P3:

Concept of Translation Invariance

• Translation invariance refers to the property where the outcome remains unchanged irrespective of the position of the input.
• This principle is essential in eliminating rotational or other variances that may arise during different transformations in image processing.

Introduction to Convolutions

• Convolutions are fundamental in digital image processing, used for statistical analysis and feature extraction from images.
• Early methods were manual (manual feature engineering), relying on expert knowledge to identify which features to extract from images.

Shift from Manual to Automated Feature Engineering

• With neural networks and convolution operations, feature engineering has moved towards automation, allowing neural networks to learn feature extraction automatically.
• Backpropagation algorithms play a crucial role in adjusting filters (kernels) to optimize outcomes based on learned information from input data.

Convolution Operations Overview

• When performing convolution, a filter (kernel) is applied to an image:
• Image and filter example: Let (W) represent the kernel values.
• The filter is slid over the image, multiplying the corresponding values, resulting in neuron activations reflecting that segment of the image.

Sliding Operation in Convolutions

• The term "sliding" refers to moving the filter across the image one step at a time to generate output for each neuron layer.
• This sliding generates feature maps that reflect various aspects of the input image.

Manual Feature Engineering Example

• Demonstrates how multiple kernels can be applied to extract different features from the same image, resulting in unique feature maps.
• Each kernel produces varying neuron activations based on specific feature detection.

Automated Feature Extraction through Backpropagation

• In automated feature extraction, the initial weights for kernels are set randomly.
• The backpropagation algorithm adjusts these weights based on output errors, refining the extracted features to minimize error rates.

Padding in Convolutions

• Padding involves adding extra layers (often zeros) around the input image to maintain edge features during convolution.
• It ensures corner pixels, which usually get less importance, are captured adequately in feature maps.
• Padding helps mitigate the boundary problem where certain features are captured multiple times at the edges of the image while others are neglected.

Stride in Convolutions

• The stride is the number of pixels by which the filter moves across the input image.
• A stride of 1 moves the filter one pixel at a time, while a stride of 2 skips a pixel.
• The stride value affects the dimensions and size of the resultant feature map.

Calculating Feature Map Size

• The general formula for calculating the feature map dimensions involves the input size, filter dimensions, padding, and stride:
• For the height of the feature map: [ fh = \frac{n + 2p - fh}{s} + 1 ]
• For the width, it follows a similar pattern.
• Understanding this formula allows for predicting how convolutions affect image dimensions through various operations and transformations.