The Semiology of Silhouettes and related terms:
The Occluding Contour is not the Silhouette - a justification
© Mahes Visvalingam, September 2002

CONTENTS

• Introduction
• Meanings pertaining to usages
• An analysis of defining properties
• Silhouettes and surfaces
• Conclusion and Summary

 This note, like the foreword, will be revised into a paper for the Working Group on Cartosemiotics of the ICA Commission on Theoretical Issues and Definitions. It elaborates on themes introduced in the foreword in order to :

1. assess the proposition that The Occluding Contour is not the Silhouette.  It does so by analysing the meanings of the two terms as established by usages;
2. identify some defining  properties of the two conceptual entities, ignoring attributes pertaining to depiction, to establish the nature of the relationships between them;
3. consider some functions of these two conceptual entities within terrain visualisation.
4. put forward some proposals for consideration.

Let us first consider how the meanings of the terms silhouette and occluding contour have changed over time.

• M Silhouette's outlines
  It is quite likely that M Silhouette cut out the outlines from drawings rather than the shadows of subjects (see Courtney, 4 Sep 02).  His silhouette acts as a signifier; the referent being M Silhouette's conception of that person's profile.  So, the silhouette does not refer to the person directly - or his/her shadow outline - only M Silhouette's conception of him.  The silhouette functions as a sign because of the conscious/subconscious inferences of others.  Such inferences may include :
  • the subconscious tendency to see forms as objects.  The Rorschach ink blot personality test is based on the assumption that perceptual and personality differences tend to affect how and what we see in an ink blot.  Previous experience is important to recognition and naming.
  • the capacity, because of shared conceptions based on common experience, to recognise the image of the person M Silhouette had in mind, as well as perceive his other intentions.

  The silhouette does this by abstracting and denoting the distinctive features of the person as known rather than as seen, and moreover, and by connoting other (perhaps emotive) meanings intended by M Silhouette.   In this sense, the silhouette is like a caricature - it is the physical counterpart (output) of a psychological construction (process). 
   

• Dictionary definitions refer to the outlines of objects - some go on to use the shadow puppet analogy.  They tend to focus on the description of the outcome rather than on the producer's intentions; i.e. on the output rather than the process. 
   
• Illusory occluding contours
  The brain has an innate automatic tendency to group and structure input.  Even differing symbols for zero dimensional points are grouped into one dimensional lines.  Similarly, vivid two-dimensional occluding surfaces are projected to group disjoint marks and infer depth relationships in 2.5D.  It is generally assumed that the illusory contour belongs to the occluding surface - this is subject to closer scrutiny below.
   
• Marr (1982, p 218) stated that "An occluding contour is simply a contour that marks a discontinuity in depth, and it usually corresponds to the silhouette of an object as seen in a two-dimensional projection".   He states (p 218) that he became interested in occluding contours from the observation that ... that when we look at the silhouettes in Picasso's Rites of Spring, we perceive them in terms of very particular 3D shapes. 
  
  He then explored the constraining assumptions which encourages us to see the 2D silhouette as a 3D form.  On p 219, he uses a drawing of a vase to propose a few assumptions.  One constraint specifies the use of an orthographic projection and rules out perspective transformation.  Orthographic projections are widely used in cartography and technical (e.g. engineering, architectural) drawings.  This assumption entails the use of a constant viewing vector to calculate the points of occlusion.  Marr argued that if we deviate from an orthographic projection, we may be misled by the occluding contour.  Gestalt psychologists had already noted why there is a tendency to interpret the hexagonal outline of a cube, seen corner to corner, as a 2D figure; additional cognitive effort is needed to see it as the outline of a cube.  Historians of art have also pointed out why artists deviate from linear perspective to convey true form, e.g. use of a circle even when the outline of a sphere projects an ellipse.
  
  Marr was therefore inspired by Picasso's creative silhouettes, but then went on to think about them, for computational purposes, as occluding contours obtained under specific conditions, not all of which are mentioned here.  He often used silhouette in preference to occluding contour, when the relationship between them is only one of correspondence as he noted at the outset.  The former serves a communicative intention while the latter serves as a truth condition or axiom for his theories.  This appears to be the origin of the confusion.
   
• NPAR researchers also use the term silhouette when they mean occluding contour.  However, they have removed some of Marr's assumptions and admitted any point of view as well as any projective transformation.  Also, like cartographers, they explicitly admit internal contours and not just the circumscribing outline.   The silhouette is the outcome of a mathematical process; it has various operational definitions.  The silhouette as the edge between front-facing and back-facing polygons is the operational definition normally used with polyhedral models (see Haines, 15 Sep 02).  Operational definitions can be scrutinised later in a separate thread.

An analysis  of defining properties

Since the original meaning of silhouette refers to a constructed entity, there is no need for a qualifying adjective, such as illusory or fictional since it is misleading.  It would be simpler if we could all agree to use the term silhouette for the mental construct and the term occluding contour for the physical phenomenon.  Their physical expressions may be very similar and sometimes identical but they are distinctly different conceptual entities.  While awaiting standardisation, I will use these meanings.  The deferred task of definition will be made easier if we can list some of the defining properties which distinguish between the various types of entities we have encountered up to now.

As I see it, the entities I have considered so far seem to belong to a super class called V-outlines ( we can call it anything we choose later on).  V-outlines are a subclass of entities which are distinguished by the property of being view-centred.  The three basic types, namely occluding contours, illusory occluding contours and silhouettes, belong to this super class.  I suggest that V-outlines (rather than silhouettes) is the class to be distinguished from others, such as creases.  I will just focus the remaining exploration on V-outlines, and will treat the other classes in a separate note.

Occluding contours, as physical phenomena, may be mathematically formulated from given inputs (the 3D model and  view) to trace the contour in 3D metric space.  This basic type denotes the fact that occlusion is present - speedy and effective rendering poses a problem and is the subject of research - but this can be explored in a separate thread.  The occluding contour may not always be sufficient for recognition. Marr's occluding contour is a sub-type of this class; it is a theoretical construct with an associated operational definition. 

Illusory occluding contours seem like their physical counterparts but they are the result of an involuntary psychological projection which organises the marks into a 2.5D structure, which only provides ordinal or topological information.  The psychological projection is believed to be due to inborn concepts of geometric form and the continuity of good form.  These virtual contours imply an organisation.

Similarly, silhouettes are interpretations of physical forms,  based on other types of shared mental concepts.  These concepts may relate to subconscious reactions (as in aesthetics) or learnt associations (as in cartographic depiction).  The signs are designed  to connote specific aspects of the portrayed forms, to facilitate the recognition, and indicate their interpositions.  Metric information is compromised to provide semi-iconic and topological cues.  

There is a need for both occluding contours and silhouettes in Digital Cartography as we shall note next.

The occluding contour is clearly important in some types of terrain visualisation, e.g. strategic military planning and environmental impact analysis.  Traditionally, these applications relied on planar visibility maps based on graphical/metric analysis.  Most examples, including Marr's, use solid objects to illustrate the concept of the occluding contour.  The (closed) occluding contour of such objects is taken to demarcate the extent of the solid object.  However, this is not its generic property.  For the occluding contour does not demarcate the limits of occluding forms in a surface, such as landforms.  It only delimits the frontal limits of occluded zones, which shrink as the viewpoint is raised in oblique map like views to reveal more and more of the form's extent.  The front no longer serves to portray the landforms, nor indicate their logical arrangement in space.  Silhouettes are abstracted (not totally contrived) to play this role.  The silhouette may include occluding contours, but it does not imply occlusion throughout its length.  So, the internal silhouettes within a surface relates to a complex entity which may be an occluding contour and/or silhouette, as the situation warrants and demands.  This representation allows for multiple inheritance. 

Conclusion and Summary

Just as the centreline of a road abstracts and stands for the irregular shape of the road, the silhouette of a hill functions as a 2D surrogate for the volumetric object.  Like the centreline, it provides positional information and conveys the necessary shape information.  But the centrelines of highly irregular topographic forms are not the mathematical median lines.  Like the centreline,  the silhouette of a hill is part fiction.  It must be contrived to represent an instance of the abstract type it denotes.  Such transformations draw on systematised geomorphological knowledge on landform types and their configurations.  Silhouettes are the graphic counterparts of the textual vocabulary of forms.

In this note,  I have analysed some of the entities which appear in sketches of terrain.  I could have labelled them A, B etc.  but have chosen to use some provisional names for the sake of readability even if not clarity.  I have provided a logical justification for distinguishing between occluding contours and silhouettes.   Both these entities fall within the class of V-outlines.  The internal silhouettes of surfaces belong to a complex type which has a real and an imaginary part.   Posited between physical reality and psychological/intellectual abstraction, the concept of the silhouette has drawn on the metaphor of the occluding contour - it is not just the occluding contour.