Perspective Measurement

A Perspective Measurement is a quantified result obtained from, through, or in relation to a perspective view, image, representation, model or spatial reality. As a Perspective Product, measurement converts a perspective relationship into values that may describe size, distance, position, angle, scale, proportion or another measurable spatial property.

Perspective measurement is not simply the measurement of marks on an image. To relate image measurements back to spatial reality, the relevant projection, viewpoint, scale, resolution and other measurement conditions must also be understood.

Measurement as a Perspective Product

The Product level asks what a perspective process produces. In many graphical, mathematical, optical and instrument systems, one such product is a measurement.

The measurement may be read directly from a calibrated representation, derived geometrically from a perspective construction, obtained through an imaging instrument, or calculated from relationships encoded within one or more perspective images.

Image-Space and Object-Space Measurement

It is useful to distinguish between measurements made in Image Space and corresponding dimensions in Object Space.

Image-space measurement concerns a measurable length, angle, position, area or other quantity within an image or representation.
Object-space measurement concerns the corresponding physical or modelled property of the represented spatial object or scene.

The relationship between the two depends upon the perspective system. A measurement made directly on an image cannot automatically be treated as the true physical measurement of the represented object.

Measurement and Scale

Scale establishes an important relationship between measurements in a representation and corresponding measurements in spatial reality.

In a uniformly scaled plan, elevation or orthographic representation, a single stated ratio may apply throughout the drawing. For example, a scale of 1:100 means that one unit in the representation corresponds to one hundred of the same units in Object Space.

Ordinary central-perspective images are different. Their projected scale normally changes with depth and position, so one universal image-to-object scale cannot usually be applied across the entire represented scene.

Local Scale in Perspective

In central projection, objects at different depths normally have different local image-to-object scale ratios. Objects of equal physical size generally appear progressively smaller as distance from the centre of projection increases, provided that orientation and other projection conditions remain comparable.

Accurate measurement from a perspective image may therefore require knowledge of depth, projection geometry, reference dimensions, measuring points or other calibration information.

Measuring Points and Perspective Construction

Traditional graphical perspective includes geometrical procedures specifically developed for measurement. Measuring points, distance points, proportional constructions and receding scales allow dimensions to be transferred or constructed through perspective space.

These methods show that perspective can be used not only to produce a spatially convincing image, but also to establish controlled geometrical relationships between Object-Space dimensions and their projected representation.

Measurement Scale and Resolution

A measurement also depends upon the scale and resolution at which something is observed or recorded. Increasing optical magnification or image resolution may reveal previously unresolved structural detail and therefore make finer measurements possible.

This does not mean that the physical object itself has changed. It means that the perspective or imaging system has made additional measurable structure available.

Conversely, digital enlargement alone cannot recover genuine structural information that was never recorded by the original imaging system.

The Scale–Shape–Size Problem

Perspective measurement is closely connected with the Scale–Shape–Size Problem. Apparent or measured size can be affected by viewpoint, foreshortening, visible shape, projection geometry, scale, resolution and measurement method.

For irregular or highly detailed forms, the measured result may also vary according to the measuring interval or sampling unit. A complex object therefore need not possess one simple scale-independent measured outline when observed at radically different scales or resolutions.

Measurement should consequently be understood as a result produced under specified conditions rather than as a number entirely independent of the perspective process through which it was obtained.

Measurement from Multiple Views

A single perspective image may not contain enough information to recover every spatial dimension uniquely. Multiple views can provide additional directional and positional relationships and may allow more complete measurement or reconstruction of a spatial object or scene.

This principle is used in many technical imaging, photogrammetric and computer-vision processes in which measurements are derived by comparing corresponding information across two or more images or viewpoints.

Measurement, Calculation and Data

Measurement, Calculation and Data / Information are related Perspective Products, but they describe different results.

Measurement gives a quantified value or relationship.
Calculation applies mathematical or geometrical operations to known or derived quantities.
Data / Information is the broader information obtained, organised or inferred from a perspective image, view, model or measurement.

A technical perspective process may produce all three. An image may first be measured, the measurements may then be used in calculations, and the resulting values may become information about spatial reality.

Examples of Perspective Measurement

measuring a projected dimension in a perspective construction;
determining image scale or magnification;
estimating distance from an image or optical view;
measuring angles or directions within a calibrated image;
deriving object dimensions from photographs;
comparing corresponding positions in stereoscopic images;
measuring spatial relationships in a CAD or computer model;
using scale bars or reference objects to relate image dimensions to Object Space;
measuring changes in position, size or form through a sequence of images.

Measurement Within the Analytical System

Within the PRC analytical framework, Measurement is treated here at the Product level because it is a result obtained through a perspective process.

The process that produces the measurement can simultaneously be classified according to Category, Class and Type; the image or representation being measured may possess a particular Form and Phenomena; and measurement itself may serve one or more Perspective Functions.

The Product question is: what has the process produced? In this case, a measurable or quantified spatial result.