Object Space

Object Space is the physical, artificial, simulated or imagined space containing the object, scene or spatial information that a perspective process or system is directed towards.

It is also called Target Space.

Object Space 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 to understanding how perspective relates spatial reality to the images and views produced from it.

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 or simulating that spatial information.

One or more Perspective Categories may participate in transforming Object Space into Image or Perspective Space.

The resulting image may preserve some characteristics of the original space while changing, reducing, concealing, compressing or distorting others.

Perspective therefore involves both correspondence between Object Space and Image Space and transformation between them.

Object Space and Image Space

Perspective normally involves a relationship between two broad kinds of space:

Object Space or Target Space — the space containing the object, scene or spatial information to be viewed, measured or represented;
Image Space or Perspective Space — the space in which the resulting image, view, model or representation is formed, located or perceived.

The distinction can be represented as:

Object Space → Perspective Transformation → Image Space

The two spaces should not be confused.

An object may possess one size, position, orientation and spatial structure in Object Space while its image possesses a different apparent size, position, shape or arrangement in Image Space.

Understanding perspective therefore requires identifying both the original spatial relationships and their transformed image-space appearances.

Object Space and Target Space

The Dictionary of Perspective treats Target Space as a synonym for Object Space: the physical, artificial, simulated or imagined space towards which a perspective process or system is directed.

The term target is particularly useful when considering a complete perspective system or image chain because it emphasises what the system is attempting to view, image, measure or represent.

For example, when photographing a landscape, the physical landscape is both the Object Space containing the scene and the Target Space towards which the camera system is directed.

When representing an entirely fictional environment, however, the target may instead be an imagined or constructed spatial reality.

Object Space therefore need not always consist of directly existing physical reality.

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;
a group of objects;
a person;
an astronomical scene;
a microscopic specimen; or
any other region of physical space addressed by a perspective system.

The resulting image may then exist in retinal, photographic, digital or another form of Image Space.

Artificial, Simulated and Imagined Object Space

Object Space is not restricted to natural physical environments.

The Dictionary definition explicitly includes:

physical space;
artificial space;
simulated space; and
imagined space.

A perspective drawing may therefore represent an artificial architectural model, a simulated environment or a completely imagined spatial scene.

A film, drawing or digital model may also use a fictional scene as its Target Space even though no corresponding physical scene exists.

This broader definition makes Object Space applicable across natural vision, graphical representation, photography, cinema, simulation and New Media Perspective.

Euclidean Object Space

In classical graphical and Linear Perspective, Object Space is commonly modelled as Euclidean three-dimensional space.

Within this model:

objects possess measurable positions;
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; and
positions can be expressed using Cartesian coordinates.

A central-perspective image then projects 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 the Object Space. They do not mean that the original Euclidean parallel lines actually converge in Object Space.

Object-Space position

The position of an object in Object Space can be specified independently of its position in the resulting image.

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

X, Y and Z coordinates;
metric distances;
angles;
directions;
orientation; and
relationships to other objects or reference structures.

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 be defined using picture-plane coordinates, pixels or other local image measurements.

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.

This establishes a relationship between:

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.

Objects, points, lines and planes in Object Space

Object Space may contain many different forms of spatial structure.

These include:

object points;
object lines;
object planes;
surfaces;
solids;
spatial frameworks;
metric grids; and
complete objects and scenes.

A perspective process establishes relationships between these Object-Space structures and their corresponding positions and forms in Image Space.

For example, parallel lines in Object Space may project towards a vanishing point in a central-perspective image, while an angled plane may undergo foreshortening or appear to collapse towards a line according to its orientation relative to the viewpoint.

From Object Space to Image Space

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

This transformation may be:

optical;
visual;
mathematical;
graphical;
instrument-based;
simulated; or
computational.

The transformation 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 must 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 transforms many of its 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.

Depth information and Object Space

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 plane. 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.

The image records particular projected relationships, but several different Object-Space arrangements may potentially produce similar or identical Image-Space appearances.

Understanding the original spatial reality therefore requires 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 in 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 → Processing → 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 may occupy 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.

Intermediate spaces

Complex perspective systems may contain intermediate spaces between the original Object Space and the final Image Space.

A camera may first transform physical Object Space into photographic or digital Image Space. That image may then become the input to another processing, projection or display system.

Thus, within a chained perspective process:

one system’s Image Space may become another system’s Target Space.

This is particularly important in photography, cinema, digital imaging, computer vision and New Media systems, where images frequently pass through several successive stages.

The distinction between Object Space and Image Space therefore depends partly upon which stage of the complete perspective chain is being analysed.

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 resulting visual experience is then organised through the human visual system.

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.

The two spaces are related but not identical.

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 the 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 therefore 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 the represented geometry rather than changes to the original Object-Space structures themselves.

Object Space in simulated and imagined perspective

A Target or Object Space can also be simulated or imagined.

A drawing of a fictional building, for example, may represent a three-dimensional spatial arrangement that has never physically existed.

A computer-generated environment may similarly define a digital or mathematical spatial world containing modelled objects, surfaces, lighting and viewpoints.

Such spaces can still function as Object or Target Spaces because they contain the spatial information towards which the relevant perspective process is directed.

The distinction between Object Space and Image Space therefore concerns their role within the perspective process, not simply whether the space is physically real.

Object Space and Perspective Categories

Different Perspective Categories can act upon or transform Object Space.

For example:

Natural Perspective may concern a physical Object Space;
Optical Perspective may transfer light from that space;
Instrument Perspective may capture or measure it;
Mathematical Perspective may calculate its geometrical relationships;
Graphical Perspective may represent it;
Simulated Perspective may alter or construct it; and
New Media Perspective may generate, process or display its representation.

Several categories may operate successively or together while spatial information passes from Object Space towards one or more Image Spaces.

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 of the fundamental problems of perspective involving scale, shape, size, depth, reconstruction and spatial ambiguity.

Why Object Space matters

Object Space provides the 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:

physical size with image size;
physical position with image position;
parallel Object-Space lines with converging image lines;
actual shape with apparent shape;
physical depth with represented depth;
the scene itself with its image; and
the geometry of spatial reality with the geometry of its representation.

The concept is therefore fundamental to the study of Perspective because it identifies the physical, artificial, simulated or imagined spatial domain containing the object, scene or information towards which a perspective process is directed.