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.

1 INTRODUCTION

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

learning.”

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

https://orcid.org/0000-0001-8991-0999

https://orcid.org/0000-0002-0521-1443

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,

etc.).

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

415-422

ISBN: 978-989-758-488-6

415

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.

2 EXAMPLE (CASE STUDY)

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

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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.

Source: https://www.lakemeadcruises.com/discover/area-

maps/getting-here/.

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.

3 NATURAL VISUAL PATTERNS

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-

Place.com, 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

http://www.imageprocessingplace.com/root_files_V3/ima

ge_databases.htm.

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

417

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-

ca.com/scienectrspectrum.

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.

4 SYMBOLIC VISUAL

PATTERNS

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

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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.

https://www.itu.int/net/itut/sigdb/genimage/test24.htm.

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

responsibilities.

5 NATURAL VS SYMBOLIC

PATTERN RECOGNITION

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:

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419

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

patterns.

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

insights.

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

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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

https://www.dais.unive.it/sspr2020/call-for-papers/.

6 CONCLUSIONS

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

patterns.

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