Artificial Intelligence and Machine Learning

6CS012 - Week 5 – Introduction to CNN

Introduction � Convolutional Neural Network

Tasks in Computer Vision

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How do computers see images?

Images are just numbers

Deep Learning task with images

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Deep Learning Tasks with Images

We need features to Identify the images

Lets Identify the features

• Nose
• Eyes
• Hair

• Wheels
• License Plate
• Lights

• Doors
• Windows
• Roof

Manual Feature Extraction

• We need Domain Expertise
• Time-consuming
• Subjectivity
• Limited Scalability

Manual Feature Extraction

Learning Feature Representations

• Can we learn the hierarchical features directly from the data instead of hand engineering?

Fully Connected Neural Network

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• Automatic feature extraction

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• Learns representations directly from data

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• Reduces human bias

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• More generalizable across domains

Disadvantage of FCNN for image classification

Still Too Much Computation!!!!

Why are too many parameters a problem?

• Computational Cost
• Model Overfitting

Training Deep FCNNs: Vanishing Gradients

• Vanishing Gradient Problem (Example case :Sigmoid activation )

Training Deep FCNNs: Vanishing Gradients

• Vanishing Gradient Problem (Example case :Sigmoid activation )

• Sigmoid function limits outputs to (0, 1) leading to saturation at extreme values.

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• In saturated regions, gradients approach zero, reducing weight updates.

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• This issue is minor in shallow networks but worsens in deep networks due to gradient multiplication.

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• As layers increase, gradients decay significantly, slowing training for early layers.

Disadvantage of FCNN for image classification

No Spatial Information

Sensitive to the location of the object in an image!!!!

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Disadvantage of FCNN for image classification

No Spatial Information

Treats local pixels same as the pixels far apart

Connects all the nodes in the hidden layers to all the nodes in the input layer !

How can we use the spatial features in the input to inform the architecture of the network?

Using Spatial Features (Idea)

• Idea: connect patches of input to neurons in hidden layer.

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• Neuron connected to region of input. Only "sees" these values.

Feature Extraction with Convolution

Intuition: Convolution Operation

• Detects local patterns (loops, lines, curves)

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• Breaks down digit "9" into meaningful features

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• Identifies spatial components independently

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• Combines detected features for classification

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• Preserves spatial relationships between features

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• Applies same filters across entire image

Convolution Operation (Mathematically)

We slide the filter over the Input image, element wise multiply and add the output!!

Understanding Convolution Operation

Understanding Convolution Operation

The Loopy Pattern Detector can detect that pattern, all across the input image, no matter the position

Remember the Terminologies

• Convolution: Operation that extracts features using filters

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• Kernel/Filter: Small matrix that detects specific patterns

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• Feature Map: Output after applying a filter to input

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• Stride: Step size when sliding the filter

Producing Feature Maps

You can change the weight values in filter to represent different filters which can detect different features in the image

Padding

Preserves pixels at image boundaries during convolution

• Prevents cumulative spatial information loss in deep networks

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• Types:

Zero Padding: Adds zeros around image borders

Same Padding: Ensures output dimensions match input (for stride 1)

Valid Padding: No padding, resulting in smaller output

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Output Dimension after Convolution Operation

A Bigger Picture (Convolution Layers)

Introducing Non-linearity

• Apply after every convolution operation (i.e., after convolutional layers)
• ReLU: pixel-by-pixel operation that replaces all negative values by zero. Non-linear operation!

Pooling Layer

• It is a layer inserted in-between successive Convolution layers in a CNN.
• It operates similar to convolution operation i.e. by sliding a filter over feature maps.
• It down samples the convolved features by reducing the spatial dimensions (height and width) of the feature maps while still preserving the most critical feature information.
• It has no learnable parameters, but it reduces the number of parameters in later layers and the computation in the network and hence also supports in controlling overfitting.
• The most common algorithm used for this operation is called max pooling.

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Week - 5 - Introduction to CNN

30

Pooling

• Reduced Dimensionality
• Spatial Invariance (robust to small shifts)

Output Dimensions After Pooling

Story So far!

Convolution Layer

ReLU Activation

Pooling

Representation Learning in Deep CNN

Feature Learning

Classification

CNNs For Classification: Feature Learning

• Learn features in input image through convolution
• Introduce non-linearity through activation function (real-world data is non-linear!)
• Reduce dimensionality and preserve spatial invariance with pooling

Feature Learning

Classification

CNNs For Classification: Classification

• CONV and POOL layers output high-level features of input
• Fully connected layer uses these features for classifying input image
• Express output as probability of image belonging to a particular class

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Case Studies-CNN Architecture.

Classic Architecture-LeNet-5:

[Conv, ReLU, Pool]*N,🡪 flatten,[FC, ReLU]*N, FC 🡪 Softmax.

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Training The CNN

Forward Computation @ Convolutional Layer.

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Same Operation happens at every Layer, the inputs shall change depending on the layer.

Image from Internet: Subject to copyright.

Backward Pass @ Convolution Layer.

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Backward Pass @ Convolution Layer.

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References

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• https://shwetarkadam25.medium.com/cnn-series-part-2-what-is-meant-by-convolution-c504f38c42b
• cnn explainer
• Convolutional Network Demo from 1989