Full math subjects for computer vision(17 steps)
For students who are interested to learn computer vision and ask which math subjects are needed this article is for you
in this article, we’re going to list, the all math subjects that you will need to study in computer vision. Also, giving for each subject free available resources to study.
1- Linear Algebra
The first thing that you should learn or begin with, is linear algebra. You have to have basic and solid information in algebra, especially matrices. In the computer image, all the images are treated as matrices.
So you have to learn or perform all matrices operations if you still have some issues with matrices. as result, we will give you all resources where to start learning computer vision math from scratch
The first step in computer vision is you will need to learn these 5 parts of linear algebra:
are links are included in each subject go and check them.
2 – Trigonometry
Trigonometry is an important subject to study computer vision because the following math subjects require trigonometry to apply in machine learning.
I will let you in this link a full course of trigonometry to revise or study before we go to the next step. Because we will need some trigonometry in the next steps.
3 – Signal value decompostion SVD
As we’ve seen before, computer vision focuses a lot on matrices and their operations like:
- add matrices
- multiplying matrices
- subtracting matrices
Signal value decomposition or SVD is a new way or operation to decompose matrices, it allows you to simplify and treat differently matrices. So you have to start with the following videos:
You can search and look for other videos but these that we mentioned are the best video that can make close to a subject. After Understanding the concept you can make some examples to practice the principle.
4 – Calculus
The fourth thing to learn or revise that you should already know about it is calculus.
In computer vision, calculus is very interesting to make many operations like:
- Taylor expansion
- use it in Fourier transform ( we’re going to talk individually about later)
Calculus is a long course is divided into 5 parts:
Some students may find precalculus a silly idea but if you don’t have the basics of precalculus you won’t be able to do calculus at all.
5 – Introductory level Pattern Recognition
pattern recognition is a mathematics field that operates and compare between numbers for instance look at these numbers:
if you look we find that if we add:
- 4 +21 we get 25
- 25 +21 we get 46
- 46+21 we get 67
So the common patter in between this number is 21, so this was the simplest example of what a computer vision system does today.
So you can find the complete full course at this link.
6 – Principal Component Analysis
PCA or principal component analysis is widely used in all different sizes of engineering not only computer vision, but it is also famous in neural network and data science.
You can watch this video below to give you an idea about PCA in computer vision and how it is used.
But studying through this video is not enough. So we invite you to watch these 2 full video courses about PCA.
You can search for more videos about this topic if you struggle to understand PCA.
7 – Linear Discriminant Analysis
As we’ve seen, PCA is a method to find a linear combination between variables, linear discriminant analysis or LDA is a similar method that aims to separate between 2 or more groups.
This might be confusing but don’t worry in these following videos you will understand what we’re talking about. we recommend watching the following videos with respecting the order.
So take your time and try to understand well the PCA and LDA because both are slightly different.
8 – Fourier Transform
Fourier transform is the great scientific invention or technic that allows us today to transform analogical functions to digitals one like image and sound. Fourier transform is a function used in many signal processing domains like:
- voice recognition
- sound filtration
- sound editing like adding removing or adding sound backgrounds
you could watch this video example about how Fourier transform is implemented in computer vision.
For students who haven’t heard about Fourier transport, you could take this full course by clicking this link.
9 – Wavelets
a wavelet is a mathematical method that principally computer vision engineers use for image compressing, which means representing the image in the smallest part of space.
we’re going to recommend watching this video to see and have precedent knowledge about wavelets.
you could watch these 5 parts videos below to know more about wavelets:
10 – Probability
The next step is to learn probability with all its aspects, especially these 3 aspects that you will need in computer vision :
- Bayes rule
- Maximum likelihood
if you aren’t good at probability we recommend taking this free course where you will study the basics of probability. But if you are stronger we can go next to the serious topics that we will mention below.
for Bayes rule, you can take this course
for Maximum likelihood there is:
for MAP or maximum posteriori you can watch this video.
11 – Mixtures and Expectation-Maximization Algorithm
Mixtures and expectations are 2 individual parts related to probability. So you will need to study them both to implement later in computer vision.
- The first one is mixtures, the famous aspect that you should study is called Gusians mixtures you can find a lesson about in this video.
- The second thing is expectation-maximization which is also related to probability you can find a full lecture in this video.
Or you can take this full course, talking about theses both principals at the same time.
The recommendation that we should give, is you have to understand well MAP subject that we noticed above in the previous paragraph before going to these subjects if you don’t want to struggle.
12 – Statistics
You have to have all the basic statistics because it is also used to solve many computer vision problems like radiometric or geometric form images or videos.
So we recommend having a full course in statistics you can find it in this link.
you will find some probability courses in this course. So don’t study them because normally you already should be knowing about them.
13 – Support Vector Machines
support vector machine or SVM is a technic used to comptuer vision to many applications the famous ones are:
- face detection
- spam filtering
- text recognition
This technic base on matric operation to not dig into details we will let you with this video, to have an intuition about this subject.
we recommend watching this course’s videos about SVM.
14 – Genetic Algorithms
Is a science or a technic that studies or takes the right combination in a system and excludes ones. In other words, in comptuer vision is used to take and filter the primary information from the secondary information.
you could watch his funny video, is easy to and explainable to understand this model.
you could follow this full course in it 2 parts:
15 – Hidden Markov Models
I will let you this video to explain to you what Markov models are because they need a lot of images to explain.
to follow the hidden Markov course you can take this free full course.
16 – Bayesian Networks
computer vision engineers use a Bayesian network to study graphical probability which means being able to predict graphical events.
You could watch this introductory video about this topic then go dipper to the next lesson that covers details about the bayesian network.
17 – Kalman filtering
The last thing in our journey is Kalman filtering which is a technic that engineers use to estimate the values of things that we can’t calculate. For instance, expecting the position of a point or object when it moving.
this option is used in object tracking for example in computer vision.
In this small course, you will find some simple explanations to approach you to a topic.
you could follow this excellent full course about Kalman filter.
learning the following steps allows you to take any computer vision course without worrying about any math subject. But you have to consider these 3 things:
learn steadily and don’t rush if you don’t understand a subject don’t jump. Because you won’t understand the next one, math is sequential. So everything that you will learn you will use in the next step.
The second thing after finishing the free source of learning as we mentioned in our article take paid courses. So you can go deeper into computer vision math.
Have a mentor. A mentor is very interesting to guide because computer vision has multiple specialties. So is better to have someone to guide and give yoiu shortcuts in the way.
by the way, we recommend following this channel it got a useful comptuer vision topics.
So these were all the math subjects that you will need for computer vision, good luck.
you could read this article if you are fun of math 20 incredible CS jobs that has a ton of math(explained).