Fundamentals of Digital Image Representation

Resolution refers to the total number of pixels existing within an image, specifically the count of pixels arranged vertically and horizontally. For example, a resolution of $1920 \times 1080$ means there are 1,920 pixels across and 1,080 pixels down.

Pixel Density is a different measurement, expressed in Pixels Per Inch (PPI). While resolution tells you how many pixels are in the file, pixel density tells you how many of those pixels are packed into a specific physical space, such as a smartphone screen or a printed poster.

Exam Tip: Remember that resolution is about the total pixel count in the digital file, whereas pixel density is about how those pixels are distributed over a physical area.

Raster vs. Vector Graphics

Digital images generally fall into two major categories: Raster and Vector.

Raster Graphics (Bitmaps)

Raster graphics, also known as bitmaps, construct images using a grid of pixels. Because they rely on a fixed number of pixels, raster images have limited scalability. If you attempt to enlarge a raster image significantly, it will lose quality and become "pixelated" or blurry. Common file types include JPEG, PNG, GIF, BMP, and TIFF. These are best suited for photographs and detailed digital paintings.

Vector Graphics

Vector graphics use mathematical geometric elements—such as points, lines, curves, circles, and polygons—to create pictures. Because they are based on mathematical formulas rather than a fixed grid of dots, they possess infinite scalability. You can make a vector image infinitely large or small without any loss in quality. Common file types include SVG, EPS, and PDF. Vectors are the ideal choice for logos, icons, and text graphics.

Calculating File Size

Understanding how to calculate the size of a bitmap image is essential for managing digital storage. The file size of a bitmap is determined by its resolution and its bit rate (bit depth).

The general formula is: $\text{File Size} = \text{Resolution} \cdot \text{Bit Rate}$

Worked Examples

Example 1: Basic Bit Calculation Suppose you have an image that is $5 \times 8$ pixels. If each pixel is equivalent to $1$ bit, what is the file size in bits?

Using the formula:

\text{File Size} &= (5 \cdot 8) \cdot 1 \\ &= 40 \text{ bits} \end{aligned}$$ **Example 2: Calculating Bytes** Suppose you have an image that is $7 \times 8$ pixels, and each pixel is equivalent to $3$ bits. What is the file size in bits and in bytes? First, find the size in bits: $$\begin{aligned} \text{File Size (bits)} &= (7 \cdot 8) \cdot 3 \\ &= 56 \cdot 3 \\ &= 168 \text{ bits} \end{aligned}$$ Next, convert bits to bytes (knowing that $8 \text{ bits} = 1 \text{ byte}$): $$\begin{aligned} \text{File Size (bytes)} &= \frac{168}{8} \\ &= 21 \text{ bytes} \end{aligned}$$ $$$ $$$