Category Chaining

Category Chaining occurs when two or more Perspective Categories operate sequentially in the formation, processing, display or viewing of an image or view.

Within Perspective Category Theory (PCT), a perspective image is therefore not necessarily the product of one isolated process. It may pass through a sequence of natural, optical, instrument-based, graphical, mathematical, simulated, computational and perceptual processes before reaching its final viewed form.

Category Chaining provides a way of identifying these successive stages and the Perspective Category associated with each of them.

In simple terms:

one perspective process → another perspective process → another perspective process → viewed image

Each stage may introduce, preserve, modify, transform, display or reinterpret aspects of the image.

Category Chaining within Perspective Category Theory

Perspective Category Theory distinguishes Perspective Categories according to the principal source or mode through which a perspective process occurs.

The principal categories are:

Natural Perspective;
Visual Perspective Type 1;
Optical Perspective;
Mathematical Perspective;
Graphical Perspective;
Instrument Perspective;
Simulated Perspective; and
New Media Perspective.

Visual Perspective Type 2 is the human retinal and perceptual subclass within the broader Visual Perspective Type 1.

These categories are not always isolated from one another. An image may move from one category to another as it is formed, captured, processed, represented, displayed and ultimately perceived.

When these categories operate sequentially, the relationship is described as Category Chaining.

A basic Category Chain

A common Category Chain can be represented as:

Natural scene → Optical and Instrument imaging → New Media processing → Instrument or New Media display → Visual Perspective Type 2

This sequence may involve:

Natural Perspective within the original physical scene;
Optical and Instrument Perspective while the scene is imaged or captured;
New Media Perspective while the image is digitally processed;
Instrument or New Media Perspective when the image is displayed; and
Visual Perspective Type 2 when the completed image is viewed and perceived through the human visual system.

The final visual experience therefore results from a chain of perspective processes rather than from a single isolated category.

From physical scene to visual experience

Category Chaining is particularly useful for analysing the passage of an image from physical reality to human visual experience.

Consider a physical scene recorded by a digital camera and subsequently viewed on a screen.

The original scene possesses spatial and visible relationships belonging to Natural Perspective. Light travelling from the scene participates in Optical Perspective. The camera introduces Instrument Perspective by forming and recording the image.

If that image is subsequently adjusted, transformed, composited or otherwise processed digitally, New Media Perspective enters the chain.

The image may then be presented on an electronic display, introducing another Instrument or New Media stage. Finally, a human observer views the displayed image, introducing Visual Perspective Type 2.

The resulting view cannot therefore be understood completely by referring only to the camera, the display, the original scene or the human observer. All participate within the complete Category Chain.

Why Category Chaining matters

Many modern perspective images are produced through several successive processes. Treating the finished image as though it belonged to only one Perspective Category can conceal much of the system that produced it.

Category Chaining makes it possible to identify:

where an image or view originates;
how it is optically formed or captured;
which instruments participate in its production;
whether mathematical or graphical transformations are applied;
whether digital processing modifies the image;
how the image is displayed; and
how it is finally viewed and perceived.

The concept therefore shifts attention from the finished image alone to the complete sequence of perspective processes through which the image has passed.

Category Chaining and image transformation

Each stage of a Category Chain may preserve some features of an earlier image while transforming others.

An optical system may alter image scale, field of view or geometry. An instrument may impose its own imaging characteristics. Digital processing may transform colour, contrast, geometry or spatial organisation. A display introduces another image surface and viewing condition. Finally, the human visual system interprets the resulting image according to its own retinal and perceptual characteristics.

The final perspective image or view may therefore embody a succession of physical, optical, instrumental, computational and perceptual transformations.

Category Chaining provides a framework for locating these different processes within the complete imaging sequence.

Category Chaining and Composite Perspective

Category Chaining and Composite Perspective are closely related but describe different aspects of a multi-category perspective system.

Category Chaining describes the sequential operation of Perspective Categories.

Composite Perspective describes the resulting multi-category process, system, image or environment when several categories or methods operate together or in sequence.

Thus, Category Chaining describes how categories are connected through a sequence, while Composite Perspective can describe the multi-category system or result produced through that sequence.

A complex photograph, film, virtual environment or digitally processed image may therefore contain a Category Chain and, considered as a complete multi-category system or image, also constitute Composite Perspective.

Category Chaining and Category Overloading

Category Chaining should also be distinguished from Category Overloading.

Category Chaining occurs when different Perspective Categories operate sequentially.

Category Overloading occurs when the same perspective term, type, process or image legitimately belongs to more than one top-level category.

For example, Linear Perspective may simultaneously be:

Mathematical, because it is governed by geometrical relationships;
Graphical, when constructed as a drawing;
Optical, when comparable convergence appears in an optical image;
Simulated, when physical arrangements deliberately reproduce its apparent effects; or
New Media, when calculated and rendered digitally.

The distinction can therefore be summarised as:

Category Chaining = categories operating in sequence
Category Overloading = one term, type or process belonging to several categories

Both can occur within the same complex perspective system.

Category Chaining and Class Chaining

Category Chaining should not be confused with Class Chaining.

A Perspective Category identifies the principal source or mode of a perspective process. A Perspective Class identifies its principal direction.

Category Chaining therefore describes a sequence of Perspective Categories or modes.

Class Chaining describes the sequential operation of the two basic directional Perspective Classes:

Viewing or Imaging Class — the image-forming or capturing direction; and
Projecting Class — the image-projecting direction.

A single perspective system may consequently contain both a Category Chain and a Class Chain.

For example:

Category chain: Optical → Instrument → New Media

Class chain: Viewing or Imaging → Projecting

The first identifies the succession of modes; the second identifies the succession of directions.

Camera and projector systems

A camera-projector system provides a particularly clear example of why several levels of analysis may be required.

A camera first forms or captures an image. This involves Optical and Instrument Perspective and operates principally within the Viewing or Imaging Class.

The recorded image may then be processed digitally, introducing New Media Perspective.

A projector subsequently sends the image forwards onto a screen. This involves Instrument and Optical Perspective and operates within the Projecting Class.

The spectator finally views the projected image through Visual Perspective Type 2.

The complete system therefore contains both Category Chaining and Class Chaining.

Category Chaining in New Media Perspective

New Media Perspective frequently contains extensive Category Chains because computational systems can connect and transform images originating from many different sources.

New Media systems may link:

maps;
satellite and aerial imagery;
photographs;
panoramic images;
three-dimensional models;
mathematically generated views;
instrument-generated information; and
interactive visual displays.

Such material can be connected, ordered, constructed, matched, mixed, overlaid, explored and cross-matched within a common system.

The resulting perspective environment may therefore contain multiple linked instances of Natural, Mathematical, Graphical, Instrument and New Media Perspective, followed ultimately by Visual Perspective Type 2 when the system is viewed by a human observer.

Category Chaining in complex images

A film image provides another useful example of multi-stage perspective.

A scene may begin with real architecture or another physical environment, establishing Natural Perspective. Elements of Forced or Simulated Perspective may be introduced physically. A camera then produces Optical and Instrument Perspective. Digital compositing or computer-generated imagery introduces New Media processes.

The finished film is subsequently displayed through another instrument or digital system and is finally viewed through Visual Perspective Type 2.

The apparent simplicity of the completed image can therefore conceal a substantial sequence of different perspective processes.

Category Chaining helps expose that hidden structure.

A perspective image is not necessarily a single-stage product

One of the main implications of Category Chaining is that a perspective image should not automatically be attributed to whichever process occurs at its final stage.

A digital image displayed on a screen, for example, may still contain geometrical and optical relationships inherited from the physical scene, the camera, mathematical processing and earlier transformations.

Similarly, the image finally perceived by a human observer reflects not only the Visual Perspective Type 2 stage but also the succession of perspective processes that preceded it.

The complete image may therefore be understood more accurately as the product of an image chain or perspective process chain.

Working boundaries

The Perspective Categories used in Perspective Category Theory are analytical tools rather than completely rigid compartments.

Perspective systems frequently overlap, combine and change as images move between physical, optical, graphical, instrumental, computational and perceptual stages.

At some points in a chain, more than one category may operate together. Optical and Instrument Perspective commonly coincide during camera imaging, for example, while a digitally produced image may simultaneously involve Mathematical, Graphical and New Media processes.

Category Chaining is therefore not intended to imply that every stage is absolutely isolated from every other stage. Its purpose is to identify the significant sequence of modes through which a perspective image or view is formed, transformed, displayed and experienced.

Why Category Chaining is important

Perspective has become increasingly dependent upon complex imaging and display systems in which images pass through numerous physical, optical, mathematical, graphical, instrumental and computational processes.

Without the concept of Category Chaining, these processes can easily be collapsed into a single label—for example, calling an entire imaging sequence simply photographic, digital or visual perspective.

Category Chaining instead allows the complete process to be decomposed into its constituent stages.

This makes it possible to determine:

which Perspective Categories are operating;
the order in which they operate;
where transformations enter the image chain;
how different media and instruments contribute;
how the final image relates to the original spatial scene; and
how the resulting image is ultimately perceived.

Category Chaining is therefore an important concept within Perspective Category Theory because it describes the sequential passage of an image or view through two or more Perspective Categories.