FCN (Fully Convolutional Network) in Computer Vision

Introduction

An FCN helps computers understand images by labeling each pixel. It turns images into meaningful maps, like coloring each part of a photo.

When you want to find objects in a photo and know exactly where they are.

When you need to separate different parts of an image, like roads and buildings on a map.

When you want to help a robot see and understand its surroundings.

When you want to analyze medical images to find areas of interest.

When you want to create special effects by changing parts of an image.

Syntax

Computer Vision

class FCN(nn.Module):
    def __init__(self, num_classes):
        super(FCN, self).__init__()
        self.conv1 = nn.Conv2d(in_channels=3, out_channels=64, kernel_size=3, padding=1)
        self.relu = nn.ReLU()
        self.conv2 = nn.Conv2d(64, num_classes, kernel_size=1)

    def forward(self, x):
        x = self.relu(self.conv1(x))
        x = self.conv2(x)
        return x

FCNs use only convolution layers, no fully connected layers.

Output is a map with the same spatial size as input, but with class scores per pixel.

Examples

Example of smaller FCN layers for fewer classes.

Computer Vision

self.conv1 = nn.Conv2d(3, 32, kernel_size=3, padding=1)
self.conv2 = nn.Conv2d(32, num_classes, kernel_size=1)

Shows how output keeps spatial dimensions for pixel-wise prediction.

Computer Vision

output = model(input_tensor)
# output shape: (batch_size, num_classes, height, width)

Sample Model

This code builds a simple FCN with two convolution layers. It takes a small image and predicts class scores for each pixel. Then it converts scores to probabilities.

Computer Vision

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

class FCN(nn.Module):
    def __init__(self, num_classes):
        super(FCN, self).__init__()
        self.conv1 = nn.Conv2d(3, 64, 3, padding=1)
        self.relu = nn.ReLU()
        self.conv2 = nn.Conv2d(64, num_classes, 1)

    def forward(self, x):
        x = self.relu(self.conv1(x))
        x = self.conv2(x)
        return x

# Create model for 2 classes
model = FCN(num_classes=2)

# Create dummy input: batch of 1 image, 3 channels, 4x4 pixels
input_tensor = torch.randn(1, 3, 4, 4)

# Forward pass
output = model(input_tensor)

# Check output shape
print(f"Output shape: {output.shape}")

# Apply softmax to get probabilities per pixel
probabilities = F.softmax(output, dim=1)

# Print probabilities for first pixel
print(f"Probabilities at pixel (0,0): {probabilities[0, :, 0, 0]}")

Important Notes

FCNs keep the image size by using padding in convolutions.

Using 1x1 convolutions helps to classify each pixel independently.

Softmax is used to turn raw scores into probabilities for each class per pixel.

Summary

FCNs label every pixel in an image using only convolution layers.

They are useful for tasks like segmentation where location matters.

Output shape matches input image size but has class scores per pixel.

Practice

1. What is the main advantage of a Fully Convolutional Network (FCN) compared to a traditional CNN for image tasks?

easy

A. It can label every pixel in the image, preserving spatial information.

B. It uses fully connected layers to improve classification accuracy.

C. It reduces the image size to a single vector for faster processing.

D. It only works with grayscale images for simplicity.

Solution

1. Step 1: Understand FCN structure

   FCNs replace fully connected layers with convolution layers to keep spatial info.

2. Step 2: Compare with traditional CNNs

   Traditional CNNs use fully connected layers that lose pixel location details, FCNs keep pixel-wise info.

3. Final Answer:

   It can label every pixel in the image, preserving spatial information. -> Option A

4. Quick Check:

   FCN labels pixels = B [OK]

Hint: FCNs keep pixel info; CNNs lose it with fully connected layers [OK]

Common Mistakes:

• Thinking FCNs use fully connected layers
• Assuming FCNs reduce image to vector
• Believing FCNs only work on grayscale

2. Which of the following is the correct way to replace a fully connected layer with a convolutional layer in an FCN?

easy

A. nn.Linear(in_features, out_features)

B. nn.ReLU()

C. nn.Conv2d(in_channels, out_channels, kernel_size=1)

D. nn.MaxPool2d(kernel_size=2)

Solution

1. Step 1: Identify layer types

   Fully connected layers are replaced by 1x1 convolution layers to keep spatial size.

2. Step 2: Match correct PyTorch layer

   nn.Conv2d with kernel size 1 acts like a fully connected layer per pixel.

3. Final Answer:

   nn.Conv2d(in_channels, out_channels, kernel_size=1) -> Option C

4. Quick Check:

   1x1 conv replaces FC layer = D [OK]

Hint: Use 1x1 conv to replace fully connected layers [OK]

Common Mistakes:

• Choosing nn.Linear which is fully connected
• Confusing pooling or activation layers as replacements
• Using wrong kernel sizes

3. Given this PyTorch FCN snippet, what is the output shape if the input is (1, 3, 64, 64)?

import torch
import torch.nn as nn

class SimpleFCN(nn.Module):
    def __init__(self):
        super().__init__()
        self.conv1 = nn.Conv2d(3, 16, 3, padding=1)
        self.conv2 = nn.Conv2d(16, 2, 1)
    def forward(self, x):
        x = self.conv1(x)
        x = self.conv2(x)
        return x

model = SimpleFCN()
input_tensor = torch.randn(1, 3, 64, 64)
output = model(input_tensor)
print(output.shape)

medium

A. (1, 2, 64, 64)

B. (1, 2, 62, 62)

C. (1, 16, 64, 64)

D. (1, 3, 64, 64)

Solution

1. Step 1: Analyze first conv layer

   Conv2d(3,16,3,padding=1) keeps spatial size 64x64, output shape (1,16,64,64).

2. Step 2: Analyze second conv layer

   Conv2d(16,2,1) with kernel size 1 keeps spatial size, output shape (1,2,64,64).

3. Final Answer:

   (1, 2, 64, 64) -> Option A

4. Quick Check:

   Padding keeps size; 1x1 conv keeps size = A [OK]

Hint: Padding keeps size; 1x1 conv keeps spatial dims [OK]

Common Mistakes:

• Ignoring padding effect on size
• Assuming kernel 3 reduces size without padding
• Confusing channel and spatial dimensions

4. You have an FCN model but the output size is smaller than the input image size. What is the most likely cause?

medium

A. Using 1x1 convolution layers increases spatial size.

B. Using convolution layers without padding reduces spatial size.

C. Using fully connected layers preserves spatial size.

D. Using batch normalization layers reduces spatial size.

Solution

1. Step 1: Understand convolution padding effect

   Convolution without padding shrinks spatial dimensions because kernel slides inside image.

2. Step 2: Identify cause of smaller output

   If output is smaller, likely padding is missing in conv layers causing shrinkage.

3. Final Answer:

   Using convolution layers without padding reduces spatial size. -> Option B

4. Quick Check:

   No padding shrinks output = A [OK]

Hint: No padding in conv layers shrinks output size [OK]

Common Mistakes:

• Thinking 1x1 conv changes size
• Believing batch norm affects size
• Assuming fully connected layers keep spatial size

5. You want to build an FCN for semantic segmentation on 128x128 images with 3 classes. Which architecture choice will produce output matching input size with class scores per pixel?

hard

A. Use fully connected layers after conv layers to classify whole image.

B. Use conv layers without padding and max pooling layers to reduce size.

C. Use conv layers with stride=2 and no upsampling layers.

D. Use conv layers with padding=1 and 1x1 conv at end, no pooling layers.

Solution

1. Step 1: Maintain spatial size

   Padding=1 with kernel size 3 keeps spatial size; no pooling avoids shrinking.

2. Step 2: Output class scores per pixel

   Use 1x1 conv with out_channels=3 to get class scores per pixel matching input size.

3. Final Answer:

   Use conv layers with padding=1 and 1x1 conv at end, no pooling layers. -> Option D

4. Quick Check:

   Padding + 1x1 conv = pixel-wise classes = C [OK]

Hint: Keep padding and no pooling for same size output [OK]

Common Mistakes:

• Using pooling reduces output size
• Using fully connected layers loses pixel info
• Using stride>1 without upsampling shrinks output