Image Memory Layout

Storing Images in Memory

A 2D image array must be stored in linear (1D) memory. The mapping from 2D coordinates to 1D memory index uses strides.

Row-Major vs Column-Major Order

Row-Major Order (Most Common)

Elements in the same row are stored contiguously: $i(x, y) = x + y \cdot n_{\text{cols}}$

Column-Major Order

Elements in the same column are stored contiguously: $i(x, y) = x \cdot n_{\text{rows}} + y$

Interleaved Colour Storage

For colour images with 3 channels (RGB), interleaved row-major: $i(x, y, c) = x \cdot 3 + y \cdot 3 \cdot n_{\text{cols}} + c$

where $c \in \{0, 1, 2\}$ for the R, G, B channels.

General Stride Formula

The most general formula for any memory layout: $i(x, y, c) = i_{\text{start}} + x \cdot s_x + y \cdot s_y + c \cdot s_c$

where:

• $i_{\text{start}}$ is the starting offset
• $s_x$, $s_y$, $s_c$ are the strides for each dimension

Common Stride Configurations

Layout	$s_x$	$s_y$	$s_c$
Row-major, grayscale	1	$n$	-
Column-major, grayscale	$m$	1	-
Row-major, interleaved RGB	3	$3n$	1
Row-major, planar RGB	1	$n$	$nm$

Padded Images

Sometimes images are padded with extra pixels for operations that need neighbourhood access (e.g., convolution).

The stride $s_y$ is larger than the image width to account for padding.

Regions of Interest (ROI)

A region of interest is a rectangular subset of an image. An ROI borrows the parent’s data array without copying:

• $i_{\text{start}}$ = offset to ROI origin
• Strides are inherited from parent

Summary

• Row-major order stores rows contiguously; column-major stores columns contiguously
• Strides define the step size for each dimension
• Interleaved RGB alternates channels; planar separates them
• ROIs share parent memory without copying

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Past Paper Questions

2023 Paper 3 Question 4: Design an ExImage class that supports ROIs. What constructor parameters are needed?