Prologue

Welcome to a marvellous intellectual adventure on perspective.

We study perspective in greater detail, broader scope, and more coherence than previously attempted. Ultimately, a new Perspective Category Theory is developed that unites all facets under a single framework, heralding a new subject discipline. 

We begin with remarks on motivations, areas, and scope of analysis, a summary of past work, and future goals on this fascinating topic. Bon-voyage!


The Fragmentation of Perspective

Perspective lies at the epicentre of progress. Yet people often fail to realise why perspective is pivotal to everything we humans will achieve in the future.

Rhetorically, there was an attack on perspective during the 20th century, to the extent that some have spoken of the death of perspective. But perspective is not a dead subject, far from it. In practice, there have been more publications than ever in the last 100 years, along with a radical increase in alternative methods and innovations in countless modern application areas.

Perspective introduced an objective method for recording or copying the physical world at different levels of abstraction in photographs, cinema, engineering drawings, maps, etc. This is the so-called conquest of realism. Ergo, understood correctly—perspective has been a fundamental driver of artistic, scientific, technological, and cultural progress over the last 500 years. But problems remain.

Unfortunately, perspective is a fragmented field without a clear purpose/direction. It has no established foundations, comprehensive artistic/scientific/technological theory, or standard operational framework. Instead, perspective has been reduced to a set of disparate visual, graphical, imaging, measuring, and modelling techniques. The result is partial and unconnected theories of vision/representation; and localised solutions that apply in only a narrow range of circumstances—leaving many unexplained facts and perplexing mysteries.

Missing is an overarching perspective theory to explore spatial reality from a universal frame of reference, complete with generally applicable concepts, principles, methods, etc. Needed are visual explanations that apply universally and allow students/researchers to leverage much that has been learned over the last 500 years about perspective.

Subject Without a Home! 

Perspective is often described as something mainly linked with the Renaissance, which continued until the nineteenth century and then died out. Such is not the case because perspective has continued unabated to the present. 

Can we identify an underlying cause for the apparent demise of perspective?

To begin, perspective never became an independent concept and was subject to the vagaries of classification of four branches of learning: optics, architecture, drawing and geometry. This had two significant consequences. 

First, classification changes, particularly in geometry, have shifted the definition of what constitutes perspective. In the nineteenth century, perspective included one, two, and three-point perspective and also various branches of parallel perspective. In the twentieth century, the scope of the term has frequently been restricted to one, two and three point perspective, whereas all parallel versions are classed as projections. Indeed, some would see perspective merely as an example of dilatation, as one of several mathematical transformations with no special role in spatial organization. 

A second consequence has been no less dramatic. Much literature pertaining to perspective has been classed as part of the larger fields. Hence, although work on perspective has continued, it has been classed as work in optics, architecture, drawing, or geometry. Our Bibliography and Encyclopaedia of Perspective have ignored the artificial barriers imposed by these fields, collecting hitherto disparate materials relating to perspective.

Distinct Field of Study 

Our ambitious aim is to unite all perspective knowledge under a single subject heading, heralding the birth of perspective as a stand-alone discipline—or primary field of study—with its own foundational theory, and above all, unified laws. 

A key goal is to use all forms of media to gather everything known on perspective. Whereby said field is to be organised in a comprehensive knowledge package, structured in ten levels as detailed below.


PERSPECTIVE

LEVELS OF KNOWLEDGE

  1. Classification (ontology): perspective types, categories, etc. **
  2. Definitions: Perspective Dictionary, lexicon of types/terms, etymology. **
  3. Explanations: Encyclopaedia of Perspective. ***
  4. Titles: Bibliography of Perspective: primary and secondary literature. ***
  5. Partial Contents: perspective abstracts, reviews, citation indexes, timeline. *
  6. Full Contents: Perspective: Library, Museum, Gallery. **
  7. Internal Analysis (facts): perspective phenomena, principles, theory, etc. **
  8. External Analysis (applications): perspective methods, functions, forms, etc. *
  9. Restorations (conservation records): history of perspective. *
  10. New Constructions and Reconstructions: perspective research. **

PRC project work: * started, ** ongoing, *** complete.


Along these lines, PRC has been studying perspective—fervently for over 30 years, and much has been achieved. For example, we have completed our Bibliography of Perspective (up to year 2020), which lists over 15,000 perspective titles; and recently, published the 8 volume Encyclopedia of Perspective.

Founder Kim Veltman has published a knowledge bank of 350 publications (mostly on perspective or related topics). Plus, as evidenced by the 15,000 titles in our Perspective Bibliography, the world has not been idle concerning ideas and work on perspective; whereby a large number of (sometimes conflicting) concepts, principles, and theories on perspective have been developed.

Evidently, and despite progress, much remains to be done. In particular, we must unify or integrate the vast number of different phenomena, concepts, principles, theories, and methods of perspective (where possible). For example, we are building a comprehensive ontology and accurate taxonomic tree of perspective types, and formulating a corresponding classification system. Plus, we are producing a lexicon or universal dictionary of all perspective terms. 

Desired is a single theory, and unified logical reality, to entirely encompass the new subject discipline of perspective—without contradiction(s). But specific problems remain that work against any grand unification of perspective theory/methods.

Ergo, it is helpful to identify pivotal issues right away.


Problem of Scale 

A fundamental tenet of Renaissance perspective was the inverse size-distance law which stated that if one doubled the distance, the represented size was one-half. If one trebled the distance, the size was one-third and so on. Indeed this law is still basic and applied to many problems in science and engineering.

In 1967 Benoit Mandelbrot (1924-2010) wrote an interesting article on Fractals that questioned the universal applicability of the size-distance law. Mandelbrot’s article concerned the size of the coast of Britain, and implicitly introduced a spanner into this assumption by showing that size was a function of both scale and distance.

The measured coastline length depends upon scale or the apparent ‘jaggedness’ of coastal outline. Accordingly, walking or taking a boat around the coastline will involve travelling vastly different distances in each case! Modern mapping systems like GoogleMaps do (or should) implicitly consider related ‘scaling’ effects when calculating different route distances/arrival-times for walking, driving, etc.

In a sense, we have been vaguely aware of this ever since the seventeenth century. The shape of an ordinary image is transformed entirely when we change its scale in a telescope or a microscope. What is needed is a new approach to perspective—Multi-scale Perspective—that takes into account scale as well as distance, whereby any given shape only applies within a given range of scales.

This multi-scale capability is vitally important in a world where we travel between scales with greater frequency. True multi-scale views/images/measurements would open the way for better understanding of, and links between, nanoscopic, atomic, microscopic structures and macroscopic happenings.

Problem of Viewpoint 

Perspective lies at the heart of many vision-related topics, theories, and inventions. It has been directly linked to the development of diverse fields such as optics and vision, astronomy, geography, engineering, cartography, architecture, stonecutting, surveying, and archaeology.

But there is a problem that is fundamental to all perspective methods and applications. Images taken from separate viewpoints are wholly different in shape, one from another. This is due to the singular optics and geometry associated with a particular vantage point. Each view contains unique (but partial) information about the scene or object under inspection.

To visually probe—or model/understand—an object/scene sufficiently, often, we need to consider multiple views. A Multi-view Perspective, is when we combine views taken from different locations or viewing directions. Usually, this can be achieved using a new media system (networked digital media). Accordingly, views taken from two or more vantage points, may be connected/linked together and then ordered, constructed, matched, mixed, explored, and cross-matched, etc.

The problem of viewpoint integration is a common, but largely unsolved, requirement for media systems in general.

Problem of Time 

Time is the dimension of spatial permanence (or change). Like space, time has three dimensions: past, present, and future. But humans live in the present, and we must observe reality using a narrow time window—at least using unaided eyesight.

Desired are ways to explore time on multiple scales; viewing images using natural-speed, slow-motion, or fast-forward time-flows, much like a typical video player. However, we are not speaking of standard Motion Perspective available from ordinary moving images; but directly manipulating time. We wish to make time more space-like; in terms of the generic connection of time-flows across multiple images, zooming/panning time-flows, plus unrestricted navigation (temporally).

We need to—capture, record, and manipulate systemised time-flows—in our perspective views—using Multi-time Perspective. With the aid of ‘temporal’ focus and lens techniques, a continuum eliminates the gap between macro- and micro-time-flows. Ergo, the viewer can jump straight to any point in space/time, and choose the correct time-flow rate to observe a particular process—for example, spanning from nano-seconds to millions of years (modelled). 

Typically today, we see a narrow range of time-flows provided by a single image stream, limited at one end by the camera frame rate—and the other by the overall length of recording time. Needed are ways to overcome this deficiency—and develop ‘conjoined’ image space(s) with hyperlinked time-flows that can be—indexed, classified, linked, searched and explored.

To those in the physical and life sciences, such total simulation techniques extend far beyond visualisation of previously invisible processes: they introduce new dimensions of study and hence ways to attain comprehensive modelling of development processes. 


Problem of Reality 

Perspective methods, and the resulting perspective views/images, are the primary way we humans obtain knowledge of physical reality.

We are constantly looking at the world directly using our eyes, or with optical and sensing instruments to observe perspective representations of all kinds. Whereby photographs, drawings, paintings, diagrams, moving TV and cinema images, plus computer/mobile screens, are ever close at hand, enabling the rapid consumption of a nearly unlimited number of perspective views.

But there is a significant problem related to the correct interpretation of each perspective view/image. How do we humans make the ‘perceptual leap’ from what is often a flat or two-dimensional picture taken from a single view-point, and then construct an accurate understanding (or model) of a three-dimensional scene/object? In particular, questions surrounding the nature of physical reality remain central to the field of perspective. The degree of correspondence with reality, and the inherent limitation(s) in this respect of perspective views/images are much debated.

Technical Perspective refers to the process/results of probing a spatial reality to produce an accurate image or ‘systematised’ representation of said reality. Patently, and regardless of type, perspective is an abstraction of reality. Perspective is a halfway station where geometry and physical reality meet—it is a link between the ideal and the actual. Hence, our views of reality are limited because data is inevitably lost while capturing visual details of, plus analysing/interpreting, a spatial scene/object.

Assessing the degree of reality correspondence achieved with any perspective image, relates to the ‘objective’ factors of vision/optics/geometry, plus ‘subjective’ elements from vision/philosophy/psychology. Unfortunately, perspective takes us only so far while comprehending physical reality. We must apply logic, scientific knowledge, contextual factors, and data from experience, to correctly and unambiguously interpret perspective views/images


Perspective Research 

Perspective has a rich history and has been diligently studied for more than 500 years. For example, our Bibliography of Perspective lists 15,000 publications on the subject, suggesting a vast undercurrent of complexity.

One might suppose that the sources, theory and methods of perspective are well-understood today and that further research into perspective would not be necessary. However, such is not the case because the field of Technical Perspective contains many unexplained facts, perplexing mysteries, and exciting possibilities.

The basic principles and techniques of Graphical Perspective have been established (for example); but there are many other classes of perspective that remain largely unexplored. Perspective is a fast-developing field with modern application areas that are predicated on perspective-related research and development activity.

In truth, much is unknown, and many questions remain unaddressed.


Fundamental areas of inquiry:

  • Space/time: nature of, underlying geometry, number of dimensions, etc.
  • Reality: accurate mapping of spatial forms/structures. Systematically model how perspective involves different levels of abstraction and hence varying degree(s) of correspondence with spatial reality. Needed are systematic techniques to reverse engineer a correct model of a spatial scene/object using the inherently reduced amount of visual information available from a perspective image. Patently such an ‘inverse perspective’ procedure is not always possible (on a particular occasion). The perspective image/view may not contain sufficient visual information to reconstruct all desirable aspects of a spatial scene/object. Nevertheless, a key perspective goal remains accuracy in prescribing/modelling spatial reality.
  • Mechanisms of human vision: perceptive processes, binocular vision, etc.
  • Perspective Phenomena: identify, map, classify, and unify all visual facets.
  • Perspective Methods, Products, Functions, Applications: identify, link, and systemise/generalise the various operations, processes, outcomes, and purposes, of all categories/forms of perspective.
  • Categories of perspective: theory of types, objective/subjective methods. **
  • Origins of perspective: map the various geometrical and optical underpinnings.
  • Nature of spatial form: understand and systematically model, spatial reality: role of analytic, descriptive, projective and fractal geometries.
  • Shape Grammars: understand and systematically model, the apparent transformations of object shape with viewing position and scale. Link to Perspective Categories, Methods, Forms etc.
  • Certification of vision: Quest for certification of sight, measurement, and representation, whereby we make accurate views, maps, and models. *
  • Powers of Ten (continuum of visual scales): Systematically explore/represent/understand the complex relations between shape/appearance and form/structure at different magnifications; whereby a continuum exists that relates changes in scale with the transformation of shape for object/scene boundaries/forms/structures.
  • Levels of Abstraction: systematically model how perspective involves more than copying the physical world, because it applies equally to different levels of abstraction and serves as a bridge between the concreteness of nature and abstractions of mathematics. *
  • Computer Vision (spatial + semantic mapping using visual comprehension model): New perspective techniques to enable the development of an embodied Artificial Intelligence (AI) that correctly perceives the optical world in all of its visual complexity, ambiguity, and variety.
  • Multi-scale, Multi-view, Multi-time perspective(s): how to attain multi-scale/view/time perspectives, using global synthesis and indexed lookup. **
  • Mapping of natural space with optical, visual, geometrical and represented space(s): Find ways to circumvent the equivalence problem whereby different 3D shapes viewed from different angles/locations, can produce the same optical image shape. Partial solutions using Ludo Geometrico, contextual features, and changing Visual Field (ref. J. Gibson). *
  • Unification of multiple perspectives: understand how the human mind achieves multiple viewpoint/scale/time correspondence and replicate with systems/automation.
  • Multi-layer / Transparent Perspectives: how to systematically look inside/through opaque objects/scenes and combine/link/orient/navigate: Multi-view, Multi-scale and Multi-time perspectives.
  • Visual Context, Way-finding and Navigation: Contextualising Instruments are automatically overlaid onto views/images, for example: Maps, Windows, Scales/Meters, Throttles, Steering-Wheels, etc.
  • Hypermedia / Hypergrams: how to achieve Focus + Context within perspective views/images; using Hyper-Links, Forward / Back / Omni / Manifold-Links. Visual organisation and rapid exploration of: Levels / Magnifications / Minifications / Spans and Scales of Knowledge, Facetted Classification, etc.
  • Instrument Perspective: Ongoing research across multiple fields to develop novel devices with improved perspective-related capabilities.
  • Media Perspective: New forms to enable accurate viewing, prescribing, matching, modelling, exploring, representing, mixing, and cross-matching images of the physical world. 

Theoretical needs (substance or definition problems):

  • Nature of perspective (convention or not – degrees of visual ‘reality’). *
  • Taxonomic tree of all perspective types (ref. a new ontological theory). **
  • Database of standard Object Forms, link to Image Forms (AI database).
  • Database of standard Scene Geometries, link to Image Forms (AI database).
  • Lexicon of integrating definitions, explanations, principles and methods. *
  • History of perspective, links to history of vision/optics/representation. *
  • Identify key visual building-blocks, shape grammars (Ludo Geometrico).
  • Explain origins of perspective (ref: world view, workshop practice, architecture, ground/plan method, surveying, cartography, astronomy). **

Theoretical needs (function or relational problems):

  • Universal theory/method: combine all perspective types into a single model. *
  • Reconciliation of the different categories of space with perspective. *
  • Applications of perspective, foundational mapping for other subjects. *
  • Relations between analytic, descriptive, projective and fractal geometries. *
  • Account for apparent failure of distance/size laws (Multi-scale). **
  • All views embody transformations of form, unify/systematise (Multi-view). **
  • Static views ignore dimension of time, reconcile (Multi-time). *

Practical needs (sample):

  • Vision: vastly expand the field/range/depth of human vision.
  • Scale: Mapping, linkage and indexing of macroscopic, microscopic and nanoscopic worlds, leading to mastery of the environment on all scales.
  • Time: Capture/link/explore views of reality using systemised time-flows. 
  • Visual Encyclopaedia: a Universal Knowledge Machine with contextualising instruments and continuous transitions between locations/scales/times, plus easy way-finding to any item/relation/pattern on the macrocosm/microcosm. *
  • Integrated perspective(s): universal media format (+ metadata) to index, link, and explore all the world’s images (stationary/moving images, 2D, 3D, etc). *
  • Structure in Art and Science: geometrisation of natural and built worlds.
  • Language of Vision: varied application(s) of human vision, eyesight manual. *
  • Art and Mathematics: linkages, euclidean and non-euclidean spaces etc.
  • Modules / Symmetry / Patterns: classify/analyse/link all of the visual dimensions of nature; identify/explore synergetic, parallel, and hierarchical structures; move through various analytical levels (natural, optical, visual, geometrical, represented spaces etc).
  • Computer/Robot Vision (analytical observation of past and present; with associated future predictions): develop new perspective methods to enable an AI to observe a spatial scene systematically while correctly identifying relevant living beings, objects, and related processes/activities. Produce a real-time ‘event model’ of possible future happenings, enabling the AI to predict outcomes (much like a human).
  • Visual User Interface: navigate the different layers of abstraction from ideas to physical objects in all their layers of magnification (and combination / abstraction). Universals to particulars, wholes, parts, and relations few and many, scales big and small etc. *
  • Merging and correspondence of different perspectives: how to achieve accurate indexing/linkages with smooth overlays and controlled transitions (use transparency and/or 3D geometry?).
  • Mapped/decoded perspective(s): universal image format enables a systematic mapping between physical, optical, visual, geometrical, graphic, and semantic space(s). Each image frame (2D/3D) contains a scaleometer that allows the user to select a scene voxel (3D spatial region), and quantify its true position, shape, and size (ref. scale in 2 senses: spatial extent, resolution). Automatic decoding of 2D view to 3D geometry by modelling using shape grammars plus multi-view perspective [ludo geometrico to identify, visualise, and freely explore the key building blocks of reality]. *
  • Hypergrams: data-rich media that may be explored freely or queried in stylised ways; and that can be arranged and linked in multiple ways. **
  • Virtual Reality: VR, AR, MR, XR: dynamism of egocentric/exocentric, inner/outer, ways to navigate the different levels of abstraction, scale, etc. *

PRC project work: * started, ** ongoing, *** complete.


Patently our list of perspective-related problems is incomplete. In addition, the task of finding solutions to some of the grander questions is monumental, and lies far beyond the capabilities of any one organisation, university, or scientific institution. Indeed, we might have to wait for the emergence of a new era before work even begins (on certain problems). Cross your fingers.


Classification of Perspective

If perspective is to be recognised as a distinct field, then to which subject class does it belong? Should we ascribe it as an art, science, or else a practical discipline?

Professor KIm Veltman makes a salient comment in this respect:


From the outset, the classification of perspective posed problems. Etymologically it was linked with optics, which could not be classed simply. Historically it was linked with architecture, which equally eluded simple classification. By the nineteenth century the nature of the problem began to come into focus. Systems of classification had forged clear distinctions between (subjective) art and (objective) science, as well as between (theoretical) science and (practical) technology. Perspective had the embarrassing characteristic of belonging clearly to all of these. It belonged to art, because it created spatial effects in paintings and it was accordingly classed under drawing. At the same time its theoretical principles were so clearly connected with the mathematical projections underlying scientific demonstrations, that it came to be listed under descriptive geometry. Finally, it also involved instruments, such that it was also classed under technology. 

The Encyclopedia of Perspective: Volume 1 [Chapter 4, p. 193] by Kim Veltman.

Perspective is a science. But it is a science that involves multiple disciplines such as physics (space/time), optics, geometry, human vision, engineering drawing, mathematics, and computing, etc. Each area consists of both theory and practice, and our new perspective science must take everything in its stride without missing a beat (unambiguously). Desired is to possess all of the logic, and hence predictive power, of true science.

Perspective is also an art. Patently, perspective, being concerned with appearance and representation, has had a strong influence on all aspects of the visual and graphic arts (drawing, painting, sculpture), the plastic arts (sculpture, modelling), the decorative arts (furniture design, mosaics), the performing arts (theatre, dance, music), and architecture (environmental design).

Perspective is also a technology. Whereby optical, matching and surveying instruments enable humans to probe dimensional reality and to obtain accurate views, images, models, and measurements. Perspective technology has been central to the development of many other technologies, including photography, cinema, geographical information systems (GIS), global positioning systems (GPS), virtual reality (VR), computer graphics (CG), computer-generated imagery (CGI), computer vision, robotics, etc.

On this site, we shall explore all of the different classes, facets, and applications of perspective; while following our primary goal of unifying all perspective knowledge into a single framework.


Perspective and the Two Cultures

We have argued for the need to establish perspective as a new subject discipline, hopefully to enable focussed development of subject matter, and hence to foster rapid and fundamental progress in this key area. But there is another compelling reason why perspective knowledge must be gathered together, and then integrated into a single subject framework, and this relates to a well-known cultural dilemma.

Patently, establishing perspective as new subject discipline is a highly ambitious goal that involves many difficulties—including problems emanating from artistic, scientific and technical domains. But perhaps one of the biggest blockages to progress in perspective knowledge is cultural, as explained by Sir C.P. Snow in his 1959 book ‘The Two Cultures and Scientific Revolution’. Whereby the science and humanities have become split into ‘two cultures’; and that division has been a major handicap to both in solving the world’s problems. 

If Dr Snow is correct—and much evidence says that he is—then our call to establish a separate subject discipline for perspective is also correct, especially given the tremendous number of relationships, and interrelations of perspective across art, science, technology, and culture. Perspective seems to be a special case in this respect; because it is deeply embedded in all of the various sub-disciplines of each subject; and it is difficult to find any visual/imaging/representation topic that is not ‘perspectival’ in one way or another.

Perspective is such a vast, broad, and profoundly influential topic that it should be taught as a distinct subject in schools, colleges, and universities. Whereby perspective is the very definition of an interdisciplinary subject, with countless sources, links, and fundamental relations penetrating to the core of key phenomena in the arts, sciences, culture, and technology.

Hopefully perspective can, at last, take its rightful place as a leading subject discipline, being classed as a legitimate field in its own right. QED.