Convert Image into Matrix - Like a Pro!

Summary

This video explores how computers perceive images, transforming what humans see as simple visuals into complex mathematical structures. Starting with the concept of pixels, the video explains how binary numbers represent black-and-white images, while grayscale and RGB systems handle more complex visuals. The RGB format, which measures red, green, and blue intensities, is explained using practical examples. The video also shows how to create matrices to represent these images mathematically. Viewers will learn how to understand and convert images into numbers, preparing them to process images using Python in future videos.

Takeaways

• 😀 Pixels are the smallest controllable elements of a digital image, and they provide a coordinate system for images.
• 🖼️ A 7x7 pixel image with only black and white colors can be represented in binary form using 0s and 1s, where 0 stands for black and 1 for white.
• 📏 Grayscale images use a range of numbers from 0 to 255 to represent different shades of gray, with 0 being black and 255 being white.
• 🎨 Grayscale values can be calculated by determining the percentage of black in a color and using that to find the corresponding value on the 0-255 scale.
• 🌈 RGB (Red, Green, Blue) format is used to describe colorful images, with each color channel ranging from 0 to 255 to represent the intensity of that color.
• 🔴 The color white in RGB is represented by the highest value (255, 255, 255), while black is represented by the lowest value (0, 0, 0).
• 🟡 The color yellow is represented in RGB by the values (255, 255, 0), indicating maximum intensity for red and green and none for blue.
• 📊 RGB images are represented mathematically as three-dimensional matrices, with each dimension representing one of the color channels.
• 👨‍🏫 The script promises to show viewers how to process images with Python in a future video, indicating a follow-up tutorial on practical image processing.
• 🔑 Understanding the numeric representation of colors and pixels is fundamental to computer vision and image processing tasks.

Q & A

What is the smallest controllable element of an image called?

The smallest controllable element of an image is called a pixel.

How does a computer perceive an image that looks like a smiley face to humans?

To a computer, an image that looks like a smiley face to humans appears as a complex piece of math.

What is the size of the image used in the video to explain the concept of pixels?

The size of the image used in the video is 7 pixels by 7 pixels.

In the context of the video, what does the binary value '0' represent in an image?

In the context of the video, the binary value '0' represents the color black in an image.

How is the grayscale format different from the binary format when describing an image?

The grayscale format uses numbers from 0 to 255 to describe the intensity of black, whereas the binary format uses only 1 or 0.

What is the grayscale value that represents 50% black?

The grayscale value that represents 50% black is 128.

How is the RGB format different from grayscale in terms of color representation?

The RGB format measures the intensity of red, green, and blue colors on a particular pixel, using values from 0 to 255 for each channel, whereas grayscale uses a single value from 0 to 255 to represent shades of black and white.

What RGB values represent the color white?

The RGB values that represent the color white are 255 for red, 255 for green, and 255 for blue.

How are RGB values used to represent a color that is not a shade of gray?

RGB values are used to represent a color that is not a shade of gray by having different values for the red, green, and blue channels, where one or more channels have values other than the maximum or minimum.

What is a three-dimensional matrix in the context of RGB images?

A three-dimensional matrix in the context of RGB images is a matrix where the first dimension holds the values for the red channel, the second dimension holds the green values, and the third dimension holds the blue values.

How can you determine the color of a pixel by looking at its RGB values?

You can determine the color of a pixel by looking at its RGB values by observing which channel's value is the highest or which colors are more dominant. For example, a high value in the red channel with lower values in green and blue would suggest a color closer to red.

Outlines

00:00

😀 Understanding Pixels and Binary Images

This paragraph introduces the concept of pixels as the fundamental building blocks of digital images. It explains that pixels are the smallest controllable elements, which when magnified, appear as tiny squares that cannot be further divided. The video aims to demonstrate how these pixels can be converted into a mathematical format. The size of the image is given as 7x7 pixels, and since it contains only black and white colors, it is best represented in binary, using 1s and 0s to denote white and black pixels, respectively. The process of assigning numeric values to each pixel based on its color is detailed, and the resulting data structure is described as a matrix, which is a simplified representation of the image using only numbers and coordinates.

05:02

📊 Grayscale and Color Intensity Representation

The second paragraph delves into the representation of images with more than two colors, focusing on grayscale. It explains that grayscale uses a range of numbers from 0 to 255 to represent different shades of black, with 0 being black and 255 being white. The paragraph illustrates how to calculate the grayscale value for different percentages of black, using the example of 50% black being represented by the value 128. It also discusses how to determine the grayscale value for more complex percentages, such as 15% black, which is calculated to be approximately 218. The process of filling in the grayscale values for an image is described, leading to a matrix representation that captures the grayscale intensity of the image.

10:02

🌈 RGB Format and Color Channel Intensity

The final paragraph discusses the RGB format used to describe colorful images. It explains that RGB stands for red, green, and blue, and each color channel is measured on a scale from 0 to 255, representing the intensity of each color in a pixel. The paragraph provides examples of how to represent colors like white, black, and yellow in RGB, emphasizing the importance of the order of values. It also touches on how to adjust the intensity of a color by modifying the values of its respective channels. The paragraph concludes with a description of how to represent an RGB image mathematically, using a three-dimensional matrix where each dimension corresponds to a color channel. The process of selecting a specific pixel and understanding the combined effect of its red, green, and blue channel values to produce a specific color is explained.

Keywords

💡Pixel

A pixel, derived from 'picture element,' is the smallest controllable element of a digital image. In the video, pixels are described as tiny squares that make up an image, and when zoomed in far enough, they are the smallest units that cannot be split into smaller squares. This concept is fundamental to understanding how computers perceive images, as each pixel has a specific value that contributes to the overall image.

💡Binary

Binary refers to the base-2 numeral system used in computing, where data is represented in terms of two digits, 0 and 1. The video explains that binary is the simplest form of image representation, where black is represented by 0 and white by 1. This is crucial for understanding how computers process images, as it simplifies the complexity of visual data into a form that can be easily manipulated by digital systems.

💡Grayscale

Grayscale is a range of shades from black to white, with various shades of gray in between. In the context of the video, grayscale is used to represent images with multiple shades of gray, each corresponding to a different intensity of black. The video uses grayscale to explain how images with more than two colors can be represented numerically, with values ranging from 0 (black) to 255 (white).

💡RGB

RGB stands for Red, Green, and Blue, which are the primary colors used in digital imaging to create a wide range of colors. The video explains that RGB format is used to describe colorful images by measuring the intensity of each color channel. Each pixel's color is represented by a combination of three values, one for each color channel, ranging from 0 to 255. This concept is essential for understanding how computers process and represent color images.

💡Matrix

A matrix in the context of the video refers to a two-dimensional array of numbers representing the values of an image. After converting an image into numerical values, the video describes how these values are organized into a matrix. This matrix is a data structure that allows for easy access to any pixel's value by its coordinates, which is crucial for image manipulation and processing.

💡Color Intensity

Color intensity refers to the strength or purity of a color. In the video, this concept is used to explain how different colors and shades are represented numerically in grayscale and RGB formats. For grayscale, intensity is represented on a scale from 0 (black) to 255 (white), while in RGB, it is represented by the combination of values for red, green, and blue channels, which determine the color's appearance.

💡Coordinates

Coordinates in the video refer to the position of a pixel within an image, typically represented by a pair of numbers indicating the pixel's row and column. Understanding coordinates is essential for accessing and manipulating specific pixels within an image matrix, as it allows for precise control over image data.

💡Shades of Gray

Shades of gray are the various tones between black and white. The video uses the concept of shades of gray to explain how grayscale images are represented numerically. Each shade of gray corresponds to a specific value between 0 (black) and 255 (white), allowing for a range of grays to be used in image representation.

💡Color Channels

Color channels are the individual components of a color image, each representing the intensity of a primary color (red, green, or blue). The video explains that in RGB format, each pixel's color is determined by the values in its red, green, and blue channels. Understanding color channels is key to manipulating and processing colors in digital images.

💡Three-Dimensional Matrix

A three-dimensional matrix, as mentioned in the video, is a data structure used to represent an RGB image, where each dimension corresponds to a different color channel (red, green, and blue). This structure allows for the organization of color data in a way that each pixel's color can be determined by the combination of its channel values, which is essential for processing and analyzing color images.

Highlights

Introduction to how computers perceive images as complex math.

Explanation of pixels as the smallest controllable element of an image.

Conversion of an image into a 7x7 matrix of binary values.

Binary representation of colors with 1 for white and 0 for black.

The concept of using matrices to represent image data.

Introduction to grayscale images and their representation with numbers from 0 to 255.

Calculating grayscale values based on the percentage of black.

Representing 50% black with a grayscale value of 128.

Calculating more complex grayscale values using percentage and ratio.

Filling in a grayscale image matrix with calculated values.

Transition to handling images with more than two colors using RGB format.

Description of RGB format measuring the intensity of red, green, and blue colors.

Representing white and black in RGB with the values 255 and 0 respectively.

Explanation of how RGB values create shades of gray when all channels have the same value.

Representing the color yellow in RGB with values 255, 255, 0.

Creating a three-dimensional matrix to represent an RGB image.

Filling in the RGB matrix with values for red, green, and blue channels.

Concept of selecting a pixel's color by accessing its RGB values in the matrix.

Anticipation of processing images with Python in the next video.

Transcripts

hi everybody it's been a while but i'm

back and today we're going to talk about

images and more specifically about how

computers perceive

images so to us humans

this looks like a smiley face to a

computer however

the exact same image looks like a very

complex piece of math

so in this video i'm going to show you

how to

make this conversion and even though it

looks

a little bit intimidating at first it is

actually super

simple i promise let's start with a

quick intro to the most

basic building block of digital images

the pixel

a pixel is the smallest controllable

element of an image

so if we take this image for example and

we zoom

in we'll eventually end up seeing all

these tiny squares

and if we keep zooming in the squares

will grow larger

but they'll never split into any more

squares

that's because we're looking at the

smallest unit of the image

so this would be one pixel this would be

another pixel

and same goes for the rest of these

squares in fact

pixels provide us with a system of

coordinates

and with that in mind let's begin

exploring it by converting

this image into math we see that the

size of the image

is 7 pixels by 7 pixels and because the

image consists of only two colors black

and white

the best way to describe it would be in

a binary form

meaning we can only use one or zero

to describe the color computers in

general

will always prefer binary input because

bits are also binary

but we'll talk about it more in a

different video so what does

1 and 0 mean in our case in a binary

image

zero stands for black and one stands for

white

which is also equivalent to false and

true by the way

and if we focus on our image and start

filling in the values

all the white pixels will become one and

all the black pixels will become

zero so we can see how each pixel

suddenly got a numeric value so now

if we want to check the value of the

fourth pixel in the fourth row

we'll get one and if we're checking

which value the second

pixel in the fifth row holds that will

be zero

so now when we understand the values and

coordinates of our image

we can finally get rid of the background

and only keep the numbers

when we do that we see that we got this

beautiful data structure

which we call a matrix pretty cool eh

but what happens if our image contains

more than just two colors

and we can no longer describe it in a

binary form

let's take this monochromatic image as

an example

we see right away that this particular

image

has one two three four five six seven

different colors and all these colors

are shades of gray

in this case the best color format to

describe this image

would be grayscale so the grayscale

format is using numbers

anywhere from 0 to 255

to describe the intensity of black where

once again

0 is black and 255 is white

so it's the highest contrast possible

with black

so first let's fill in the colors that

we already know

so 255 is white and 0

is of course black any other shade of

gray

can be represented with numbers from 1

to 254

so let's say that we want to find out

how we represent

a color that's only 50 black which is

the color we see in the very center of

our image

to calculate this we would have to

divide our number of available values by

two and because zero also represents a

color which is black

our total number of available values

would be 256

rather than 255. therefore

50 black in grayscale is represented by

the value

128 which we can now also fill in

but let's try to calculate a slightly

more complicated percentage

let's say we want to find out what 15

black would look like first we subtract

15 percent from 100

and we get 85 percent then we'll divide

100 by 85 to get the ratio we need

and then we'll do the exact same as in

the above example

divide 256 which is the total number of

available values

by 1.176 which is the ratio we just got

and the result is 217.68

which we can definitely round up and get

218.

and again we can fill it in in our image

in the appropriate spots

and by using the exact same principles

we can fill in the rest of the values

and if you'll trace these back you can

also figure out which percentage of

black i've used for these colors

so coordinate wise let's quickly check

what's the value of the fifth pixel

on row number three and we can see it's

128

so let's get rid of the background add a

bunch of commas

and two huge square brackets and we got

our matrix again

this time it represents a grayscale

image rather than binary

cool so we're done with the easy part

because so far we've been measuring the

intensity of

one particular shade but what happens

when we need to measure the intensity of

colors

across several shades let's take this

colorful image as an example

we can clearly see one two three four

five six

colors this time however these

are not just different shades of the

same color they are

actually very particular shades of red

blue

yellow and green so how exactly are we

supposed to handle it

we actually have special formats to deal

with these sort of situations

it is common to use the rgb format to

describe a colorful

image so rgb actually stands

for red green and blue and it measures

the intensity of

each of these colors on a particular

pixel

here we are also using values from 0 to

255

the only difference is we'll be checking

across three different color channels

and not just one so i'll explain it with

an example

so let's say that we want to find out

how we describe the color

white in rgb okay so

we already know that white was

represented by the top most numeric

value in grayscale

it is also true for rgb however

since we're measuring the intensity of

red green

and blue we'll say that white is

represented

by a set of three values 255 for red

255 for green and 255 for blue

in this particular order this is very

important

similarly if we want to represent the

color black

with rgb we'll get the value 0 on the

red channel

0 on the green channel and 0 on the blue

channel

and as a matter of fact whenever you see

an rgb

color mix consisting of three identical

values

for an example rgb 777 or

rgb 50 5050 you'll always be looking at

a shade of gray

and this is because no color is

overpowering the other

okay but what happens if we want to

represent the color yellow

which luckily we happen to have in our

image we already know

that it would take in three values one

for each channel

and also we know that these three values

will not be identical because yellow is

not a shade of gray

so the numeric values which produce

yellow are 255

on the red channel on the green channel

and finally zero on the blue channel

and this particular combination is

actually as yellow as possible

because we're using the top most and the

bottom most values available

but what if our shade is somewhere in

between if we take this green color for

example

it is represented by 0 for the red

channel

200 on the green and 20 on the blue

so potentially we can make this green

even greener

if we boost the value of the green

channel to 255 or 250 for example

well so far it's all rainbows and

butterflies but how on earth

are we going to represent this rgb image

mathematically

and will actually start from this green

color now because each rgb

image has three different color channels

we'll need to multiply the image by the

amount of channels

in our case we'll have three of them

when the left copy

represents red the center copy

represents green

and the right copy blue and if you

remember

this green was produced by rgb 0

220 which as you can see we can easily

fill in across our channels

and as a matter of fact each of the

green pixels will hold the exact same

values

now we also know that black was rgb000

and that white was rgb 255 255.

255. and also yellow if you guys

remember

is 255 for the red 255 for the green and

0 for the blue

and we can fill in the red which will

obviously have a higher intensity of red

as opposed to green and blue while this

particular cyan shade

will have a higher intensity of green

and blue rather than red

so you can kind of guesstimate which

color you're getting

just by looking at the values so okay

now all the numeric values are in place

we can get rid of all the image copies

in the background

now you may think we're getting three

different matrices here

however what we are actually getting is

a single matrix

with three different dimensions aka

a three-dimensional matrix where the

first dimension

holds the values for the red channel of

the image the second dimension

holds the green values the third

dimension holds the blue values

in a multi-dimensional matrix we stagger

the channels

one behind the other to form this

complex data structure

for example if we want to select a

particular pixel in our image

let's say the sixth pixel on row number

three

we are actually selecting all three

channels at once

and we see that together they produce

the color rgb

100 220 and 230

which is probably cyan because the green

and blue values are overpowering the red

thank you so much for watching you guys

i'll see you next time where

i'll show you how to process images with

python