Imaging Reality and Abstraction
an Exploration of Natural and Symbolic Patterns
Alexandra Branzan Albu
and George Nagy
Electrical and Computer Engineering, University of Victoria, Victoria, BC, Canada
Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, Troy, NY, U.S.A.
Keywords: Physical Scenes, Symbols, Perception, Cognition.
Abstract: Understanding visual symbols is a strictly human skill, as opposed to comprehending natural scenes—which
is an essential survival skill, common to many species. As an illustration of the natural vs. symbolic dichotomy,
selective features are computed for differentiating a satellite photograph from a map of the same geographical
region. Images of physical scenes /objects are currently captured in all parts of the electromagnetic spectrum.
Symbols, whether produced by man or machine, are almost always imaged in the visible range. Although
natural and symbolic images differ in many ways, there is no universal set of differentiating characteristics.
With respect to the traditional branches of pattern recognition, it is tempting to suggest that statistical, neural
network and genetic/evolutionary pattern recognition methods are eminently suitable for images of scenes
and simple symbols, whereas structural and syntactic approaches are best for more complex, composite
graphical symbols.
Patterns are arrangements of perceptible elements
which play a critical role in human cognition
processes, such as visualization, memorization and
decision-making. Furthermore, there is evidence that
humans learn abstract concepts such as mathematical
ones using pattern recognition techniques (Mulligan
and Mitchelmore, 2009). As stated by Warren (2005),
“The power of mathematics lies in relations and
transformations which give rise to patterns and
generalizations. Abstracting patterns is the basis of
structural knowledge, the goal of mathematics
From an evolutionary viewpoint, humans first
dealt with natural patterns, informed by their direct
interactions with the environment. A small amount of
“relevant” information is extracted from a large,
continuous influx of data and encoded into a
persistent mental structure called pattern (Del Viva,
2013). While this process is not limited to visual data
(as all sensory modalities may contribute to the
formation of one pattern) our paper focuses on visual
patterns only. This is justified by the dominance of
the visual perception (Stokes and Biggs, 2004), as
well as by the need to establish reasonable boundaries
for this exploratory journey.
Natural pattern processing is a survival skill
shared with other primates, allowing for generating
cognitive maps of the physical environment, which
encode locations of food sources, potential predators
and navigation landmarks (Mattson, 2014).
Symbolic patterns are specific to humans.
Symbols denote ‘something which stands for
something else’ (a meaning first recorded in ‘Faerie
Queene’ in 1590), thus they are representations of
representations. The processing of symbolic patterns
forms the basis of “unique features of the human brain
including intelligence, language, imagination,
invention, and the belief in imaginary entities such as
ghosts and gods” (Mattson, 2014). Some simple types
of symbolic patterns are embedded in our
environment (for instance, traffic signs and pavement
markings). Others form the basis of written language
and communication (letters, digits, flowcharts, tables,
Semiotics explores the connection between signs,
symbols and significance. From a semiotic
Albu, A. and Nagy, G.
Imaging Reality and Abstraction an Exploration of Natural and Symbolic Patterns.
DOI: 10.5220/0010295704150422
In Proceedings of the 16th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2021) - Volume 4: VISAPP, pages
ISBN: 978-989-758-488-6
2021 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
perspective, natural images fall into the category of
iconic signs. Symbolic images are symbolic
(arbitrary) signs, regarded as conventional and
culture-specific mems for conveying concepts. These
definitions do not bear directly on algorithms,
features and pixels. Since natural and symbolic
pattern processing do exhibit different neural
mechanisms (Mattson, 2014), it seems appropriate to
investigate how computer vision deals with these two
meta-categories of patterns.
Among the most important shared tasks are
segmentation and classification. Other common
objectives are visualization, e.g. depth-from-shading
for natural and OCR results for symbolic, and author
identification or counterfeit/plagiarism detection of
paintings (natural) and manuscripts (symbolic). An
example of a hybrid (natural and symbolic) pattern
recognition task would be a self-driving car reading
all the highway signs, as well as detecting vehicles
and pedestrians.
Although art critics may object, our perspective
precludes attaching symbolism to a still life or an
abstract painting. But Leonardo da Vinci’s sketches
of muscles and catapults and Edward Tufte’s artful
visual displays of quantitative information (in his
eponymous book) are symbolic. Artistic applications
of image processing, such as photomosaics, are
skillfully explored by Tanimoto (2012).
The remainder of this paper is structured as
follows. Section II presents a case study comparing a
natural image with its symbolic representation.
Sections III and IV discuss characteristics of natural
and symbolic patterns respectively. Section V
examines how pattern recognition techniques align
with the natural/symbolic realms. Section VI
summarizes our findings and concludes this work.
Two images of the Hoover Dam area in Fig. 2.1 are
chosen to illustrate the proposed dichotomy. They
exemplify the potentially extreme difference between
natural and symbolic images. Their respective sizes
are 1050×1600 and 895×1433 pixels, thus much
detail is lost in the figures.
The features below, extracted with MATLAB
2016a, show some noticeable differences, which may
be quantified in many possible ways. Any ICPR
participant could propose other equally plausible
features. However, only experimentation on large and
diverse data sets could provide statistically significant
evidence that the postulated subpopulations can be
objectively and accurately discriminated. Almost no
sample datasets are currently available for such
experimentation (Nayef 2019). With a few exceptions
(e.g. scene text), most of the available collections fall
squarely into relatively homogenous subdomains of
either Natural or Symbolic images.
Symbolic images tend to consist of high-contrast
curve segments, glyphs (graphical symbols) and
regions of nearly constant color because drawings and
symbols have been traced for millennia using a stylus,
and printing has loosely mimicked this process.
Contrast helps perception; glyphs encode
information. Both foreground and background of
symbolic documents typically exhibit locally uniform
reflectance. In natural images the distinction between
foreground and background is either arbitrary,
application-dependent, or refers to distance from the
imaging instrument.
The logarithmic grayscale histogram (Fig. 2. 2)
provides a measure of contrast. Documents usually
show high peaks near opposite ends of the gray-scale,
with intermediate values only at edge pixels. The
proportion of edge pixels depends, of course, on the
spatial sampling frequency and the point-spread
function. In our map, the only two sharp peaks are
near each other because the intensity of the water and
land areas is almost the same. The satellite image has
a wider peak for Mead Lake, and a narrow white peak
due to the superimposed labels. The rest of the image
has a continuous albedo distribution.
Fig. 2.3 is the 2-D Fourier transforms of the
images. Strong orthogonal components are typical of
document images because of their rectilinear print
layout, but much less so of line drawings and maps.
The small higher-frequency components of our map
fall outside the range of FFT coefficients visible in
the figure.
In addition to extracting the intensity distribution,
we have chosen for this illustration features that are
sensitive to local variability like edges. Fig. 2.4
indicates that the natural image has a far greater
density of Canny edge features than the symbolic
image (Canny, 1986). Although their sizes differ by
only 30%, the edge count is 251,332 vs. 14, 320. The
superimposed geodetics are detected in the satellite
image, and most of road network, barely visible in
Fig. 2.1, on the map. The FAST features of Fig. 2.5,
extracted with the popular algorithm proposed by
Rosten and Drummond (2005), exhibit a similar
configuration (8316 vs. 353 corners).
None of the above features suffice by themselves
for differentiating natural from symbolic images. For
example, the snow-covered shores of unfrozen lakes
offer high contrast like printed pages, fingerprints
abound in curvilinear features as do caricatures, and
VISAPP 2021 - 16th International Conference on Computer Vision Theory and Applications
both documents (symbolic) and aerial photos of cities
(natural), exhibit a profusion of corners and edges.
Furthermore, many of the above features are class-
conditionally statistically dependent. Automated
classification would require many more features and
a highly nonlinear classifier.
Figure 2.1: Examples of a natural and of a symbolic image.
Figure 2.2: Logarithmic intensity histogram.
Figure: 2.3: 2-D Fast Fourier Transforms (FFTs).
Figure 2.4: Canny edges.
Figure 2.5: FAST features.
Fig. 3.1 is a montage of photographs that often appear
in image processing research and illustrate the variety
of aspects (color, contrast, level of detail) that affect
processing. The source site, ImageProcessing-, also offers free downloads of many larger
image collections. Although Fig. 3.1 is drawn from
the visible regions of the spectrum, natural images
span almost twenty orders of magnitude in
wavelength or frequency (Fig. 3.2). Regardless of
their source spectrum, they can be rendered to be
visible at an appropriate scale for human inspection.
Figure 3.1: Standard (natural) test images
Photography gained mass appeal soon after its
invention early in the 19th Century. It became
ubiquitous after digital cameras were grafted onto cell
phone and photo-sharing social media applications,
such as Facebook and Instagram, gained wide
popularity. An early quantitative application was
cartography with photographs from balloons
(Redmond, retrieved 2020). Natural Image
Processing (IP) started in the 1950’s with the analysis
of photographs of the tracks of elementary particles
in spark, bubble and cloud chambers. Algorithmic
path tracking was a disruptive technology, as it
displaced the dozens of operators who had traced the
tracks on projection screens. Computer Cartography
and Geographic Information Systems (now
Geospatial Data Processing) eventually grew to
encompass earth observation and weather satellites
that currently produce over one million images per
day. Many earth and ocean observation facilities
produce a huge amount of visual data, which exhibits
typical Big Data problems (storage, curation,
provenance, manipulation).
Imaging Reality and Abstraction an Exploration of Natural and Symbolic Patterns
Cosmic-ray muography (muon tomography)
Atomic force and electron microscopy
Medical and industrial radiography (X-rays)
Industrial surface inspection, fluorography (UV)
Photography, microscopy, telescopy (visible light)
Night vision, thermography, FLIR, LIDAR (IR)
Weather, traffic and military RADAR (microwaves)
Radio-telescopy, MRI (radio frequency)
Medical and industrial ultrasound
Figure 3.2: Natural images span the entire electromagnetic and sound spectra. https://www.britannice/elomagnetic-
Modalities outside the narrow visible range reveal
details varying in scale from nanometers for atomic
lattices, to micrometers for biological cells, at
“human scale” for animals, plants and organs, and
light years for astronomical observations. A single
infrared, visible or radar image for automotive, ship
and aircraft applications may cover an area with a
diameter of a few meters or hundreds of kilometers.
Thus some Natural IP modalities have extended our
understanding of the world far beyond the original
goals inherited from animal vision of wayfinding and
navigation in environments constrained by our
limited visual abilities. Moreover, some Natural IP
techniques allow us to gain not only structural, but
also phenomenological insights. Many striking
examples of such techniques come from medical
imaging, where modalities such as computed
tomography (CT), magnetic resonance imaging
(MRI), Doppler ultrasound, scintigraphy, single
photon emission computed tomography (SPECT) and
positron emission tomography (PET), rendered in the
visible spectrum, are used to examine physiological
and metabolic phenomena.
Scientific and industrial Natural IP often includes
input from non-imaging sensors. Furthermore, the
most interesting applications require processing
groups of images. The grouping may be based on
spatial contiguity (mosaicking or slices of a 3-D
volume), sparse time sequences (monitoring the
growth of vegetation or beach erosion), or movie-rate
sequences (motion from video). Natural IP now
includes 2 1/2 D, 3D, and 4D, grayscale, color, and
multispectral images. For example, sequences of high
energy X-rays (from a synchrotron) have been used
to study crack propagation in concrete under load
(Landis et al., 2007). Cosmic-ray muography, first
used to map hidden chambers in pyramids (Alvarez et
al., 1970), is used for inspecting nuclear waste sites
Linkeos Technology Ltd, 2020).
Current applications include video from multiple
cameras for analyzing traffic, athletic events, and
crowd activity in premises with high security
concerns. Natural IP is gradually merging into
Computer Vision because images from robots,
drones, self-driving cars and wearable cameras must
accommodate variable lighting and relative motion
between multiple sensors and targets. As we will see
in the next section, Document Analysis is moving in
an entirely different direction, shifting emphasis from
images to computer-native text and graphics.
Most symbolic images are, by definition, documents
(or parts of documents). This overarching category
includes books, magazines, newspapers, handwritten
letters and notes, plans and diagrams, musical scores,
tables, maps, charts and graphs.
The first patents on Optical Character
Recognition (OCR) were filed more than one hundred
years ago, but until the 1960s OCR had to run on
hardwired machines because computers took a long
time to process even a 256 x 256 image. Figure 4.1
shows postage stamps from the CCITT test sequence
prepared for the standardization of facsimile in the
1970’s. They are available full-size at the website in
the figure caption (of the International
Telecommunications Union) which also houses many
excellent sets of test data and calibration charts with
complete metadata. Some (like the graph and the
circuit diagram) may have been originally intended
for visualization.
Many applications that fueled optical character
recognition and document image processing in the
last century have virtually disappeared (Nagy, 2016).
The list includes postal address reading, bank check
reading, and invoice image processing. Forensic
VISAPP 2021 - 16th International Conference on Computer Vision Theory and Applications
document analysis is giving way to white-hat hacking
Al-Muhammed and Daraiseh, 2018)
. Research on
document analysis is shifting from processing images
to manipulating documents already in a computer-
readable symbolic format such as plain text or XM.
Current objectives include deep document
understanding, search, summarization, translation,
information extraction, table analysis, and sketch
understanding (Nagy, 2016).
Figure 4.1: Symbolic test images for evaluating
compression algorithms for facsimile transmission.
Until the invention of the printing press, every
image could be traced to the person or group who
prepared (or copied) it. The largest libraries
contained only a few thousand items. With the advent
of printing and lithography, the direct connection
between the image and its creator was lost. The
number of physical images grew exponentially
because each reproduction could be replicated at will.
By the end of the last century, public and university
libraries (and museums) had to store much of their
holdings at remote locations. Progress in digitization
and storage technology is now impelling libraries to
move their shelves to a Cloud.
We are now on the threshold of losing even the
indirect link from image to creator (author, printer,
artist, draftsman, or composer). Computers can
dissect and reassemble symbolic images in myriad
ways. The provenance of the whole or of parts thereof
becomes untraceable. Furthermore, computers
routinely convert signals from measuring instruments
into symbolic images. More and more symbolic
images have no human genesis, which is worrisome
since computer-generated semantics may be arbitrary
and not consistent with human reasoning, values, and
While recognizing and categorizing patterns is an
essential philosophical endeavor first formulated by
Aristotle (Ammonius, 1991), from a more pragmatic
viewpoint it can be considered as a critical step in
decision-making. Natural and symbolic visual
patterns support, in general, different decision paths.
For instance, recognizing landscape cues supports
wayfinding, while recognizing written words
supports reading and comprehension. A question
arises naturally: for choosing the ‘right’ pattern
recognition technique, does it matter whether patterns
depict some aspect of the natural world or if they
belong to a more abstract (symbolic) realm?
The design of a computational technique for
recognizing visual patterns may start by
contemplating two interrelated questions:
a) what type of data representation is most
relevant for describing the patterns of interest?
b) what formalisms and methodologies are
associated to the data representation?
The answers to these questions lay the
foundations of three main schools of thought
(statistical, structural, and syntactic) in computer-
based pattern recognition (which might or might not
be inspired by biological mechanisms). The
underlying principles are compared below. The
interested reader is referred to Bunke and Riesen
(2012) for more details regarding this comparison.
Statistical pattern recognition represents a given
pattern by a feature vector of fixed length n (i.e., as a
point in an n-dimensional feature space) which
enables the use of a rich arsenal of algorithmic tools
grounded in linear algebra and probability. However,
representing patterns via a simple concatenation of
features has two main limitations, namely:
Imaging Reality and Abstraction an Exploration of Natural and Symbolic Patterns
a) the fixed length constraint, which prevents
tailoring the representation to the complexity of
the pattern;
b) the difficulty of encoding binary or higher-
order relationships that may exist between
different components of the pattern.
Both limitations are elegantly addressed by
structural and syntactic pattern recognition, which
encode patterns using sophisticated paradigms.
Structural techniques are intrinsically associated with
graph-based representations, which allow for
describing patterns by decomposing them into
semantically meaningful parts (primitives) and
describing properties of these parts as node labels,
and inter-part relationships as edges. An illustrative
example of a graph-based approach for architectural
symbol recognition is provided by Llados and
Sanchez (2003).
The syntactic approach to pattern recognition is
inspired by formal language theory, and attempts to
describe a complex pattern by decomposing it into a
set of smaller, simpler patterns, which are connected
via grammatical rules (Searls and Taylor, 1992). It is
thus similar to the structural approach, but it is less
popular because of the difficulty of defining
grammars for parsing visual entities. Some successes
have been reported in early works such as
(O’Gorman, 1988) and (
Ripley and Hjort, 1995).
Structural and syntactic pattern recognition
techniques rely upon rich, complex representations.
This is both a blessing and a curse, since there is little
mathematical structure to support the analysis of such
representations. It becomes thus obvious that
statistical and structural pattern recognition
techniques exhibit complementary strengths and
weaknesses, which has motivated research on
combining data-rich, structural representations with
statistical analysis tools (Bunke and Riesen, 2012).
The deep learning revolution, occurring within the
last decade, has clearly established the dominance of
the statistical school of thought over the other two.
Can deep learning be considered as belonging to
statistical pattern recognition? A positive,
mathematically justified answer to this question is
offered by Ripley and Hjort (1995), who outline two
main paradigms (sampling and diagnostic) for
learning posterior probabilities in pattern recognition.
Core to the deep learning paradigm is the concept of
neural networks, which can be thought as a
generalization of the diagnostic paradigm. This
paradigm learns posterior probabilities directly from
examples in the training set which are similar to the
sample to be recognized. Bishop (2006) also
considers neural networks as efficient models for
statistical pattern recognition, as they provide a
convenient solution to the curse of dimensionality
(Bellman, 1961). This solution formulates the non-
linear mapping function (from the feature space to the
classification space) as a linear combination of non-
linear activation functions (the ‘neurons’).
The appeal of deep learning techniques might be
partially explained by the elimination of the feature
extraction step from traditional statistical pattern
recognition pipelines (i.e., the handcrafting process)
which involved a careful analysis of the dimensions
of variability of the patterns of interest, as well a study
of visual cues used by humans for performing the
same detection/localization/classification task. Deep
learning networks accept image patches as inputs, and
discover not only the mapping from the feature vector
representation to the output, but also the
representation itself; thus, they perform
representation learning (Goodfellow et al., 2016).
This works well for most natural patterns where
image patches of reasonable size are information-
rich. However, some symbolic patterns may consist
of just a few linear/circular segments; this is the case
of symbols composing architectural floor plans
(Rezvanifar et al., 2019). In such cases, examples
from small-sized training datasets do not provide
enough information for a successful learning process.
Yosinski et al. (2014) show that transfer learning
procedures, which allow to learn general features
from base networks trained on rich, generic datasets,
and specific features from target networks and
smaller datasets, yield decreased performance when
the distance between the base task and the target task
increases. This explains, in part, the limited success
of deep learning methods on sparse symbolic
We cannot ignore game-changing results of deep
learning architectures on both natural and symbolic
public datasets (Farabet et al., 2013; LeCun et al.,
1998; LeCun et al., 2015). Deep learning networks
presumably also played a role in digitizing Google
Books, the largest collection of symbols in the word.
However, none of the applications supported by these
public datasets suffer from sparsity of data, such as
the one in (Rezvanifar et al., 2019). The plethora of
labeled and unlabeled training data (sometimes
millions of samples) overcomes any benefit of
syntactic or structural representation of human
To summarize, statistical methods work better for
most natural patterns and simple symbolic patterns
(such as digits/printed or handwritten characters or
musical scores), while structural/syntactic techniques
VISAPP 2021 - 16th International Conference on Computer Vision Theory and Applications
are more suitable for more complex and/or sparse
symbolic patterns. This is, of course, only a starting
point, which is nevertheless useful for pondering the
entire pattern recognition repertoire before delving
into a more nuanced exploration.
Indeed, the boundaries of structural and statistical
approaches are blurring (e.g. probabilistic grammars,
Markov random fields). The recent emergence of
Graph Neural Networks which inject deep learning
into computational graph analysis is of particular
interest (Renton et al., 2009; Battaglia et al., 2018).
Nevertheless, applications (such as multimedia and
document image analysis) relying heavily on
symbolic patterns are still mentioned as belonging to
the area of structural approaches, as shown is the
2020 Call for Papers of the S+SSPR Workshop
We explored some characteristics that can reveal
whether the source of an image is a real-world scene
or an abstract concept. The proposed distinction
between natural and symbolic images focuses
attention on an essential difference between human
and animal cognition and suggests a pathway to
advance the study of both. The distinction also helps
explain why syntactic and structural methods are
seldom applied to scenery and to scientific imaging
(especially beyond the visible spectrum), and the
popularity of statistical and neural network
approaches wherever human annotation becomes
overwhelming. The scarcity of databases of
heterogeneous (symbolic AND natural) image
samples confirms our intuition regarding the
fundamental nature of the distinction.
Our future work will address the differences
within both natural and symbolic images; we intend
to survey image types in computer vision and image
processing literature, which will hopefully clarify
their links to pattern recognition methods.
We also intend to explore interactions and
mappings between natural and symbolic patterns. The
world of visual art (left out of this preliminary
exploration) offers abundant opportunities for
studying how natural scenes are mapped onto more
abstract, symbolic representations. Augmented
reality environments will enable us to look at
symbiotic co-occurrences of natural and symbolic
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