Receptive fields in convolutional neural networks (CNN)

In the field of deep learning, neural networks convolutional (CNN) have revolutionized image processing and computer vision. Inspired by the structure of the brain's visual cortex, these networks have demonstrated a remarkable ability to recognize patterns in images, from basic edges to complex shapes.

One of the key concepts in a CNN is the receptive field, a term describing the area of ​​the input image that influences the activation of a neuron at a specific layer. Understanding the role of receptive fields is crucial to optimizing the performance of a CNN and knowing how visual features are extracted throughout the layers of the network.

What is a receptive field in a CNN?

El receptive field In a convolutional neural network, it refers to the portion of the input image to which a neuron in the convolutional layer responds. In other words, it is the specific region of the input that affects the activation of a neuron in a given layer.

This is analogous to how cells in the visual cortex of the brain work. Simple cells respond to basic patterns, such as horizontal lines o vertical, while complex cells detect more advanced features by combining information from several simple cells.

How is the receptive field calculated?

The size of the receptive field of a neuron in a CNN depends on several factors, such as the size of the filter (kernel), the screeches (filter step) and the padding (padding added to the input). The general formula for calculating the receptive field size in a convolutional layer is:

o = (n + 2p – m) / s + 1

• o: Output size
• n: Entry size
• m: Filter size
• p: Padding
• s: Stride

For example, if we have a convolutional layer With a 3×3 filter, no padding and a stride of 1, the receptive field of each neuron spans 3 pixels in the input image.

Receptive field behavior in different layers

As an image passes through the convolutional network, the receptive field of neurons in the deeper layers increases, since they combine the information from multiple neurons in previous layers. In the first layers, the receptive field is small and detects borders y textures simple. In intermediate layers, they are recognized structures more complex, while in the final layers they are identified complete objects in the image.

The role of receptive field in improving CNN performance

Understanding the concept of receptive field is crucial to designing efficient CNNs. Some key aspects to optimize include:

• Selecting the filter size: Small filters (3x3) allow capturing fine details and are more computationally efficient.
• Using Padding: Adding padding allows you to maintain the dimensions of the output and avoid the loss of information on the edges.
• Suitable Stride: Small strides preserve more detail, while large strides reduce the resolution of the processed image.

Responsive Fields in Practice: Python Implementation with PyTorch

In bookstores like PyTorch, it is possible to define convolutional layers and tune the receptive field parameters in a simple way. Here is an example of how to define a convolutional layer in PyTorch:

import torch
import torch.nn as nn

# Definir una capa convolucional
conv_layer = nn.Conv2d(in_channels=3, out_channels=10, kernel_size=3, stride=1, padding=1)

# Imprimir los parámetros
print(f"Kernel size: {conv_layer.kernel_size}")
print(f"Stride: {conv_layer.stride}")
print(f"Padding: {conv_layer.padding}")

Importance of feature hierarchy

One of the great benefits of designing a CNN is its ability to build a feature hierarchy. While the first layers detect borders y textures, later layers combine these patterns to recognize structures more complex. This is key for applications such as:

• Medical Image Recognition: Tumor detection in X-rays.
• Autonomous vehicles: Identification of pedestrians on the road.
• Security and vigilance: Facial analysis in authentication systems.

The receptive fields Convolutional networks play a critical role in image processing within CNNs. Understanding their impact helps optimize the design of convolutional networks, improving accuracy in classification and object detection tasks. By properly tuning filter sizes, stride, and padding, it is possible to improve model performance and ensure that relevant features are captured at different levels of abstraction.