Digital Image Processing Lecture 3.2

Questions and Answers

What is the primary purpose of spatial filtering in digital image processing?

To process pixel values using their surrounding neighbors (correct)

To convert images into different color spaces

To reduce the overall size of an image file

To enhance image sharpness by increasing pixel values

What is a characteristic of a linear filtering method?

It involves applying a fixed mathematical transformation to each pixel

It generates output as a weighted sum of the input pixels (correct)

It produces output without considering neighboring pixel values

It produces output based solely on the maximum input pixel value

Which of the following is NOT a common term for the area in spatial filtering that includes the pixel being processed?

Filter

Artifact (correct)

Mask

Kernel

In the context of spatial convolution, what does the term 'coefficients' refer to?

Weights assigned to each neighboring pixel Signup and view all the answers

What is a typical size for a mask used in spatial filtering to ensure symmetry?

5x5 Signup and view all the answers

What can be deduced about the transformation from the original image to the processed image based on the given examples?

The transformation increases the average value in each non-zero element. Signup and view all the answers

Which fraction correctly represents the final non-zero value in the last processed image mentioned?

2/9 Signup and view all the answers

How do the resulting matrices differ in terms of dimensions from the original matrices?

The dimensions remain the same throughout the transformation. Signup and view all the answers

Which pattern changes most noticeably in the transition from the original to the processed images?

Distribution of non-zero values adjacent to each other. Signup and view all the answers

In the context of the transformations, what is the significance of repeating the fraction '1/9' in both matrices?

It indicates that a normalization process has occurred. Signup and view all the answers

Study Notes

Digital Image Processing Overview

Course Title: Digital Image Processing
Lecture Focus: Image Enhancement in the Spatial Domain
Instructor: Dr. Jacqueline J. George

Spatial Filters

Definition: Techniques for processing a pixel using surrounding neighbor pixels.
Tools Used: Filter, mask, kernel, template, or window; these terms describe the area of pixel influence.
Coefficients: Filter values are referred to as coefficients rather than pixels.

Spatial Processing Techniques

Spatial Filtering: Involves calculating filter responses through a weighted sum of products of filter coefficients and image pixels located within the filter mask.

Linear Spatial Filtering

General Formula:
- For an image ( f ) of size ( M \times N ) with filter mask of size ( m \times n ):
  
  ( g(x, y) = \sum_{s=-a}^{a} \sum_{t=-b}^{b} w(s, t) f(x+s, y+t) )
- Where ( a = (m-1)/2 ) and ( b = (n-1)/2 ).

Mask Positioning

Mask response is computed and positioned in the output image, typically at coordinates [x,y].

Filtering Process

The entire process involves moving the filter mask across the image from left to right and top to bottom, typically using an odd-size mask (e.g., 3x3, 5x5) for symmetry.

Linear vs Non-Linear Spatial Filtering

Linear Filtering: The output is a weighted sum of input pixels.
Non-Linear Filtering: Output does not follow the weighted sum property.

Border Handling in Filtering

Border issues arise when the filter mask exceeds image boundaries, leading to:
- Ignoring certain rows and columns, resulting in a smaller output image.
- Three main boundary handling techniques:
  - Zero Boundary: Pixels outside the boundary set to zero.
  - Replicate Boundary: Boundary pixels are duplicated.
  - Periodic Images: The image is treated as a tiling of periodic copies.

Boundary Handling Techniques

Zero Boundary: Potential artifacts arise; outside pixels are set to zero, affecting the results.
Replicate Boundary: By duplicating edge pixels, artifacts during filtering can be minimized.

Periodic Image Replication

Involves tiling the entire image to create a 2D periodic representation, useful for edge effects.

Region of Interest (ROI)

Refers to specific parts of the image targeted for separate processing, commonly where spatial filters are applied.

Zooming Algorithm (x2 zoom)

Creates a new ( (2n) \times (2n) ) image based on the original ( n \times n ) image, with copies of original pixels at even coordinates and others set to zero.
A spatial linear filter is then applied to smooth the newly created image.

Summary

Spatial filtering is a fundamental technique in digital image processing, essential for enhancing image quality through various methodologies while avoiding artifacts, especially at the image borders.

Description

This quiz covers Lecture 3.2 of Digital Image Processing, focusing on image enhancement techniques in the spatial domain. Key concepts include spatial filters, spatial correlation, and spatial convolution. Test your understanding of these fundamental topics in image processing.