Introduction to convolutional neural networks (CNN)

Convolutional neural networks (CNNs) have emerged as a powerful tool in the field of artificial intelligence and machine learning. Specifically designed for processing and analyzing data with a grid-like structure, CNNs excel in tasks such as image recognition, object detection (used in autonomous vehicles like Tesla’s Autopilot system), and image segmentation (applied in medical imaging for identifying tumors or abnormalities in X-ray images). Inspired by the human visual system, CNNs are capable of interpreting visual information with remarkable accuracy. This comprehensive blog aims to provide a thorough understanding of CNNs, covering their key operations, and practical implementation for multi-class image classification.

Motivation#

The motivation behind the development of convolutional neural networks (CNNs) can be summarized as follows:

• Addressing limitations: Traditional neural networks struggle with capturing spatial dependencies in image data. This is because they treat each pixel in an image as an independent feature, disregarding the spatial relationships between neighboring pixels. For instance, traditional networks might fail to recognize objects in image classification tasks if their spatial arrangement differs from the training data. In contrast, CNNs overcome this limitation with specialized layers, such as convolutional and pooling layers. These layers efficiently capture local patterns and spatial hierarchies within images.

• Leveraging spatial information: CNNs exploit inherent spatial characteristics in images through local connections, preserving spatial relationships.

• Automatic feature learning: CNNs automatically learn relevant features during training, adapting to diverse image variations without hand-crafted features.

• Weight sharing for efficiency: CNNs employ weight sharing across the image, reducing parameters and enhancing generalization and computational efficiency. For example, in a convolutional layer, a filter/kernel is applied across the entire input image, and the same set of weights is used for each local receptive field. This sharing of weights allows the network to learn spatial hierarchies of features while significantly reducing the number of parameters needed to be learned, therefore improving efficiency and generalization.

• Revolutionizing computer vision: CNNs have transformed computer vision, enabling accurate recognition of objects, patterns, and features in images, powering tasks like image recognition and object detection.

Overview of CNN architecture#

CNNs have become the cornerstone of image processing and computer vision tasks, achieving remarkable success in various domains. Understanding the architecture of a CNN is crucial for harnessing its power in tasks such as image classification, object detection, and segmentation. The following example illustrates how CNNs work:

Here’s an overview of the key components that constitute a typical CNN architecture:

1. Input layer: The input layer represents the raw pixel values of an image, and its dimensions are determined by the size of the input image. Each pixel serves as a feature for further processing.

2. Convolutional layers: These layers consist of filters that slide over the input, extracting local patterns and features. They enable the capture of hierarchical representations, starting from simple edges to more complex structures.

3. Pooling layers: Following the convolutional layers, pooling layers downsample the feature maps to reduce computational complexity. Techniques like max pooling and average pooling are commonly used to retain essential information.

4. Flatten layer: The flatten layer takes the outputs from the convolutional and pooling layers and flattens them into a 1D vector. This step prepares the data for the fully connected layers.

5. Fully connected layers: These layers are densely connected and process the flattened features for making predictions. For classification tasks, a softmax activation function is often used to produce class probability distributions.

6. Output layer: The output layer provides the final predictions based on the learned information. The number of neurons in this layer corresponds to the number of classes in the classification task.

Now, let’s delve into a detailed exploration of each component of the CNN architecture one by one.

1. Input layer#

The input layer in a CNN is the entry point for data. It receives raw information, usually images, and prepares it for processing within the network. Its main functions include:

• Data reception: Accepting data typically represented as 3D tensors for images. Each element corresponds to a pixel value, with dimensions indicating width, height, and color channels (e.g., RGB).

• Preprocessing: Performing tasks like normalization, resizing, and data augmentation (e.g., cropping, flipping, adding noise) to enhance training data diversity.

• Forwarding data: Passing preprocessed data to the first convolutional layer. This layer applies filters to generate feature maps contributing to the desired output, such as image classification or object detection.

Key points to remember:

• The input layer itself is not trainable and doesn’t have adjustable parameters during training.

• The specific size and format of the input layer depend on the chosen CNN architecture and the data type being processed.

Understanding the role of the input layer is crucial for comprehending how CNNs receive and process information, enabling their remarkable capabilities in computer vision tasks. The input layer preserves the spatial structure of the input data. It sets the stage for subsequent layers to extract features and perform classification tasks. Preprocessing within the input layer helps prepare the data for efficient learning and representation by the neural network.

2. Convolutional layer#

The convolutional layer is a fundamental building block in CNNs. It’s a specialized type of neural network designed for processing and analyzing visual data, such as images. The convolutional layer plays a crucial role in feature extraction and hierarchical representation learning.

The following illustration represents the convolution operation:

In a convolutional layer:

• Filters (kernels): The layer consists of small filters (also known as kernels), which are small, learnable matrices. These filters slide or convolve across the input data, performing a mathematical operation called convolution.

• Convolution operation: The convolution operation involves element-wise multiplication and summation between the filter and a local region of the input data. As the filter slides across the entire input, it captures different patterns and features.

• Feature maps: The output of the convolution operation is a feature map. Each filter in the convolutional layer produces its own feature map, highlighting specific patterns present in the input data.

• Parameter sharing: One key advantage of convolutional layers is parameter sharing. The same filter is used across the entire input, reducing the number of parameters in the model. This parameter sharing enhances the network’s ability to generalize and recognize patterns efficiently.

• Hierarchical representation: By stacking multiple convolutional layers with varying filter sizes, the network learns a hierarchical representation of features. Early layers capture simple features like edges and textures. The deeper layers combine these features to recognize more complex structures.

Convolutional layers are effective in image recognition, object detection, and other tasks involving spatial relationships in data. They enable CNNs to automatically learn and extract meaningful features from input images, making them well-suited for a wide range of computer vision applications.

Why padding in convolution?#

Let’s explore the issues that highlight why we often need padding:

• Edge information loss: When we use a filter to analyze our image, it tends to focus more on the pixels in the middle and less on the ones at the edges. This overlooking of edge pixels can result in losing valuable information and intricate details located at the boundaries of the image.

• Reduced feature map dimensions: Imagine our image as a puzzle, and the filter is trying to understand each piece. Without padding, the puzzle gets smaller with each filter application. This reduction in size is a bit like zooming in too much, potentially causing us to miss significant details around the edges of the picture.

Padding#

Padding acts like a protective border added around our image before applying the filter. This additional border ensures that all pixels, including those at the edges, receive adequate attention. By preventing the loss of details, padding enables the network to comprehend the entirety of the image, not just its central part.

Here are some common padding types used in CNNs, along with short definitions:

• Zero padding: Zero padding adds extra rows and columns of zeros around the input image, preserving its spatial dimensions. It helps maintain spatial resolution and prevents information loss at the edges of the image.

• Same padding: The same padding pads the input image with zeros in such a way that the output feature map has the same spatial dimensions as the input image. It ensures that the convolution operation does not reduce the size of the input.

• Valid padding: Valid padding, also known as no padding, means no padding is added to the input image. As a result, the spatial dimensions of the output feature map are reduced after the convolution operation, which can lead to information loss at the edges of the image.

These padding types are essential for controlling the spatial dimensions of feature maps and ensuring effective feature extraction during the convolutional layers of a CNN.

The following illustration demonstrates the zero-padded convolution operation:

Let’s further explore how padding becomes a helpful ally in optimizing the convolution process.

• Preserves edge details: Padding guarantees that the edges of our image are not neglected, preserving crucial details that might otherwise be overlooked.

• Maintains information at peripheries: It prevents our image from becoming excessively small during the filtering process, aiding in capturing valuable information at the outer regions.

Keep in mind:

• Computational cost: Introducing extra border pixels means additional work for the computer. However, the computational cost is considered a worthy trade-off for preserving the completeness and understanding of our image.

• Balance is key: While we strive to ensure all pixels receive attention, excessive padding may introduce its own set of challenges. Striking the right balance is essential to achieve optimal results in image processing.

Stride#

Stride in convolution refers to the step size at which the convolutional filter moves across the input data. It determines how much the filter shifts or strides as it scans the input, affecting the spatial dimensions of the resulting feature maps.

The following illustration represents the strided convolution operation:

Now, let’s look at the advantages and drawbacks associated with the stride parameter:

Selecting the perfect stride in a CNN is like finding the right balance. It’s about adjusting the pace of the filter movement across the image to efficiently extract features while managing computational resources. Aim for a stride that captures essential details without overburdening the system, considering the specific needs of our task and the characteristics of our data. The goal is a stride that’s adaptable, optimizing both performance and efficiency across the layers of the network.

3. Pooling layers#

Pooling layers are crucial components of CNNs that are utilized primarily to reduce the dimensions (width and height, not depth) of the input volumes they process. By performing this dimensionality reduction, pooling layers help in decreasing the computational load for the network, reducing the number of parameters. Pooling layers also aid in making the detection of features somewhat invariant to scale and orientation changes. Another key benefit of pooling is that it helps in preventing overfitting by providing an abstracted form of the representation.

The most common types of pooling are:

• Max pooling: This is the most frequently used form of pooling, where the pooling operation partitions the input image into a set of nonoverlapping rectangles and, for each such subregion, outputs the maximum value. For example, with a $2$ x $2$ filter and stride $2$ (common settings for max pooling), each max-pooling operation will select the maximum element from $4$ ($2$ x $2$) elements.

• Average pooling: Instead of taking the maximum value from the part of the image covered by the filter, average pooling takes the arithmetic mean of the values. This method is less common than max pooling in practice for deep networks, but it is still useful in certain contexts. Average pooling distributes the contribution of all pixels in the window equally to the output, which can have a smoothing effect on the input features.

The following illustration represents how the max pooling operation works:

4. Flatten layer#

The flatten layer in a neural network architecture is a simple yet crucial component, especially in the context of CNNs. The flatten layer transforms its multidimensional input into a single, long linear vector. This process is necessary when transitioning between convolutional/pooling layers and fully connected (dense) layers.

Purpose of the flatten layer#

The flatten layer serves two main purposes:

• Transition between convolutional and dense layers: In CNN architectures, it bridges the gap between multidimensional convolutional layers and one-dimensional dense layers by flattening the spatially organized feature maps into a one-dimensional form.

• Preparing for classification or regression: It prepares the feature data for final tasks like classification or regression by reshaping them into a format suitable for processing by fully connected layers.

How the flatten layer works#

Suppose that we have the output from a convolutional or a pooling layer, and this output is a two-dimensional grid (for instance, $9$ x $9$ in case of an image). When this output is passed through a flatten layer, the layer reshapes this 2D output into a 1D vector. It does so by arranging each row of the grid sequentially into a long linear vector. The resulting vector for the given example would have a size of $9 * 9 = 81$ elements.

5. Fully connected layers#

Fully connected layers, also known as dense layers, are a fundamental component in neural networks, especially in the architecture of CNNs. After the input data has been processed by a series of convolutional and pooling layers, fully connected layers are typically utilized toward the end of the network. Their primary role is to perform high-level reasoning and make predictions based on the features extracted and transformed by the preceding layers.

Structure of fully connected layers#

A fully connected layer is so named because each of its neurons is connected to every neuron in the previous layer. This comprehensive connectivity ensures that the layer has a global understanding of the input features. In the context of a CNN, after convolutional and pooling layers have detected features and reduced the dimensionality of the input data, the role of the fully connected layers is to map these detected patterns to the desired output format, such as class scores in classification tasks.

How fully connected layers work#

Fully connected layers receive input as vectors or matrices, typically flattened from convolutional or pooling layers.

• Weight matrix: Neurons in fully connected layers possess weights and biases, constituting a weight matrix whose size is determined by input and neuron count.

• Matrix multiplication and activation: Input undergoes matrix multiplication with weights, followed by bias addition. Nonlinear activation functions introduce complexity for pattern learning.

• Output: Fully connected layer output varies by position. It may feed subsequent layers or produce final predictions like class scores or regression values.

Importance of fully connected layers#

Fully connected layers play a crucial role in the functionality and adaptability of CNNs. They serve as the bridge between the extracted features and the final decision-making process. Let’s delve into their significance further:

• Decision making: Fully connected layers in CNNs perform the final decision-making process, combining high-level features extracted by preceding layers.

• Flexibility in output: Fully connected layer architecture can be customized for various output tasks, such as classification or regression, enabling tailored outputs.

• Learning nonlinear combinations: Nonlinear activation functions in fully connected layers enable the network to learn intricate patterns, essential for capturing complex relationships in data.

6. Output layer#

The output layer in a CNN is the final stage responsible for generating predictions based on learned features.

• Prediction generation: Produces outputs corresponding to the network’s predictions tailored to the task (e.g., class probabilities for classification).

• Activation function application: Applies appropriate activation functions (e.g., softmax for classification, linear for regression) to transform raw outputs.

• Loss calculation: Computes the error between predictions and ground truth, guiding training via backpropagation and gradient descent.

The output layer’s design impacts the network’s performance and effectiveness in fulfilling its task.

Convolutions on RGB images#

In a CNN, an image is convolved using different filters to extract its features. This can be summarized as follows:

1. An input RGB image is represented as a matrix of size ($width$ x $height$ x $3$), for example, $64$ x $64$ x $3$.

2. The convolution operation is performed on this image with $n$ filters of size ($filter\_width$ x $filter\_height$ x $3$), stride $1$, and no padding. The formula to calculate the size of the output feature map is: $\scriptsize\left(\frac{{\text{{Width}} - \text{{Filter\_Width}}}}{\text{{Stride}}} + 1\right) \times \left(\frac{{\text{{Height}} - \text{{Filter\_Height}}}}{\text{{Stride}}} + 1\right) \times \text{{No\_of\_Filters}}\normalsize$. For example, with $8$ filters of size $5$ x $5$, the output size is$\left( \frac{{64 - 5}}{{1}} \right) + 1 = 37$, so $\text{output size} = 60 \times 60 \times 8$.

3. This output (feature maps) is passed to a max pooling layer with a $2$ x $2$ filter size and a stride of $2$. This process reduces feature map dimensions, aiding computational efficiency and mitigating overfitting.

4. After passing through the convolution layer again followed by the pooling layer again, the output size becomes $13$ x $13$ x $16$.

5. Next, a flattening operation is done by unrolling the output into a 1D vector. The size of this vector is calculated as: $Width \times Height \times Depth$. For the given example, the flattened vector would have a size of $13*13*16 = 2704$ units.

6. Finally, this flattened vector is fed to a classifier (e.g., a fully connected layer in a neural network) to make predictions. The output of the classifier is calculated using a softmax function, which gives the probability distribution over the class labels. The class with the highest probability is selected as the final output. The softmax formula is: $\text{{softmax}}(x_i) = \frac{{e^{(x_i)}}}{{\sum_j e^{(x_j)}}}$, where $x$ is the input vector to the softmax function, and $i$ and $j$ are the indexes of the elements in this vector.

CNN for handwritten digit recognition#

We are implementing a CNN using TensorFlow/Keras to classify handwritten digits from the MNIST dataset. Below is the implementation code:

The following is an explanation of the above implementation:

• Lines 2­–5: Necessary libraries, including TensorFlow, are imported for building the CNN model, along with components like layers and datasets from Keras.

• Lines 8–19: The MNIST dataset is loaded and preprocessed. Images are normalized to have pixel values between $0$ and $1$. The dimensions are expanded to include a channel dimension for CNN compatibility, and labels are one-hot encoded.

• Lines 23–44: Sequential model implementation steps:

  • Step 1: Creation of a sequential model.

  • Step 2: Addition of a convolutional layer with $32$ filters, a $3$ x $3$ kernel, and ReLU activation.

  • Step 3: Addition of a max pooling layer with a $2$ x $2$ pool size.

  • Step 4: Addition of another convolutional layer with $64$ filters and a $3$ x $3$ kernel.

  • Step 5: Addition of another max pooling layer.

  • Step 6: Flattening the output to a 1D array.

  • Step 7: Addition of a dense layer with $64$ units and ReLU activation.

  • Step 8: Addition of the output layer with $10$ units (for $10$ classes) and softmax activation.

• Lines 47–49: Compiling the model with the Adam optimizer, categorical cross-entropy loss function, and accuracy metric.

• Lines 52: Training the model for $5$ epochs with a batch size of $64$, using the training data and validating on the test data.

• Lines 55–56: Evaluating the trained model on the test set, printing the test accuracy.

CNN applications#

From classifying images to enabling autonomous vehicles, CNNs find diverse applications across various domains:

Classical pretrained models#

The ImageNet Large Scale Visual Recognition Challenge (ILSVRC) is an annual competition where research teams assess their algorithms on the task of detecting objects and categories in images from the large-scale ImageNet database. The competition has been influential in fostering the development of deep learning and CNNs for computer vision tasks.

Here’s an overview of the common models that have emerged as significant in this space:

These models have played a significant role in advancing the field of computer vision, each with its own strengths and weaknesses.

Conclusion #

CNNs are a cornerstone in the field of artificial intelligence, offering unparalleled proficiency in tasks ranging from image recognition to complex pattern detection across varied domains. Inspired by the human visual system, their hierarchical structure enables effective feature extraction and analysis, leading to significant advancements in computer vision and beyond. The practical success of applications such as autonomous driving, medical diagnostics, and facial recognition underlines their transformative potential. As technology evolves, CNNs continue to push the boundaries of what machines can understand and achieve from visual data.

Next steps#

If you want to expand your knowledge and learn more about CNNs, the following courses are an excellent starting point for you: