Introduction to Image Pixels and Resolution

Questions and Answers

What is the correct representation of a color in floating-point format for RGB?

c ∈ R3[0,1] (correct)

c ∈ Z3[0,255]

c ∈ Z4[0,255]

c ∈ R4[0,1]

Which of the following statements about fixed-point representation is true?

RGB and RGBA use the same representation

RGBA values are represented as c ∈ Z3[0,255]

RGBA values are represented as c ∈ Z4[0,255] (correct)

RGB values are represented as c ∈ R3[0,1]

What is the main purpose of RGB color spaces?

To represent colors in a binary format

To represent colors in the invisible spectrum

To display only grayscale images

To process images using trichromacy (correct)

Hyper-spectral imaging allows for which of the following?

Obtaining data across multiple wavelengths Signup and view all the answers

How is an image conceptually represented as a collection of pixels?

As a rectangular grid of height H and width W Signup and view all the answers

Which of the following best describes 'color spaces'?

They define how colors are numerically represented. Signup and view all the answers

Which color representation is used when working with 8-bit fixed-point representation for RGB?

c ∈ Z3[0,255] Signup and view all the answers

Which of the following represents the relationship between color perception and light?

Color perception is determined by light absorption and reflection. Signup and view all the answers

How is a grayscale image with resolution H × W with floating-point representation described mathematically?

x ∈ R[0,255]1×H×W Signup and view all the answers

What is the correct mathematical representation of a grayscale image with 8-bit fixed-point representation?

x ∈ Z[0,255]1×H×W Signup and view all the answers

For a grayscale image represented with a 16-bit fixed-point representation, which of these is true?

x ∈ Z[0,65535]1×H×W Signup and view all the answers

Which option correctly describes an RGB image mathematically?

x ∈ Z[0,255]3×H×W Signup and view all the answers

What is implied by the term 'color table' in image storage?

It stores an index for colors rather than full color information. Signup and view all the answers

For an uncompressed FHD RGB image resolution, what is the minimum size in bytes, excluding header?

8,294,400 Signup and view all the answers

What is the minimum size in bytes for storing an uncompressed RGBA image at FHD resolution, excluding header?

4,194,304 Signup and view all the answers

In hyper-spectral imaging, how is the representation of image channels typically characterized?

x ∈ ZN×H×W for N channels Signup and view all the answers

What is the representation of an RGB image with resolution H × W?

x ∈ R3×H×W [0,1] Signup and view all the answers

Which of the following best describes a hyper-spectral image?

An image that may contain many channels, capturing more frequencies Signup and view all the answers

What is the most commonly used fixed-point representation for images?

8-bit per channel Signup and view all the answers

How are the channels of a color image typically denoted?

R, G, B, A Signup and view all the answers

In floating-point representation, which bit depth is least likely to be used for color channels?

8-bit Signup and view all the answers

What is the structure of an image with resolution H × W and C channels in floating-point format?

x ∈ RC×H×W Signup and view all the answers

Which of the following statements about pixel representation is true?

A pixel is the smallest unit of area and contains uniform color Signup and view all the answers

What differentiates RGBA images from RGB images?

RGBA images include an additional Alpha channel Signup and view all the answers

Study Notes

Image Representation Fundamentals

A pixel is the smallest unit of an image, displaying a uniform color.
Resolution of an image is denoted as H × W, representing height (H) and width (W).
An image is viewed as a bounded two-dimensional space limited on all sides.

Camera Sensor Functionality

Optical camera sensors capture colored signals through their shutter.
Sensors convert incoming signals into energy/intensity for each red, green, and blue (RGB) wavelength.
Signals are continuous in space but are sampled discretely to create images.

Image Channels

Each channel (e.g., R, G, B, A) represents a different color component.
An RGB image consists of three channels, while an RGBA image contains four channels.
Hyper-spectral images can capture more than three channels, incorporating ultra- and infra-optical spectra.

Image Representation in Different Formats

Floating-Point Representation: Represents colors in 16-bit, 32-bit, or 64-bit precision.
- RGB image is expressed as x ∈ R³×H×W [0,1].
- RGBA image is expressed as x ∈ R⁴×H×W [0,1].
8-Bit Fixed-Point Representation: Generally uses 8-bit per channel.
- RGB image is expressed as x ∈ Z₃×H×W [0,255].
- RGBA image is expressed as x ∈ Z₄×H×W [0,255].

Grayscale Image Representation

A grayscale image with floating-point representation can be described as x ∈ R¹×H×W [0,1].
For 8-bit fixed-point representation, it is described as x ∈ Z¹×H×W [0,255].
In 16-bit fixed-point representation, it is described as x ∈ Z¹×H×W [0,65535].

Storage Requirements for Uncompressed Images

Minimum size for storing FHD resolution RGB image (1920×1080):
- Size = H × W × 3 bytes + H bytes (for header).
Minimum size for storing FHD resolution RGBA image:
- Size = H × W × 4 bytes + H bytes (for header).

Color Theory Overview

Color is the visual perception linked to the electromagnetic spectrum and varies based on object light absorption and reflection characteristics.

RGB Color Model

Human perception of color involves trichromacy, utilizing three types of cone cells sensitive to different light wavelengths.
Common RGB representation includes a 3-vector in machine format:
- Color in floating-point: c ∈ R³ [0,1].
- Color in 8-bit fixed-point: c ∈ Z³ [0,255].

Image Composition

An image can be conceptually divided into a rectangular grid composed of individual pixels.
Each pixel in the grid corresponds to a specific visual component of the overall image.

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Description

This quiz covers the basic concepts of pixels, their role as the smallest unit in an image, and how resolution is determined by height and width. Additionally, it explores how optical camera sensors capture and register colored signals. Test your understanding of these fundamental concepts in digital imaging.