📸 Concept of an Image

An image can be thought of as a 2D function:

$$ f(x, y) $$

• Each point \( (x, y) \) in the function maps to an intensity or color value.
• A point in the image is called a pixel.
• In single-channel images (e.g., binary, grayscale), each pixel has one value.
• In color images (e.g., RGB), each pixel has three values:
  $$ (r_{x,y}, g_{x,y}, b_{x,y}) $$

💻 Digitalization of an Image

To process images on computers, they must be digitalized:

• Image sampling: Discretizes spatial coordinates \( (x, y) \)
• Gray-level quantization: Discretizes intensity/amplitude values
• Pixel values are typically:
  • Integer: 0–255
  • Float: 0.0–1.0

💾 How Are Images Stored on a Computer?

Images are stored as files (e.g., .jpg, .png) that include:

• Metadata (e.g., resolution, color profile)
• Pixel data (in array format)

Typical formats:

• Grayscale image: 2D array → width × height
• RGB image: 3D array → width × height × 3

⚫ Black and White (Binary) Image

A binary image uses 1 bit per pixel:

• Pixel value is either 0 (black) or 1 (white)
• Represented as a 2D matrix of 0s and 1s

Example:

1 0 1 0 1  
0 1 0 1 0  
1 0 1 0 1  
0 1 0 1 0  
1 0 1 0 1  

Matrix: height × width
Values: 0–1

🌫️ Grayscale Image

A grayscale image uses 8 bits per pixel, with intensity values from 0 to 255:

• 0 = black, 255 = white
• Stored as a 2D matrix of integers

Matrix: height × width

🌈 RGB (Color) Image

An RGB image uses 3 channels:

• Red, Green, and Blue (each 8 bits)
• Each channel is a 2D array
• Combined into a 3D array: height × width × 3

Common in digital photos and web images

🧠 What is Image Processing?

Image processing is the automatic manipulation and analysis of images using algorithms and code.

Applications include:

• Robotics and remote sensing
• Medical imaging and diagnostics
• Industrial quality control
• Photography and social media platforms (e.g., Instagram, Facebook)

🐍 Reading, Saving, and Displaying an Image with Python (PIL)

Using Python’s Pillow (PIL) library:

from PIL import Image
im = Image.open("brown_val1.jpg") # read the image
print(im.width, im.height, im.mode, im.format, type(im))
im.show() # display the image

• im.mode tells the image type (e.g., “RGB” or “L”)
• show() opens the image in a viewer
• 

⚙️ Convert RGB to Grayscale with PIL

You can easily convert a color image to grayscale:

im_g = im.convert('L')              # convert to grayscale
im_g.save('brown_val1.jpg')         # save grayscale image
Image.open("brown_val1.jpg").show() # read & display

• 'L' stands for luminance (grayscale)
• You can view the result with .show()
• 

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