Measurement Function

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Measurement Function concerns the use of perspective relationships to determine, compare or derive quantitative and spatial information about objects, scenes, views and images.

Perspective is therefore not only concerned with how spatial reality appears. It can also provide systematic information concerning size, scale, distance, position, angle, orientation, proportion and other relationships within spatial reality.

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Measurement as a Perspective Function

A perspective process performs a measurement function when information contained in a view, image, projection or spatial relationship is used to establish or compare quantities, dimensions, scales or positions.

Measurement may be visual, graphical, geometrical, optical, mathematical, instrument-based or computational.

The important point is that measurement is an operation performed by the perspective system, rather than merely an appearance contained within an image.

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Principal Measurement Operations

Within the PRC Functions of Perspective map, the Measurement Function includes five principal operations:

• Delineate — establish or define spatial boundaries, dimensions or relationships;
• Map scales — relate quantities or positions to an ordered spatial scale;
• Index or gauge — register, indicate or compare a spatial property;
• Calculate — derive values or relationships mathematically; and
• Establish Perspective Phenomena — determine the presence, amount or behaviour of a perspective effect.

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What Perspective Can Measure

Depending on the method or system, perspective may assist in determining or comparing:

• size;
• shape;
• scale;
• distance;
• position;
• angle;
• orientation;
• proportion;
• relative location;
• depth;
• change through time; and
• other quantitative or spatial relationships.

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Measurement from Perspective Images

A perspective image can contain information from which properties of a spatial object or scene may be estimated, compared or calculated.

This principle is fundamental to activities such as surveying, photogrammetry, mapping, architectural documentation, scientific imaging, remote sensing and computer vision.

The image therefore functions not only as a representation but also as a potential source of spatial data.

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Measurement and Scale

Scale is particularly important because perspective repeatedly relates apparent or represented dimensions to spatial dimensions.

A measuring system may establish a known scale, derive one from reference information or compare different quantities within a common spatial framework.

Perspective measurement can therefore connect an image-space quantity with a corresponding relationship in object or spatial reality.

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Indexing and Gauging

Measurement does not always require the production of a conventional numerical dimension.

A perspective system may index or gauge a spatial property by indicating its relative state, extent or position on a scale.

This can include comparison against calibrated marks, reference dimensions, known objects, graphical scales, optical indicators or computationally derived values.

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Calculation

Calculation extends the Measurement Function by deriving information that may not be immediately visible in the original image or view.

Geometrical, mathematical or computational relationships may be used to infer dimensions, positions, angles, scales, distances or other spatial properties.

This distinguishes calculation as an operation within the measurement process while allowing the resulting calculation itself to be treated separately as a Perspective Product.

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Measuring Perspective Phenomena

Perspective Phenomena can themselves be objects of measurement.

A system may quantify or compare apparent changes of size, shape, position, angle, clarity, colour, convergence, foreshortening, depth or other viewpoint-dependent effects.

Measurement therefore provides one route from simply noticing a phenomenon to establishing its extent, pattern or relationship to spatial reality.

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Measurement and the Two Perspective Classes

Measurement may operate through the Viewing or Imaging Class, the Projecting Class, or through a system combining both.

An imaging system may capture spatial information that is subsequently measured. A projecting system may use measured or calculated relationships to place, align or construct a projected image or spatial pattern.

Class therefore identifies the direction of the perspective process, while Measurement identifies what that process is being used to do.

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Measurement and Matching

Measurement belongs principally beneath the broad Match family because measured information enables images, views and spatial forms to be compared with standards, scales, known objects or one another.

Measurement can therefore support surveying, classification, identification, cross-matching, modelling and verification.

The Measurement and Classification Functions are closely related but distinct: measurement establishes or compares quantities and spatial relationships, whereas classification identifies, groups or orders what those relationships signify.

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Measurement Function and Measurement Product

The Measurement Function should be distinguished from the Perspective Measurement product.

The Function describes the operation by which a perspective system determines or compares a spatial quantity or relationship.

The Product is the resulting measurement itself.

In simplified form:

Measurement Function → measured value or relationship → Perspective Measurement Product

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Measurement Within the Analytical System

Measurement belongs to the Function level of the seven-part analytical system:

• Category — principal source or mode;
• Class — fundamental direction;
• Type — method, system or process;
• Form — resulting appearance;
• Phenomenon — visible or detectable effect;
• Function — what the process does; and
• Product — what the process produces.

Measurement is therefore not itself a Perspective Category, Class or Type. It is an operation that may be performed by many different perspective systems and may lead to several different Products.

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Related Perspective Topics

Functions of Perspective →
Matching — Goal of Perspective →
Capture / Project Function →
Observation Function →
Perspective Measurement Product →
Perspective Calculation →
Perspective Process →
Perspective Phenomena →
Perspective Product →