pixels and the centre pixel.