Representing images: pixels and bitmaps

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수업 노트

What is a Bitmap Image?

A bitmap image (also called a raster image) is made up of a rectangular grid of tiny coloured squares called pixels.
Each pixel stores the exact colour of that tiny area, so bitmaps are great for photographs and images with complex colours and fine detail.
Unlike vector graphics (which use mathematical formulas for shapes), bitmaps store colour information for every single pixel.
The word 'raster' comes from the Latin×rastrum×(a rake) and relates to how old CRT monitors drew images line by line.

Key Characteristics: Resolution and Colour Depth

A bitmap is defined by its dimensions (width and height in pixels) and its colour depth (number of bits per pixel).
Resolution refers to the number of pixels in the image – often given as width × height (e.g., 1920 × 1080). Higher resolution means more detail but larger file size.
Colour depth (also called bit depth) is the number of bits used to store the colour of each pixel.
A 1-bit image can only show 2 colours (usually black and white) because 2¹ = 2.
An 8-bit image can show 256 colours (2⁸ = 256).
A 24-bit image uses 8 bits for each of the red, green, and blue channels, giving over 16 million possible colours (2²⁴ = 16,777,216).

More pixels capture and keep more detail; fewer pixels lose it.

How Colour Depth Affects the Image

Higher colour depth means more possible colours, so the image can look more realistic and smooth.
Lower colour depth reduces the number of colours, which can cause banding or visible jumps between shades.
For example, a 4-bit image can only show 16 colours, which might be enough for simple graphics but not for photos.
Most modern colour formats use 24-bit colour (true colour) for high-quality images.

More bits stored per pixel means more possible shades and smoother gradients.

Estimating File Size of a Bitmap

The file size of an uncompressed bitmap depends on the total number of pixels and the colour depth.
Formula: file size (in bits) = width × height × colour depth (bits per pixel).
To get the size in bytes, divide the number of bits by 8.
Example: A 100 × 100 image with 24-bit colour has 100 × 100 × 24 = 240,000 bits = 30,000 bytes (about 30 KB).
Increasing either resolution or colour depth will increase the file size.

Bitmap file size depends on width, height and colour depth, and on how efficiently the data is compressed.

Effects of Changing Resolution and Depth

Increasing resolution (more pixels) adds detail but makes the file larger.
Decreasing resolution reduces file size but can make the image look blocky or pixelated when enlarged.
Increasing colour depth improves colour accuracy but also increases file size.
Decreasing colour depth reduces file size but may make colours look flat or banded.
There is a trade-off: you must balance quality against storage space.

The pixel dimensions of an image do not change when the physical size of the display does.

Pixel Formats

Common pixel formats include binary (black and white), grayscale, palettized (using a colour lookup table), and full-colour (e.g., 24-bit RGB).
Binary images use 1 bit per pixel – only two colours.
Grayscale images use shades of grey, often 8 bits per pixel (256 shades).
Palettized images use a limited set of colours stored in a table; each pixel stores an index into that table.
Full-colour images typically use 24 bits per pixel, with 8 bits for red, green, and blue.

How Bitmaps are Stored in Files

The grid of pixels is stored in a row-major order: the top row is written left to right, then the second row, and so on.
A file header contains essential information like the number of columns and the pixel datatype (bits per value).
Headers may also include the number of rows and other metadata (e.g., camera settings in Exif).
Without the header, the computer wouldn't know how to reconstruct the 2D grid from the serial list of numbers.

Compression: Making Files Smaller

High-resolution bitmaps can be very large, so compression is used to reduce file size.
Lossless compression (e.g., PNG, GIF, RLE) preserves every pixel exactly – the original can be perfectly restored.
Lossy compression (e.g., JPEG) discards some detail to achieve smaller files – the original cannot be perfectly restored.
Run-length encoding (RLE) replaces repeated values with a count and the value – efficient for images with large areas of the same colour (like line drawings).
For photographs, RLE can make the file larger because pixels are rarely identical, so other methods like JPEG are used.

A bitmap image is a grid of pixels, and each pixel colour is stored as binary.

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1.A bitmap image is made up of a rectangular grid of pixels.
Easy
True or false?
2.What does the term 'pixel' stand for?
Easy
- Apicture element
- Bpixel element
- Cpoint element
- Dpicture electron
3.Vector graphics store the exact color of each pixel.
Easy
True or false?
4.Which of the following is NOT a common raster image file format?
Easy
- AGIF
- BJPEG
- CPNG
- DSVG
5.A higher color depth allows an image to display more distinct colors.
Easy
True or false?
6.In a 24-bit color image, how many bits are typically used for each of the red, green, and blue channels?
Medium
- A8 bits each
- B6 bits each
- C12 bits each
- D4 bits each
7.Run-length encoding (RLE) is always a lossless compression method.
Medium
True or false?
8.An image has a resolution of 100 pixels wide and 200 pixels high. How many pixels in total?
Medium
- A20000
- B300
- C10000
- D200

더 많은 문제

9.Increasing the resolution of a bitmap image always increases the file size.
Medium
True or false?
10.Which of the following are lossless compression algorithms? (Select all that apply)
Hard
- ARLE
- BJPEG
- CLZW
- DPNG
- EGIF
11.Match each term to its correct definition.
Hard
- Resolution
- Color depth
- Pixel
- Number of bits per pixel
- A single picture element
- Width and height of an image in pixels
12.Arrange the following steps in the order they occur when a bitmap image is displayed on a screen.
Hard
- Image file is read
- Pixel data is decoded
- Image is rendered on the display
- Each pixel's color is mapped to screen
13.A raster image with a higher resolution always has a larger file size than one with a lower resolution, regardless of compression.
Hard
True or false?
14.Lossy compression algorithms can perfectly reconstruct the original image from the compressed data.
Challenge
True or false?
15.Which of the following best explains why a photograph is more suitable for raster graphics than vector graphics?
Challenge
- ARaster images can store the exact color of each pixel, allowing complex color variations.
- BVector graphics are not supported by most devices.
- CRaster images use less storage than vector graphics.
- DVector graphics cannot be displayed on screens.
16.Put the following steps in the order they occur when a bitmap image is displayed on a screen.
Easy
- Read the header to get the number of columns and bits per pixel
- Read the pixel values in row-major order
- Reconstruct the two-dimensional grid of pixels
- Display the grid on the screen
17.Which of the following are common raster image file formats? (Select all that apply)
Medium
- AGIF
- BJPEG
- CPNG
- DSVG
- EPDF
18.A bitmap image with a color depth of 4 bits per pixel can display up to 16 different colors.
Easy
True or false?
19.Which of the following best explains why run-length encoding (RLE) is often more efficient for line drawings than for photographs?
Medium
- ALine drawings have large areas of identical colors, so RLE can replace long runs with short codes.
- BPhotographs have fewer pixels than line drawings.
- CRLE is a lossy compression method, which is better for photographs.
- DLine drawings use more colors than photographs.
20.The word 'raster' comes from the Latin word for 'rake'.
Easy
True or false?
21.Which of the following statements about lossy compression are true? (Select all that apply)
Medium
- ALossy compression can perfectly reconstruct the original image.
- BLossy compression produces smaller file sizes than lossless compression for the same image quality.
- CJPEG is an example of lossy compression.
- DLossy compression is always better than lossless compression.
- ELossy compression approximates the original pixel values.
22.A bitmap image is 8 pixels wide and 8 pixels high. If it uses 1 bit per pixel, how many bits are needed to store the image without compression?
Easy
- A64
- B16
- C8
- D128
23.A photograph is stored as a 24-bit bitmap with resolution 1920 × 1080. What is the uncompressed file size in megabytes (MB) if 1 MB = 1,048,576 bytes?
Medium
- A5.9 MB
- B6.2 MB
- C4.9 MB
- D7.1 MB
24.A bitmap image with a color depth of 8 bits per pixel can display 256 distinct colors.
Medium
True or false?
25.Which of the following factors directly affect the file size of an uncompressed bitmap image? (Select all that apply)
Medium
- AWidth in pixels
- BColor depth (bits per pixel)
- CThe image's subject matter
- DHeight in pixels
26.Run-length encoding (RLE) is always more efficient than storing the original pixel values for any bitmap image.
Medium
True or false?
27.A bitmap image is 10 pixels wide and 10 pixels high, with a color depth of 4 bits per pixel. It is compressed using run-length encoding. The first row of pixels has the values: 5, 5, 5, 5, 5, 5, 5, 5, 5, 5. How many bits would be needed to store this row using RLE, assuming each value and count is stored as a 4-bit number?
Hard
- A8 bits
- B16 bits
- C24 bits
- D32 bits
28.In a row-major format, the cells of the image are stored starting from the bottom row and moving upward.
Easy
True or false?
29.Which of the following best describes the purpose of the header in a raster image file?
Medium
- ATo store the actual pixel values
- BTo contain metadata such as the number of columns and the pixel data type
- CTo compress the image data
- DTo convert the image to vector graphics
30.In a raster image, the size of each pixel is constant across the grid.
Medium
True or false?
31.Arrange the following steps in the correct order for storing a raster image in a file using row-major format.
Medium
- Read the header to get the number of columns and pixel data type.
- Serialize the two-dimensional array into a one-dimensional sequence.
- List the cells of the first row left to right, then the second row, and so on.
- Reconstruct the grid by reading the serialized values in order.
32.A raster image has a color depth of 4 bits per pixel and a resolution of 1024 × 768. It is compressed using run-length encoding. The image consists entirely of a single solid color. What is the compressed file size in bytes, assuming the header is negligible and each run is stored as two bytes?
Hard
- A2 bytes
- B4 bytes
- C1024 bytes
- D768 bytes
33.The word 'raster' originates from the Latin word 'rastrum', meaning a rake.
Easy
True or false?
34.In a raster image, the size of each pixel can vary across the grid.
Easy
True or false?
35.In a row-major format, the cells of a raster image are listed starting from the bottom row and moving upward.
Easy
True or false?
36.Which of the following are characteristics of raster images? (Select all that apply)
Easy
- AThey are made up of a rectangular grid of pixels.
- BThey store the exact color of each pixel.
- CThey use mathematical formulas to describe shapes.
- DThey are ideal for photographs.
- EThey can be scaled without loss of quality.
37.A raster image with a color depth of 4 bits per pixel can display up to 16 different colors.
Easy
True or false?
38.In a raster image, the header section at the beginning of the file must contain at least the number of columns and the pixel datatype.
Medium
True or false?
39.Put the following steps in the correct order when storing a bitmap image in a file using row-major format.
Easy
- Read the header to know the number of columns and pixel datatype.
- Store the first row of pixels from left to right.
- Store the second row of pixels from left to right.
- Continue storing each subsequent row until all rows are stored.
40.Which of the following are common raster compression algorithms? (Select all that apply)
Medium
- ARun-length encoding (RLE)
- BJPEG
- CLZW
- DVectorization
- EPNG
41.Complete the sentence.
Easy
The word 'raster' originates from the Latin word ____, meaning a rake.
42.Fill in the blank.
Easy
The number of bits used to represent each pixel in a bitmap image is called the ____.
43.How many distinct colors can be represented with 8 bits per pixel?
Medium
44.What is the main advantage of using raster graphics for photographs compared to vector graphics?
Medium
45.A bitmap image is 10 pixels wide and 10 pixels high, with a color depth of 4 bits per pixel. How many bits are needed to store the image without compression?
Hard
46.A 24-bit bitmap image has a resolution of 1920 × 1080 pixels. Calculate the uncompressed file size in bytes.
Challenge
47.An image has a resolution of 800 pixels wide and 600 pixels high, with a color depth of 16 bits per pixel. How many bits are needed to store this image without compression?
Medium
48.What is the term for the process of converting a raster image to a vector image?
Medium
49.A bitmap image has a resolution of 100 pixels wide and 100 pixels high, and uses 8-bit color depth. Calculate the uncompressed file size in bytes.
Medium
50.Complete the sentence:
Medium
A bitmap image with a color depth of ____ bits per pixel can display 16,777,216 distinct colors.
51.A bitmap image has a resolution of 200 pixels wide and 150 pixels high, with a color depth of 16 bits per pixel. What is the uncompressed file size in bytes?
Hard
52.A bitmap image is 20 pixels wide and 15 pixels high. How many pixels does it contain in total?
Easy
53.Explain why increasing the color depth of an image from 8-bit to 24-bit increases the file size, and give an example calculation.
Hard
54.Explain why increasing the resolution of a bitmap image from 100x100 to 200x200 will increase the file size, and calculate the factor by which the number of pixels increases.
Hard
55.Explain why a photograph stored as a bitmap with a color depth of 24 bits and high resolution will have a much larger file size than a simple line drawing stored with the same resolution but a color depth of 1 bit. Use calculations to support your answer.
Hard
56.Explain why increasing the resolution of a bitmap image from 100×100 to 200×200 will increase the file size, and calculate the factor by which the number of pixels increases.
Hard
57.Explain why run-length encoding (RLE) can be up to twice the size of the original file for a photograph, but very efficient for a line drawing.
Medium
58.How many distinct colors can be represented with 8 bits per pixel?
Medium
- A256 colors
- B308 colors
- C230 colors
- D282 colors
59.A bitmap image is 10 pixels wide and 10 pixels high, with a color depth of 4 bits per pixel. How many bits are needed to store the image without compression?
Hard
- A480 bits
- B400 bits
- C360 bits
- D440 bits
60.A 24-bit bitmap image has a resolution of 1920 × 1080 pixels. Calculate the uncompressed file size in bytes.
Challenge
- A6220800 bytes
- B6842880 bytes
- C7464960 bytes
- D5598720 bytes
61.An image has a resolution of 800 pixels wide and 600 pixels high, with a color depth of 16 bits per pixel. How many bits are needed to store this image without compression?
Medium
- A9216000 bits
- B8448000 bits
- C6912000 bits
- D7680000 bits
62.A bitmap image has a resolution of 200 pixels wide and 150 pixels high, with a color depth of 16 bits per pixel. What is the uncompressed file size in bytes?
Hard
- A72000 bytes
- B66000 bytes
- C60000 bytes
- D54000 bytes
63.A bitmap image is 20 pixels wide and 15 pixels high. How many pixels does it contain in total?
Easy
- A300 pixels
- B270 pixels
- C330 pixels
- D360 pixels

복습 노트

## Representing Images: Pixels and Bitmaps ### Key Idea A **bitmap** (or **raster**) image is a rectangular grid of tiny colored squares called **pixels** (picture elements). Each pixel stores a single color value. Unlike vector graphics (which use mathematical formulas), bitmaps store the exact color of every pixel, making them ideal for photos and complex images. ### Resolution - **Resolution** = width × height in pixels (e.g., 1920×1080). - Higher resolution = more pixels = more detail, but larger file size. - Resolution is constant across the grid (each pixel is the same size). ### Colour Depth - **Colour depth** = number of bits used per pixel. - More bits per pixel = more possible colours. - Formula: **Number of colours = 2^bits per pixel**. - Common depths: - 1-bit: 2 colours (black & white) - 8-bit: 256 colours - 24-bit: 16,777,216 colours (true colour, 8 bits per RGB channel) ### Estimating File Size - **File size (bits)** = width × height × colour depth (bits per pixel). - Convert to bytes: divide by 8. - Example: 100×100 image, 24-bit colour → 100×100×24 = 240,000 bits = 30,000 bytes. ### Effects of Changing Depth and Resolution - Increasing resolution or colour depth **increases file size** and quality. - Decreasing them reduces file size but may cause visible pixelation or colour banding. - Trade-off: quality vs. storage space. ### Storage and Compression - Bitmaps are stored in formats like GIF, JPEG, PNG. - Compression reduces file size: - **Lossless** (e.g., RLE, PNG): original pixels can be perfectly restored. - **Lossy** (e.g., JPEG): some detail is lost, but file is much smaller. - RLE replaces repeated values (e.g., `AAAA` → `4A`), efficient for simple images but poor for photos. ### Quick Facts - The word "raster" comes from Latin *rastrum* (a rake), from CRT monitors drawing lines. - A bitmap file needs a header with width, height, and pixel format to reconstruct the image. --- ## Key Terms - **Bitmap/Raster**: An image made of a grid of pixels. - **Pixel**: The smallest unit of a bitmap image, a single coloured square. - **Resolution**: The number of pixels in an image (width × height). - **Colour Depth**: The number of bits used to represent the colour of each pixel. - **File Size**: The amount of storage an image takes, calculated as width × height × colour depth. - **Lossless Compression**: Reduces file size without losing any pixel data. - **Lossy Compression**: Reduces file size by discarding some data, causing quality loss. - **RLE (Run-Length Encoding)**: A lossless compression method that replaces repeated values with a count.

Bitmap: A digital image made up of a rectangular grid of pixels, each storing a colour value.
Pixel: The smallest unit of a bitmap image; a tiny square with a single colour.
Resolution: The dimensions of an image in pixels (width × height), determining detail.
Colour Depth: The number of bits used per pixel to represent colour; determines the number of possible colours (2^bits).
File Size: The amount of storage an image requires, estimated as width × height × colour depth (in bits), then divided by 8 for bytes.
Lossless Compression: Compression that reduces file size without losing any pixel data, allowing perfect reconstruction (e.g., RLE, PNG).
Lossy Compression: Compression that reduces file size by approximating pixel data, causing some quality loss (e.g., JPEG).
RLE (Run-Length Encoding): A lossless compression method that replaces repeated pixel values with a count and value, efficient for simple images.

플래시카드

What is a bitmap image?

A bitmap image is a digital image made up of a rectangular grid of tiny colored squares called pixels. Each pixel stores the exact color value.

What is a pixel?

A pixel (short for 'picture element') is the smallest unit of a bitmap image, a tiny square that has a single color.

How do bitmap images differ from vector graphics?

Bitmap images store the exact color of each pixel, while vector graphics use mathematical formulas to describe shapes and lines. Bitmaps are ideal for photographs and complex images.

What are the two main characteristics of a raster image?

The two main characteristics are dimensions (width and height in pixels) and color depth (the number of bits per pixel).

What is color depth?

Color depth is the number of bits used to represent the color of each pixel. It determines how many distinct colors an image can have.

How many colors can be represented with 24-bit color depth?

24-bit color depth can represent over 16 million distinct colors (2²⁴ = 16,777,216).

In 24-bit color, how many bits are used for each of the red, green, and blue channels?

8 bits are used for each channel, giving values from 0 to 255 for red, green, and blue.

What is resolution in a bitmap image?

Resolution refers to the number of pixels in the image, typically given as width × height. It can also refer to the size of each pixel (support).

How does increasing color depth affect file size?

Increasing color depth increases the number of bits per pixel, so the file size increases proportionally.

How does increasing resolution affect file size?

Increasing resolution increases the total number of pixels, which increases the file size.

How do you estimate the file size of an uncompressed bitmap image?

Multiply the width by the height to get the total number of pixels, then multiply by the number of bits per pixel (color depth), and divide by 8 to get bytes.

What is the origin of the word 'raster'?

The word 'raster' comes from the Latin 'rastrum' (a rake), derived from 'radere' (to scrape). It originated from the raster scan of CRT monitors.

What is a common pixel format for full-color images?

Full-color images typically use 24 bits per pixel, with 8 bits for each of red, green, and blue channels.

What is a binary pixel format?

A binary pixel format uses 1 bit per pixel, so each pixel is either black or white.

What is a grayscale pixel format?

A grayscale pixel format uses multiple bits per pixel to represent shades of gray, typically 8 bits giving 256 shades.

What is a palettized pixel format?

A palettized image uses a color lookup table (palette) where each pixel value is an index into the table, allowing a limited number of colors.

What is row-major order in storing bitmap data?

Row-major order stores the pixels row by row, listing the cells of the top row left to right, then the second row, and so on.

What information must a bitmap file header contain?

The header must contain at least the number of columns (width) and the pixel datatype (bits per pixel) so the reader knows where each value ends.

What is run-length encoding (RLE)?

RLE is a lossless compression method that replaces repeated values with the value and the number of times it appears. It works well for images with large areas of identical colors.

What is lossless compression?

Lossless compression allows the original pixel values to be perfectly regenerated from the compressed data. Examples include RLE and LZW.

What is lossy compression?

Lossy compression approximates the original pixel values, so the decompressed image is not exactly the same. JPEG is a common lossy format.

Why are photographs usually stored as raster images?

Photographs have complex colors and details that are best represented by storing the exact color of each pixel, which is what raster images do.

What is a common raster file format used on the web?

Common raster formats include GIF, JPEG, and PNG.

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