Convolutional Neural Networks (CNN)

Why CNNs for Images?

Traditional dense layers treat image as flat vector:

Image: 32×32 pixels
↓
Flatten: 1024 values
↓
Dense layer: 1024 × 512 parameters

Problem: Loses spatial structure!
- Pixel at (0,0) connected to pixel at (31,31)
- No local structure exploited
- VERY slow on large images

CNNs preserve spatial structure:

• Learn local features (edges, corners, shapes)
• Share weights (same filter applied to all locations)
• Reduce parameters dramatically

The Convolution Operation

A filter (kernel) slides over the image, computing dot products:

Image:
[1 2 3]
[4 5 6]
[7 8 9]

Filter (3×3):
[1 0 -1]
[2 0 -2]
[1 0 -1]

Convolution at position (0,0):
(1×1 + 2×0 + 3×(-1) + 4×2 + 5×0 + 6×(-2) + 7×1 + 8×0 + 9×(-9))
= 1 + 0 - 3 + 8 + 0 - 12 + 7 + 0 - 81
= Output: -80

Result: Feature map (one number per position)

Feature Detection

Different filters detect different features:

Key insight: CNNs automatically learn these filters!

Stacking Layers

Input Image (32×32×3)
      ↓
Conv1 (16 filters) → 32×32×16  (detect low-level: edges)
      ↓
Conv2 (32 filters) → 16×16×32  (detect mid-level: shapes)
      ↓
Conv3 (64 filters) → 8×8×64    (detect high-level: objects)
      ↓
Global Average Pool → 64
      ↓
Dense → 10 classes (output)

Hierarchy:

• Early layers: edges, colors
• Middle layers: shapes, textures
• Late layers: whole objects