Lecture 17: First Order Derivative Filters

Introduction

• Lecture presented by Anushri
• Topic: First order derivative filters mainly used for edge detection

Edge Detection

• Example of an image with a center pixel to detect edges towards the diagonal.
• Robert's Operator:
  • First edge detector
  • Uses a 2x2 mask, also known as the cross gradient operator.
  • Operates on the concept of cross diagonal differences.
  • Focuses only on diagonal elements, ignoring neighboring pixels.

Limitations of Robert's Operator

1. Implementation Complexity

   • 2x2 masks are not easy to implement.
   • Even order masks complicate convolution.

2. High Calculation Demand

   • Smaller mask requires more calculations, increasing chances for errors and time consumption.

3. Limited Pixel Consideration

   • Only considers diagonal neighboring pixels, ignoring horizontal and vertical pixels.

Improvements and New Operators

• To address the limitations, modifications were made:
  1. Increase the size of the mask.
  2. Change the number of neighboring pixels considered.

New Operators Developed

1. Sobel Operator

   • Emphasis on pixels closer to the center of the mask.
   • Example mask:

     [-1 -2 -1]
     [ 0  0  0]
     [ 1  2  1]
     

2. Prewitt Operator

   • Similar to Sobel, but used specifically for detecting vertical and horizontal edges.
   • Example mask:

     [-1 -1 -1]
     [ 0  0  0]
     [ 1  1  1]
     

Example Calculation

• Apply Robert's, Sobel, and Prewitt operators on pixel (1,1) in a given image.

Robert's Operator Calculation

• Mask multiplication:
  • Result: 50

Sobel Operator Calculation

• Mask multiplication:
  • Result: 0

Prewitt Operator Calculation

• Mask multiplication:
  • Result: 0

Conclusion

• Final values obtained from applying the operators:
  • Robert's: 50
  • Sobel: 0
  • Prewitt: 0
• Closing statement and preview for the next lecture.