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Perspective
A Perspective Product is an outcome produced by a perspective process. Perspective does not produce only pictures: depending upon the process and its purpose, it may produce a view, image, representation, model, measurement, calculation, data or other spatial information.
The Product level therefore asks a different question from the other analytical levels: what has the perspective process produced?
Perspective Products
The principal representative products shown in the diagram are:
- Perspective View — an appearance of an object or scene from a particular viewpoint.
- Perspective Image — a visual result formed, captured, projected, displayed or generated through a perspective process.
- Perspective Representation — a depiction or representational pattern corresponding to some aspect of spatial reality.
- Perspective Model — a structured physical, graphical, mathematical or computational representation of a spatial object, scene or perspective system.
- Perspective Measurement — a quantified result obtained from or through a perspective relationship.
- Perspective Calculation — a mathematical or geometrical result derived through a perspective process.
- Perspective Data / Information — information obtained from a perspective image, view, measurement, calculation, representation or model in relation to spatial reality.
These are representative rather than exhaustive. A single perspective process may produce several of them simultaneously.
A Process Can Produce More Than One Product
The Product categories should not be treated as mutually exclusive. A photograph, for example, may simultaneously be an Image, a View and a Representation. If it is calibrated, it may also support Measurement, Calculation and the extraction of Data / Information.
Likewise, a computer model can be a Product in its own right while also generating many different images, views, measurements and calculations.
Visible Products and Information Products
Some Perspective Products are directly visible or representational, such as a View, Image, Representation or Model. Others may be derived from them, such as a Measurement, Calculation or item of Data / Information.
This distinction is useful, but it is not an absolute division. A model may contain measured data; a graphical representation may itself embody a calculation; and an image may be both a visual product and the source of further information.
Perspective Data
The Perspective Product framework also includes information derived from a perspective image and its relationship to spatial reality. Three useful kinds are:
- Subsumptive Data — whole and part relationships;
- Ordinal Data — figure, shape, size, scale and position;
- Determinative Data — state or activity.
Perspective images and views may additionally provide information concerning location, orientation, focus, arrangement, texture, colour, depth and other spatial or visible properties.
Product Is Not the Same as Function
Function and Product answer different questions.
- Function asks: what does the perspective process do?
- Product asks: what does the perspective process produce?
A process may perform a measuring Function and produce a Measurement; it may perform a modelling Function and produce a Model; or it may perform an imaging Function and produce an Image. The relationship is often close, but the analytical distinction remains useful.
Products Across Perspective Categories
Perspective Products can arise through many different Category modes. A graphical process may produce a drawing or representation; a mathematical process may produce a calculation; an instrument system may produce an image or measurement; and a New Media system may produce an interactive model, simulated view or structured data.
A single Product can therefore arise through more than one Category, and one perspective process can itself involve several Category modes.
Product Within the Analytical System
Product is the seventh of the seven principal analytical levels used to organise perspective:
Category · Class · Type · Form · Phenomenon · Function · Product
These levels describe different aspects of the same perspective process. Category concerns its principal source or mode; Class its fundamental direction; Type the system, method or process; Form the resulting appearance; Phenomenon the visible effect; Function what the process does; and Product what it produces.
The analytical levels are therefore complementary rather than competing classifications.
Explore the Product Pages
- Perspective View
- Perspective Image
- Perspective Representation
- Perspective Model
- Perspective Measurement
- Perspective Calculation
- Perspective Data / Information
Related Perspective Topics
- Perspective Category
- Perspective Class
- Perspective Type
- Perspective Form
- Perspective Phenomena
- Functions of Perspective
- Perspective Process
- Abridged Dictionary of Perspective
A Perspective Product is the outcome produced by a perspective process.
A Perspective Product may take the form of a detailed visual image, view, measurement, calculation, representation, model or spatial appearance. It may also consist of structured information obtained from a perspective image or view and related back to spatial reality.
Within Perspective Category Theory (PCT), the distinction between process and product is fundamental:
Perspective Process → operation
Perspective Product → resulting outcome
The product is therefore what perspective ultimately produces, communicates or makes available for observation, measurement, analysis or use.
Perspective Product within Perspective Category Theory
Perspective Category Theory distinguishes the Perspective Product from the Category, Class, Type, Form, Method, Process, Function and Goal of Perspective.
- Perspective Category — the principal source or mode of a perspective process;
- Perspective Class — the principal direction in which the process operates;
- Perspective Type — a particular method, system, process or subdivision;
- Perspective Form — the visual, optical, geometrical or spatial appearance produced;
- Perspective Method — the organised procedure or means employed;
- Perspective Process — the operation performed;
- Perspective Function or Goal — what the operation is intended to achieve;
- Perspective Product or Outcome — what results from the process.
The same perspective system can therefore be analysed at several different levels without confusing the process with its result.
Principal Products of Perspective
The principal products of perspective include:
- visual images;
- views;
- measurements;
- calculations;
- representations;
- models; and
- spatial appearances.
Perspective therefore produces much more than pictures.
A perspective system can provide visual information, quantitative measurements, geometrical relationships, models of spatial reality or live views of objects and scenes.
The appropriate Perspective Product depends upon the goals, methods and processes of the particular system.
The Perspective Image as a Product
A Perspective Image is one of the most familiar Perspective Products.
It may be produced through:
- drawing;
- painting;
- photography;
- optical imaging;
- scientific instrumentation;
- cinema;
- computer graphics;
- digital imaging; or
- other visual and technical processes.
The image contains or presents information about a spatial object, scene or represented spatial reality.
Depending upon the perspective process, it may preserve, transform, reduce, distort or selectively represent the properties of the original Object or Target Space.
Perspective Image and Perspective View
A Perspective Image and a Perspective View are related products but should be distinguished.
A Perspective Image is a fixed visual representation, copy or picture of a spatial object or scene.
A Perspective View is the act or condition of looking directly at a spatial object, scene or apparent spatial reality—a live or real-time visual relationship.
A view may be:
- seen directly by the eye;
- captured in real time by a camera or perspective instrument; or
- presented or projected through a screen or display system.
Thus:
Perspective Image → fixed or recorded visual product
Perspective View → live or real-time visual product
Both can serve as products of perspective, but their temporal and representational relationships differ.
Measurement as a Perspective Product
A perspective system may produce a measurement rather than—or in addition to—a conventional image.
Perspective measurements can concern:
- size;
- shape;
- scale;
- position;
- distance;
- orientation;
- spatial arrangement; or
- other measurable properties of objects and scenes.
Surveying, photogrammetry, calibrated imaging and other technical perspective systems can therefore produce numerical or spatial information as their principal product.
The image may function as an intermediate means through which the final measurement is obtained.
Calculation as a Perspective Product
Calculation is another Perspective Product.
Mathematical Perspective can transform spatial relationships into calculated quantities, coordinates, geometrical relationships or projected positions.
The final product may therefore be:
- a calculated point position;
- a projected line or plane;
- a scale relationship;
- a geometrical transformation;
- a spatial coordinate;
- a projection matrix; or
- another mathematically derived spatial relation.
Such products may subsequently be used to construct an image, guide an instrument, produce a model or analyse spatial reality.
Representation as a Perspective Product
A representation is a Perspective Product that presents, records, describes or models some aspect of spatial reality.
Representations may include:
- drawings;
- paintings;
- photographs;
- diagrams;
- maps;
- technical drawings;
- computer-generated images;
- scientific visualisations; and
- other visual models.
A representation need not reproduce every property of its target. It may select, simplify, measure, transform or emphasise particular spatial relationships according to its intended function.
Model as a Perspective Product
A model is another important Perspective Product.
A perspective model may describe or reconstruct the spatial relationships of an object, scene or environment.
Models may be:
- graphical;
- geometrical;
- mathematical;
- physical;
- digital; or
- computational.
A model can be used to explore spatial relationships, compare alternatives, generate new viewpoints or represent a spatial reality that does not yet physically exist.
Perspective therefore provides not only images of existing reality but also models through which spatial possibilities can be examined.
Spatial Appearance as a Product
The resulting spatial appearance may itself constitute a Perspective Product.
A perspective process can alter or organise the apparent:
- size;
- shape;
- position;
- orientation;
- depth;
- scale;
- clarity;
- colour;
- contrast; or
- spatial organisation of objects and scenes.
In Simulated Perspective, for example, the principal product may be a deliberately altered spatial appearance or illusion rather than a separately recorded image.
In immersive systems, the resulting experienced spatial environment may similarly be an important product of the perspective process.
Perspective Products as Information
A Perspective Product can also be understood as information obtained about spatial reality.
Volume 1 identifies perspective products as including information concerning:
- object or scene location;
- size and shape;
- orientation;
- focus;
- arrangement;
- texture; and
- colour.
Perspective therefore converts spatial objects, scenes and processes into information that can be viewed, compared, measured, classified, represented or analysed.
The visible image is often the medium through which this information becomes available.
Three Broad Types of Perspective Data
The Dictionary and Volume 1 organise some of the information obtained through Perspective Products into three broad kinds of data:
- Subsumptive Data — information concerning whole and part relationships;
- Ordinal Data — information concerning figure, size, scale and position;
- Determinative Data — information concerning state and activity.
These categories emphasise that the product of a perspective process may consist not merely of a visible image but of knowledge derived from that image and its relationship to spatial reality.
Subsumptive Data
Subsumptive Data concerns relationships between wholes and their constituent parts.
A perspective image or model may enable an observer or analytical system to determine:
- which objects belong to a scene;
- which components belong to an object;
- how parts are grouped;
- how local structures relate to larger structures; and
- how an object or scene is organised as a whole.
This type of information is important when perspective is used for identification, classification, modelling or analysis.
Ordinal Data
Ordinal Data concerns properties such as:
- figure;
- size;
- scale; and
- position.
These properties are central to many perspective problems because the apparent size, shape and position of an object may change according to viewpoint, distance, orientation and projection method.
A Perspective Product can therefore provide information that allows these relationships to be estimated, compared, measured or reconstructed.
Determinative Data
Determinative Data concerns the state or activity of an object, scene or process.
A perspective image or sequence of views may therefore provide information about:
- what an object or scene is doing;
- whether it is changing;
- its current spatial state;
- movement or activity; and
- relationships that develop through time.
This becomes especially important in motion imaging, scientific observation, machine vision and other systems in which perspective products are analysed dynamically rather than as isolated static pictures.
Perspective Product and Perspective Process
The distinction between Perspective Process and Perspective Product is fundamental.
A Perspective Process is the operation through which principles or methods form, capture, calculate, project, represent, simulate, display or interpret a view, image or spatial relation.
The Perspective Product is what emerges from that operation.
Thus:
Process → what happens
Product → what results
For example:
photographic imaging process → photograph
surveying process → spatial measurement
graphical construction process → perspective drawing
computer modelling process → digital model
Perspective Product and Perspective Goal
A Perspective Goal describes what a perspective process is intended to achieve.
A Perspective Product is the result actually produced.
The principal Goals of Perspective include:
- viewing;
- imaging;
- projecting;
- measuring;
- matching;
- representing;
- creating illusion; and
- producing immersion.
The relationship can therefore be expressed as:
Goal → Process → Product
For example:
Goal: measure reality → Perspective Process: surveying → Product: measurement or spatial model
or:
Goal: represent reality → Perspective Process: drawing or imaging → Product: perspective image
Perspective Product and Perspective Function
Perspective Functions describe operations through which broader perspective goals are achieved.
The Dictionary identifies functions including:
- capturing;
- observing;
- prescribing;
- measuring;
- calculating;
- classifying;
- modelling;
- surveying;
- mapping;
- indexing;
- gauging;
- certifying;
- linking;
- mixing;
- exploring;
- displaying; and
- projecting.
The status and fulfilment of these functions determine the kinds of Perspective Products that a system can provide.
A modelling function may produce a model, a measuring function a measurement, an imaging function a visual image, and a representing function a representation.
Perspective Product and Perspective Form
A Perspective Form describes the visual, optical, geometrical or spatial appearance produced by a Perspective Process.
A Perspective Product is broader.
The product may be an image or spatial appearance, but it may instead be a measurement, calculation, model or other information derived from the process.
Thus:
Perspective Form → the appearance produced
Perspective Product → the complete resulting output or information
A Perspective Form can therefore constitute one aspect or kind of Perspective Product without exhausting the broader concept.
Perspective Product and Perspective Type
A Perspective Type identifies a particular method, system, process or subdivision of perspective.
The Type should not be confused with the Product it generates.
For example:
Linear Perspective → Type or method/process
Linear-perspective drawing → Product
Similarly:
Stereoscopic Perspective → Type or system
Stereoscopic image or view → Product
The distinction helps prevent a frequent ambiguity in perspective terminology whereby the same term may be used both for a process and for its resulting image.
Perspective Products in Computer Vision
Computer vision demonstrates particularly clearly that Perspective Products are not restricted to pictures intended for human viewing.
A visual system may analyse images in order to derive information concerning:
- object location;
- size and shape;
- orientation;
- arrangement;
- texture;
- colour;
- object identity; or
- other properties of the observed spatial scene.
The Perspective Product may therefore consist partly or principally of structured spatial information extracted from an image.
Such information can subsequently support classification, modelling, measurement, identification or decision-making.
Perspective Products and Visual Knowledge
The Products of Perspective contribute to the broader acquisition of visual knowledge.
Perspective enables spatial reality to be:
- viewed;
- recorded;
- measured;
- represented;
- modelled;
- compared;
- classified;
- explored; and
- communicated.
The resulting images, views, measurements, models and information provide means through which humans and technical systems can acquire knowledge about physical, represented, simulated or imagined spatial realities.
The value of a Perspective Product therefore lies not only in its visible appearance but also in the spatial information and relationships that it makes available.
Several Products can arise from one Perspective Process
A single Perspective Process or system may produce more than one kind of product.
A calibrated camera system, for example, might provide:
- a visual image;
- a measured position;
- a scale estimate;
- a model of object geometry;
- classification information; and
- a recorded view for later analysis.
The Product of Perspective should therefore not always be understood as one isolated output.
A complex perspective system may generate a family of related visual, quantitative and informational products.
The Product may become the input to another process
Within a complex image chain, the Perspective Product of one process may become the input or target of another Perspective Process.
For example:
physical scene → camera process → photographic image
The photograph is the Product of the camera process.
If it is then digitally analysed or transformed:
photographic image → digital process → processed image or measurement
The first Product has become the target of a second process.
This relationship is particularly important in photography, cinema, scientific imaging and New Media Perspective, where images can pass through many successive stages before reaching their final form or use.
Why Perspective Product matters
The concept of Perspective Product makes clear that perspective should not be defined only by the method used to construct an image.
Perspective processes can produce many different kinds of outcomes, including images, views, measurements, calculations, representations, models and structured information about spatial reality.
Identifying the Product makes it possible to distinguish:
- the process from its outcome;
- the method from the thing produced;
- the intended goal from the achieved result;
- the visual Form from broader quantitative or informational outputs;
- the image itself from information extracted from that image; and
- one stage of an image chain from the next.
Perspective Product is therefore the resulting image, view, representation, measurement, calculation, model, spatial appearance or information produced through a Perspective Process and related to a spatial reality.
Related Perspective Topics
Perspective Process →
Goals of Perspective →
Functions of Perspective →
Perspective Method →
Perspective Form →
Perspective Category Theory →
Explore Theory
Explore the principal theories, classifications, types, forms, geometries, spatial concepts and visual phenomena of perspective.
Theory Hubs
Foundations of Perspective Theory · Perspective Category Theory & Classification · Perspective Types and Forms · Perspective Geometry & Projection · Vanishing, Horizons & Directional Reference · Form, Space & Perspective Images · Perspective Phenomena, Vision & Problems · Advanced & Additional Perspective Concepts
Foundations & Classification
Theory of Perspective · Functions of Perspective · Perspective Process · Perspective Principle · Perspective System · Perspective Category Theory · Perspective Category · Perspective Type · Categorical Ambiguity · Combined Perspective
Perspective Types & Forms
Types of Perspective · Central Perspective · Parallel Perspective · Linear Perspective · Curvilinear Perspective · Axonometric Perspective · Camera Perspective · Digital Perspective · Artificial Perspective · 360-Degree Perspective · Panoramic Perspective
Geometry, Vanishing & Spatial Reference
Perspective Projection · Perspective Geometry · Projective Transformation · Picture Plane · Station Point · Vanishing Point · Horizon Line · Viewpoint · Vanishing Structures · Optical Versus Geometrical Vanishing
Form, Space & Perspective Images
Perspective and 3-D Space · Object Space · Image Space · Perspective Image / View · Optical Image Chain · Linear Perspective Images · Perspective Product
Vision, Phenomena & Problems
Perspective Phenomena · Foreshortening · Depth Cues · Field of View · Binocular Vision · Scale–Shape–Size Problem · Equivalence / Correspondence Problem · Perspective and Illusion · Perspective and Spatial Immersion
Further reference:
Dictionary of Perspective ·
Perspective Research Centre