Object Space

Object Space is the physical, artificial, simulated or imagined space containing the object, scene or spatial information towards which a Perspective Process or System is directed.

It is also called Target Space.

Object Space is the spatial domain containing what is to be viewed, imaged, measured, calculated, represented, modelled or otherwise addressed by perspective. It should be distinguished from Image Space or Perspective Space, in which the resulting image, view, model or representation is formed, located or perceived.

The basic relationship can therefore be expressed as:

Object or Target Space → Perspective Process or System → Image or Perspective Space

This distinction is fundamental because the spatial properties of an original object or scene are not necessarily identical to their resulting appearance in a perspective image or view.

Object Space within Perspective Category Theory

Within Perspective Category Theory (PCT), Object Space identifies the spatial domain containing the subject matter towards which a Perspective Process is directed.

The process may involve viewing, imaging, measuring, calculating, constructing, projecting, representing, modelling or simulating spatial information.

One or more Perspective Categories may participate in transforming information from Object Space into Image or Perspective Space. A physical or modelled scene may, for example, be viewed through Natural or Visual Perspective, imaged through Optical Perspective, captured through Instrument Perspective, measured through Mathematical Perspective, represented through Graphical Perspective, altered through Simulated Perspective, or processed through New Media Perspective.

The resulting image may preserve some characteristics of the original space while changing, reducing, concealing, compressing or transforming others. Perspective therefore involves both correspondence between Object Space and Image Space and transformation between them.

Object Space and Target Space

Object Space and Target Space are closely related terms and are treated as synonyms in the Dictionary of Perspective.

The term Object Space emphasises the space containing the spatial objects, scenes and structures under consideration. Target Space emphasises that the Perspective System is directed towards that spatial domain.

Object Space → what the spatial domain contains
Target Space → the spatial domain towards which the system is directed

In many situations they therefore describe the same spatial domain from different analytical standpoints. When photographing a landscape, for example, the physical landscape is both the Object Space containing the scene and the Target Space towards which the camera is directed.

Object or Target Space need not consist of directly existing physical reality. It may also be artificial, simulated, modelled or imagined.

Object Space and the Perspective Object / Scene

Object Space should also be distinguished from the particular Perspective Object / Scene contained within it.

Object Space → spatial domain
Perspective Object / Scene → target contained within that domain

A room, for example, may constitute an Object Space while a table within the room is the particular object being viewed or measured. Alternatively, the complete room and everything within it may itself constitute the Perspective Scene.

The analytical boundary therefore depends upon what the Perspective Process is intended to address.

Physical Object Space

The most familiar form of Object Space is the physical three-dimensional environment containing real spatial objects and scenes.

For direct human vision, the Object Space may be the surrounding physical environment towards which the eyes are directed. For a camera, the same region of physical reality may form the Object or Target Space from which an optical image is captured.

Examples include:

a room;
a landscape;
a building or street;
a person or group of people;
a group of objects;
a geometrical arrangement;
a microscopic specimen;
an astronomical scene; or
any other region of physical space addressed by a Perspective System.

The same physical Object Space may be viewed directly, photographed, measured, surveyed, modelled or represented through many different Perspective Systems and may consequently generate many different Perspective Images or Views.

Artificial Object Space

Object Space need not be naturally occurring. An Artificial Object Space may contain deliberately constructed objects, models or environments.

architectural models;
stage sets;
technical models;
miniature environments;
constructed spatial frameworks; and
deliberately arranged objects.

The artificial environment remains Object Space because it contains the spatial target towards which the Perspective Process is directed.

Simulated Object Space

A Simulated Object Space may be a physical or modelled spatial environment deliberately structured, modified or generated to produce a selected perspective appearance or effect.

Forced Perspective provides an important example. The physical size, scale, position or geometry of objects may be altered so that the resulting view suggests a different spatial reality. In such cases, the Object Space itself becomes part of the Perspective Method: the unusual appearance does not arise only from an image transformation, because the spatial target has itself been deliberately constructed or modified.

Digital and computer-generated environments may likewise provide simulated Object Spaces containing modelled objects, surfaces, lighting, viewpoints and other spatial information.

Imagined Object Space

Object Space may also be imagined. A drawing, painting, mathematical model or digital environment may represent a spatial reality that has never physically existed.

an imaginary building;
a fictional landscape;
a proposed engineering structure;
a virtual environment;
a computer-generated scene; or
a theoretical geometrical construction.

The imagined spatial organisation can still function as Object or Target Space because it provides the spatial information that is calculated, represented or visualised.

The Classical and Euclidean Model of Object Space

In many traditional geometrical, graphical and Linear Perspective applications, Object Space is modelled as three-dimensional Euclidean space and is commonly assumed to be homogeneous and isotropic.

Within this model:

objects possess measurable positions and dimensions;
straight lines remain straight;
parallel lines remain parallel in Object Space;
planes and solids possess geometrically defined relationships;
distances can be measured using a Euclidean metric;
angles and directions can be specified; and
positions can be expressed using Cartesian coordinates.

These characteristics are modelling assumptions appropriate to particular Perspective Systems, rather than universal properties that every possible conception of space must possess.

A central-perspective image can project this Object Space onto an image or picture plane. The convergence of parallel lines and diminution of apparent size visible in the resulting image are therefore projective transformations of Object Space; they do not mean that the original Euclidean parallel lines actually converge in Object Space.

Object-Space Geometry

Object-Space Geometry concerns spatial relationships existing before their transformation into an image or representation.

Object Space may contain:

object points;
lines and curves;
planes and surfaces;
solids;
one-, two- and three-dimensional structures;
individual objects and groups of objects;
spatial frameworks;
metric grids; and
complete scenes or environments.

One-, two- and three-dimensional structures may all occur within a three-dimensional Object Space. A line, plane or flat object is therefore not excluded merely because its surrounding spatial environment is three-dimensional.

Object-Space relationships may include actual dimensions, positions, distances, directions, angles, parallel and perpendicular relationships, orientation and spatial arrangement. These should be distinguished from their corresponding appearances within Image Space.

For example, parallel lines may remain parallel in Object Space while their images converge towards a vanishing point; an angled plane may undergo foreshortening or appear to collapse towards a line according to its orientation relative to the viewpoint.

Object-Space Position

An object possesses a position within Object Space independently of where its image appears in Image Space.

In a Euclidean system, Object-Space position may be described using:

X, Y and Z coordinates;
metric distances;
angles and directions;
a ground plane;
relationships to other objects;
relationships to the observer or camera;
relationships to the picture or projection plane; or
another spatial reference structure.

In other spatial systems, such as spherical space, position may instead be expressed through angular coordinates and radial distance.

Object-Space position should therefore be distinguished from Image-Space position, which may instead use picture-plane coordinates, pixels or other local image measurements.

Object-Space Orientation

The orientation of an object is likewise an Object-Space property.

An object can remain at the same position while being rotated relative to the viewpoint, optical axis or image surface. This may alter its resulting:

apparent shape;
visible surfaces;
foreshortening;
projected line directions;
apparent width or height; and
overall Perspective Form.

The distinction between position and orientation is therefore essential when analysing how spatial Form becomes transformed through perspective.

Object-Space and Image-Space Measurements

Measurements in Object Space and Image Space normally use different scales and reference systems.

An object may, for example, measure ten metres in Object Space but only ten centimetres within a represented Image Space.

Object-Space units → projection or image scale → Image-Space units

Maps, technical drawings, photographs and other measured representations may include scales or calibration information that allow Image-Space measurements to be related back to Object-Space dimensions.

This relationship is fundamental to surveying, mapping, photogrammetry, scientific imaging and other forms of Technical Perspective.

From Object Space to Image Space

A Perspective Process transforms information from Object Space into an image, view, measurement, representation or model.

The transformation may be optical, visual, mathematical, graphical, instrument-based, simulated or computational, and it need not preserve every Object-Space property.

Three-dimensional depth may be reduced in a two-dimensional image. Apparent size may change with distance. Shapes may be foreshortened. Parallel lines may appear to converge. Objects may overlap and conceal one another.

Perspective therefore maps selected spatial relationships from Object Space into a different spatial organisation within Image Space.

Correspondence and Transformation

The relationship between Object Space and Image Space involves both correspondence and transformation.

An image may preserve enough information about its target for the represented object or scene to be recognised, measured, interpreted or reconstructed. At the same time, the Perspective Process may transform many spatial characteristics.

These transformations can include changes in:

apparent size;
apparent shape;
position;
orientation;
line direction;
depth;
scale;
visibility;
colour;
clarity; and
contrast.

The resulting Perspective Form therefore depends upon both the original Object Space and the Perspective Process applied to it.

Loss of Depth Information

A Perspective Image does not necessarily preserve all of the depth information present in Object Space.

A three-dimensional object or scene may be projected onto a two-dimensional Image Space. The resulting image can be geometrically valid for the selected projection method while nevertheless losing information about the original depth relationships.

This is one reason why reconstructing Object Space from a single Perspective Image can be difficult or ambiguous. Several different Object-Space arrangements may potentially produce similar or identical Image-Space appearances.

Understanding the original spatial reality may therefore require knowledge not only of the image but also of the Perspective System, viewpoint, projection geometry and other conditions through which the image was produced.

Object Space and the Optical Image Chain

Object Space forms the starting spatial domain of an optical image chain.

A simplified image chain may contain:

Object → Imager → Sensor → Image → Processor → Display → Analysis

The object exists within Object Space, while the resulting Perspective Image exists within Image Space.

For a camera system, for example, a physical scene occupies the Object Space. Light from that scene enters the camera, an image is formed or recorded, the image may be processed and it may subsequently be displayed. At each stage, spatial information can be preserved, transformed, reduced or supplemented.

Target Space and Intermediate Spaces

Complex Perspective Systems may contain Intermediate Spaces between the original Object Space and the final Image Space.

For example:

Physical Object Space → Camera Image Space → Digital Processing Space → Display Space → Visual Space

A physical landscape may remain the original Target Space whether it is viewed directly, photographed, filmed, measured, represented graphically or subsequently displayed through another image system.

Each intermediate stage can preserve or transform some part of the spatial information received from the previous stage. Understanding a final Perspective Image may therefore require identifying the intermediate spaces and processes through which it has passed.

When Image Space Becomes Object Space

The distinction between Object Space and Image Space is partly relative to the particular Perspective Process being analysed.

An image produced by one system may subsequently become the target of another system:

physical scene → photograph → scanned photograph → digital image

The photograph is initially an Image-Space product. When it is scanned or photographed again, however, it becomes the Object or Target Space of the next imaging process.

One system’s Image Space may therefore become another system’s Object or Target Space.

This is particularly important in chained and Composite Perspective systems, photography, cinema, digital imaging, computer vision and New Media Perspective.

Object Space in Human Vision

In ordinary human viewing, the surrounding physical environment forms the principal Object or Target Space.

Light from objects and scenes travels towards the eyes and forms retinal images. The physical Object Space should therefore be distinguished from:

the optical retinal image;
the visual field;
Visual Space; and
the perceived visual world.

Visual Space may differ from the measurable geometry of physical Object Space because visual experience is shaped by optical and perceptual processes.

Object Space in Photography

In photography, the photographed scene normally forms the Object or Target Space. The camera forms a corresponding image within photographic or digital Image Space.

A three-dimensional scene may become a two-dimensional photograph. Depth becomes represented indirectly through Perspective Phenomena such as diminution, foreshortening, overlap, convergence, gradients and other spatial cues.

The resulting photograph therefore provides a transformed representation of Object Space rather than a duplicate of it.

Object Space in Graphical Perspective

Graphical Perspective likewise establishes a relationship between an assumed Object Space and a represented Image Space.

In central or Linear Perspective, three-dimensional Object-Space geometry is projected towards a two-dimensional picture plane according to a selected viewpoint and geometrical construction.

Parallel lines that remain parallel in Object Space may appear to converge in the image. Objects of equal physical size located at different depths may project to different Image-Space sizes. Planes seen obliquely may appear foreshortened.

These are transformations of represented geometry rather than changes to the original Object-Space structures themselves.

Object Space and Perspective Categories

Different Perspective Categories may relate to or transform Object Space in different ways.

Natural Perspective concerns spatial and visible relationships arising within natural or physical reality;
Optical Perspective forms or transfers images through light or other electromagnetic radiation;
Mathematical Perspective calculates spatial relationships;
Graphical Perspective constructs or represents them graphically;
Instrument Perspective views, images, measures or projects spatial information through instruments;
Simulated Perspective deliberately constructs or modifies spatial appearances; and
New Media Perspective generates, processes, displays or explores spatial information computationally.

One Object Space may therefore participate in several Perspective Categories as spatial information passes through a complete Perspective System.

Object Space and Perspective Form

The original spatial Form of an object belongs to Object Space. Its resulting Perspective Form concerns its transformed visual, optical, geometrical or spatial appearance.

An Object-Space rectangle may, for example, project as a trapezoidal or otherwise foreshortened form in Image Space. A circular object may produce an elliptical image. Parallel lines may produce converging image lines.

The original Form and the resulting Perspective Form should therefore not be confused.

Object Space and the Scale–Shape–Size Problem

Object Space provides the reference against which differences between actual and apparent spatial properties can be analysed.

An object possesses an Object-Space:

size;
shape;
position;
orientation; and
scale relative to surrounding structures.

Its resulting appearance may then vary according to distance, viewpoint, projection geometry, orientation, foreshortening, image scale and resolution.

Separating Object-Space properties from Image-Space appearances is therefore essential when analysing relationships between scale, shape and size.

Object Space is not Image Space

One of the most important principles in perspective analysis is that Object Space is not Image Space.

The object or scene possesses spatial relationships independently of the particular image made from it. A change of viewpoint, projection method, lens, image surface, scale or representation can produce a different image of the same Object Space.

Conversely, a single Image-Space configuration may not uniquely determine the original Object-Space arrangement from which it was derived.

This distinction lies behind many fundamental problems of perspective involving scale, shape, size, depth, reconstruction and spatial ambiguity.

Why Object Space Matters

Object Space provides the original spatial reference against which a Perspective Image, View, Measurement or Representation can be understood.

Without distinguishing Object Space from Image Space, it becomes easy to confuse:

actual or physical size with apparent or image size;
actual shape with projected or apparent shape;
physical position with image position;
actual orientation with apparent orientation;
parallel Object-Space lines with converging image lines;
physical depth with represented depth;
the spatial target with its visual representation; and
the geometry of spatial reality with transformations introduced by the Perspective Process.

Object Space is therefore the physical, artificial, simulated or imagined spatial domain containing the object, scene or spatial information towards which a Perspective Process or System is directed.

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