Convolution & Pooling Operations

This interactive demonstration explores two fundamental operations in convolutional neural networks (CNNs): convolution and pooling.

Convolution applies filters (kernels) to detect features like edges, patterns, and textures in images. Different filters highlight different characteristics of the input data.

Pooling reduces the spatial dimensions of feature maps while preserving the most important information, making the network more efficient and translation-invariant.

Use the interactive controls to experiment with different input patterns, filters, and pooling operations to understand how these operations transform data in deep learning systems.

Mathematical Foundation

Convolution Operation

Convolution applies a filter F to an input image I to produce a feature map O:

O(i,j)=∑m=0M−1∑n=0N−1I(i+m,j+n)⋅F(m,n)

Key Concepts:

  • Filters/Kernels: Small matrices (typically 3×3) that detect specific features
  • Feature Maps: Output matrices showing where features were detected
  • Translation Equivariance: Same features detected regardless of position

Pooling Operations

Max Pooling: P(i,j)=max(m,n)∈Ri,jF(m,n)

Average Pooling: P(i,j)=1|Ri,j|∑(m,n)∈Ri,jF(m,n)

Where Ri,j represents the pooling window region.

Benefits:

  • Dimensionality Reduction: Reduces computational load
  • Translation Invariance: Small shifts don't change output
  • Feature Abstraction: Focuses on most relevant information

How to Use This Demo

Input Controls

  • Input Image: Select different patterns to see how filters respond
    • Simple Pattern: Cross shape for basic testing
    • Vertical/Horizontal Edges: Test edge detection filters
    • Checkerboard: High-frequency pattern
    • Gradient: Smooth intensity transition

Filter Controls

  • Filter Type: Choose predefined filters or create custom ones
    • Vertical/Horizontal Edge: Detect specific edge orientations
    • Blur: Smooth the image
    • Sharpen: Enhance edges and details
    • Custom: Design your own 3×3 filter
  • Custom Filter Editor: Manually adjust filter values when "Custom" is selected

Pooling Controls

  • Pooling Type: Choose between max and average pooling
  • Window Size: Adjust pooling window (2×2, 3×3, 4×4)

Interactive Features

  • Hover Highlighting: Mouse over output cells to see corresponding input regions
  • Real-time Updates: All changes update visualizations immediately
  • Color Coding: Values use consistent color mapping across all displays

Exploration Tips

Understanding Filters

  • Edge Detection: Try vertical edge filter on horizontal edges input - notice weak response
  • Filter Design: Positive values detect light-to-dark transitions, negative detect dark-to-light
  • Blur vs Sharpen: Compare how blur smooths features while sharpen enhances them

Pooling Insights

  • Max vs Average: Max pooling preserves strong features, average provides smoother results
  • Window Size: Larger windows create more aggressive downsampling
  • Information Loss: Notice how pooling reduces detail but maintains overall structure

Interactive Learning

  • Hover Exploration: Use mouse hover to understand spatial relationships
  • Custom Experiments: Create custom filters to test specific hypotheses
  • Pattern Matching: Try different input-filter combinations to see feature detection

Real-World Applications

  • Computer Vision: These operations are fundamental to image recognition
  • Medical Imaging: Edge detection helps identify tissue boundaries
  • Engineering: Feature detection in structural analysis and defect identification

Input Image

Convolution Output

Pooling Output

Filter Visualization