Resolution and Aspect Ratio | Sahithyan's Notes

\text{visible image} = f(\text{resolution}, \text{size}, \text{aspect ratio})

Resolution
Dots per unit length.
Image size
Number of dots, or pixels, in the image.
Aspect ratio
Ratio of rows to columns in the pixel grid.
Pixel aspect ratio
Exact shape ( $\Delta x : \Delta y$ ) of a single pixel.

Physical dimensions of the image follow from these, with $R$ defined along the vertical axis so the vertical dot pitch is $1/R$ and the horizontal dot pitch is $\frac{\Delta x}{\Delta y} \cdot \frac{1}{R}$ .

\text{width} = N_c \cdot \frac{\Delta x}{\Delta y} \cdot \frac{1}{R}

\text{height} = \frac{N_r}{R}

Here:

$R$: resolution in dots per unit length
$N_c$: number of columns
$N_r$: number of rows
$\Delta x : \Delta y$: pixel aspect ratio

For square pixels $\Delta x = \Delta y$ , so $\text{width} = N_c / R$ .

Changing Geometry

Changing resolution affects image granularity, potentially causing a checkerboard effect when upscaling
Changing pixel count affects file size
Changing physical pixel size or aspect ratio affects object geometry, potentially causing distortion

Stretching versus cropping to change aspect ratio — Left: Original. Centre: Stretched to a wider frame, distorting object geometry. Right: Cropped to the same frame, keeping geometry but losing content.
Generated from a photo by Hannes Röst, CC BY-SA 3.0.

Worked Example

Physical Image Size

An image has $N_c = 1200$ , $N_r = 800$ , $R = 100\text{ dots/in}$ and square pixels. Find its physical dimensions.

Solution Reveal Hide

\text{width} = \frac{1200}{100} = 12\text{ in}

\text{height} = \frac{800}{100} = 8\text{ in}

The image is $12\text{ in} \times 8\text{ in}$ .