Data Warehousing and Data Science

1 July 2021

What is Convolution?

Filed under: Machine Learning — Vincent Rainardi @ 7:32 am

For me image classification/recognition is one of the most exciting topics in machine learning (ML). Today all good image classifications are using neural network. For image classification we use a specific type of neural network called Convolutional Neural Network (CNN).

I have heard this term so many times in the last 3 years but I never understood what convolution mean. So in this article I would like to explain what convolution means.

Image Classification

Since 2015 ML is better than human when classifying images. A lot faster no doubt, but also more accurate. Here are a few ML algorithms which made historical landmark in the ImageNet image classification competition (source: Gordon Cooper, Semiconductor Engineering, link)

The competition is about classifying 1.2m training images into 1000 categories (link). All the dark purple deep learning architectures above are convolutional neural networks (CNN). Over the years, the number of layers gradually increases as the available computing power increases.

  • AlexNet started the deep learning revolution in 2012 by using CNN and graphics processing unit (GPU), achieving massive improvement to the previous year result (link).
  • ResNet (stands for Residual Neural Network) can bypass 2-3 layers if those layers are not useful (link). This concept was inspired by the pyramid cells in the celebral cortex.
  • SENet (stands for Squeeze and Excitation Network) can adaptively recalibrate channel-wise feature responses (link).

The application is massive and live changing, from detecting cancer in medical images to self driving cars, from product search to face recognition (link).

What is Convolution?

Convolution is a mathematical operation between two functions, as follows: reverse and shift one function, then take the product of both functions, then take the integral (link).

But in image processing, convolution is a process of applying a filter on an image. This is because::

  1. Mathematically speaking, a “convolution” in the time domain becomes a “multiplication” in the frequency domain (link).
  2. Applying a filter on an image is multiplication process.

Let’s go through some examples so point 2 above becomes clear.

If we have this image and this filter, this is the convolution:

We get the yellow 5 on the convolution by multiplying the yellow area on the image by the filter:

So we multiply green cell on the image with the green cell on the filter (1×1), the blue cell on the image with blue cell on the image (0x1), etc. and then add them up to get 5 on the convolution:

Similarly to get the yellow 4 on the convolution, we multiply the yellow area on the image by the filter:

Why do convolution?

The purpose of doing convolution is to detect a pattern on the image.

If we want to detect if there is a horisontal line on the image then we apply this filter:

If we want to detect if there is vertical line on the image then we apply this filter:

And if we want to detect if there is a diagonal line on the image then we apply this filter:

This is called “feature extraction”. We use convolution to detect “lines” on the image.

The same 3 filters above not only detect “lines” on the image but they also detect “area”. It is probably easier to see if we don’t have the numbers on the cell, see below right:

Note: we call this line and area as “edge”, meaning the border of an area. The 3 filters above detect “edges”.

So next time people say Convolutional Neural Network, you know what Convolution means 🙂

In this article (link) I explain what CNN is.

1 Comment »

  1. […] the previous article I explained what convolution was (link). We use convolution in image classification/recognition, to power a special type of neural network […]

    Pingback by What is Convolutional Neural Network (CNN)? | Data Warehousing and Machine Learning — 4 July 2021 @ 7:52 am | Reply

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