Computer Vision & Convolutional Networks (CNNs)

1. The PyTorch Image Tensor Convention: [N, C, H, W]

Unlike frameworks such as TensorFlow or OpenCV that store images as "channels-last" ([Height, Width, Channels]), PyTorch uses the "channels-first" standard:

import torch

# Converting a standard HWC image (NumPy / PIL) to PyTorch NCHW tensor:
# Standard NumPy image shape: (Height=224, Width=224, Channels=3)
import numpy as np
raw_image = np.random.randint(0, 256, size=(224, 224, 3), dtype=np.uint8)

# 1. Convert to float tensor and scale to [0.0, 1.0]
tensor_img = torch.from_numpy(raw_image).float() / 255.0

# 2. Permute dimensions: (H, W, C) -> (C, H, W)
tensor_img = tensor_img.permute(2, 0, 1)

# 3. Add batch dimension: (C, H, W) -> (1, C, H, W)
tensor_batch = tensor_img.unsqueeze(0)
print(f"PyTorch Batch Shape: {tensor_batch.shape}")  # torch.Size([1, 3, 224, 224])

2. Convolutional Math & Output Geometry

When passing a feature map through nn.Conv2d with input dimension W_in, kernel size K, padding P, and stride S, the output dimension W_out is calculated via:

3. Building a Residual Block (ResNet Skip Connection)

In plain deep networks, stacking 20+ layers causes training degradation because gradients vanish as they backpropagate through many non-linear matrix products. He et al. (2015) introduced Residual Skip Connections:

If the identity mapping is optimal, the optimizer easily drives weights toward zero without hurting representation.

import torch
import torch.nn as nn
import torch.nn.functional as F

class ResidualBlock(nn.Module):
    """
    Standard ResNet basic residual block with 3x3 convolutions,
    Batch Normalization, and an optional 1x1 projection shortcut.
    """
    def __init__(self, in_channels: int, out_channels: int, stride: int = 1):
        super().__init__()
        # Conv 1: optionally downsamples spatial dimension
        self.conv1 = nn.Conv2d(in_channels, out_channels, kernel_size=3, stride=stride, padding=1, bias=False)
        self.bn1 = nn.BatchNorm2d(out_channels)
        
        # Conv 2: keeps spatial dimension same
        self.conv2 = nn.Conv2d(out_channels, out_channels, kernel_size=3, stride=1, padding=1, bias=False)
        self.bn2 = nn.BatchNorm2d(out_channels)

        # Shortcut connection
        self.shortcut = nn.Sequential()
        if stride != 1 or in_channels != out_channels:
            # Match channel and spatial dimensions using a 1x1 conv
            self.shortcut = nn.Sequential(
                nn.Conv2d(in_channels, out_channels, kernel_size=1, stride=stride, bias=False),
                nn.BatchNorm2d(out_channels)
            )

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        # Save residual identity
        residual = self.shortcut(x)

        # Main branch
        out = F.relu(self.bn1(self.conv1(x)))
        out = self.bn2(self.conv2(out))

        # Add skip connection
        out += residual
        return F.relu(out)

4. Assembling a Modern ResNet Image Classifier

By combining a stem convolutional layer, stacked residual stages, and AdaptiveAvgPool2d, we construct a robust image classifier capable of processing arbitrary input resolutions:

class MiniResNet(nn.Module):
    def __init__(self, num_classes: int = 10):
        super().__init__()
        # Stem: Initial 7x7 conv to extract low-level edges
        self.stem = nn.Sequential(
            nn.Conv2d(3, 32, kernel_size=3, stride=1, padding=1, bias=False),
            nn.BatchNorm2d(32),
            nn.ReLU(inplace=True)
        )

        # Residual Stages
        self.stage1 = ResidualBlock(32, 64, stride=2)   # [B, 64, H/2, W/2]
        self.stage2 = ResidualBlock(64, 128, stride=2)  # [B, 128, H/4, W/4]

        # Global Average Pooling collapses (H, W) -> (1, 1) regardless of image size
        self.gap = nn.AdaptiveAvgPool2d((1, 1))
        
        # Classification Head
        self.classifier = nn.Linear(128, num_classes)

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        x = self.stem(x)
        x = self.stage1(x)
        x = self.stage2(x)
        x = self.gap(x)
        x = torch.flatten(x, 1)  # Flatten [B, 128, 1, 1] -> [B, 128]
        logits = self.classifier(x)
        return logits

# Verification
model = MiniResNet(num_classes=10)
dummy_batch = torch.randn(8, 3, 64, 64)
outputs = model(dummy_batch)
print(f"Output Logits Shape: {outputs.shape}")  # torch.Size([8, 10])