Image Filters and Edge Detection

Introduction to Image Filters

• Image filter: Takes an image, processes it, and outputs a modified image.
• Previous lecture covered Kernel convolution with Gaussian and mean blurs.
• Today’s topic: Edge detection using Kernel convolution.

Edge Detection Overview

• Edge Detection: Identifying regions with sharp changes in intensity or color.
  • High value = steep change
  • Low value = shallow change
• Common operator: Sobel Operator.
  • Approximation of the derivative of an image.
  • Separate calculations for x and y directions.

Sobel Operator

X-Direction Gradient

• Kernel for x-direction gradient:

  | -1 | -2 | -1 | | 0 | 0 | 0 | | 1 | 2 | 1 |

• Applies to 3x3 kernel, quick processing.

• Preserves center pixel values, focusing on differences between left and right sides.

• Example: Given pixel values, it calculates the difference to identify edges.

Y-Direction Gradient

• Kernel for y-direction gradient:

  | -1 | 0 | 1 | | -2 | 0 | 2 | | -1 | 0 | 1 |

• Similar approach to the x-direction, but focuses on vertical edges.

Combining Gradients

• Both x and y gradients give information about edge direction and strength.
• Total gradient magnitude is calculated:
  • Magnitude = sqrt(Gx² + Gy²)
  • This removes sign, ensuring all values are positive.
  • A consistent color results in a value of zero.

Orientation Calculation

• Edge orientation can be determined:
  • Orientation = arctan(Gy / Gx)
  • Provides information on pixel angle, useful for detecting structures.

Preprocessing Steps

1. Convert color images to grayscale (Sobel is a grayscale operator).
2. Apply Gaussian blur to reduce noise before edge detection:
   • Reduces high-frequency noise while preserving important low-frequency structures.
3. Then apply Sobel edge detector to get clear edges.

Implementation Notes

• Example code provided with comments for clarity.
• C# implementation noted; flexibility in programming language is acknowledged.

Key Takeaways

• Understanding edge detection is crucial for image processing tasks.
• The Sobel operator is foundational for identifying edges by analyzing intensity changes in images.