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Computer Vision & Convolutional Neural Networks (CNNs)
Convolutions, kernels, pooling, and spatial feature hierarchies
Convolutional Neural Networks (CNNs) process spatial grid data like images by sliding learnable filter kernels across pixels to capture edges, textures, and high-level objects.
Architecture of a Convolutional Layer
Kernels (Filters): Small 2D or 3D matrices (e.g., 3x3) containing weights that slide over the input image performing element-wise multiplication and summing to create Feature Maps.
Translation Invariance: A vertical edge or circle detected by a kernel will be recognized regardless of where it appears in the frame.
Pooling Layers (Max Pooling): Downsamples spatial dimensions (e.g. reducing 64x64 to 32x32 by taking the max value in each 2x2 patch), reducing parameter count and compute while preserving dominant features.
import numpy as np
# Simple 4x4 grayscale image patch
image = np.array([
[10, 10, 80, 80],
[10, 10, 80, 80],
[10, 10, 80, 80],
[10, 10, 80, 80]
])
# Sobel vertical edge detection kernel
kernel = np.array([
[-1, 0, 1],
[-2, 0, 2],
[-1, 0, 1]
])
# Calculate single convolution at top-left 3x3 patch
patch = image[0:3, 0:3]
edge_response = np.sum(patch * kernel)
print("Detected vertical edge magnitude:", edge_response)Modern vision models also utilize Vision Transformers (ViT), which slice images into 16x16 pixel patches and process them like words using self-attention.
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Test Yourself With Exercise
What is the primary function of a Max Pooling layer in a Convolutional Neural Network?