THE DESCRIPTIVE TECHNIQUES FOR IMAGE ANALYSIS
AND RECOGNITION
Igor Gurevich
Dorodnicyn Computing Center, Russian Academy of Sciences, 40 Vavilov str., 119991 Moscow, Russia
Keywords: Image mining, descriptive approach, image algebras, image models, Generative Descriptive Trees.
Abstract: The presentation is devoted to the research of mathematical fundamentals for image analysis and
recognition procedures. The final goal of this research is automated image mining: a) automated design, test
and adaptation of techniques and algorithms for image recognition, estimation and understanding; b)
automated selection of techniques and algorithms for image recognition, estimation and understanding; c)
automated testing of the raw data quality and suitability for solving the image recognition problem. The
main instrument is the Descriptive Approach to Image Analysis, which provides: 1) standardization of
image analysis and recognition problems representation; 2) standardization of a descriptive language for
image analysis and recognition procedures; 3) means to apply common mathematical apparatus for
operations over image analysis and recognition algorithms, and over image models. It is shown also how
and where to link theoretical results in the foundations of image analysis with the techniques used to solve
application problems.
1 INTRODUCTION
Automation of image processing, analysis,
estimating and understanding is one of the crucial
points of theoretical computer science having
decisive importance for applications, in particular,
for diversification of solvable problem types and for
increasing the efficiency of its solving.
The presentation is devoted to the research of
mathematical fundamentals for image analysis and
recognition procedures being conducted previously
in the Scientific Council “Cybernetics” of the
Russian Academy of Sciences, Moscow, Russian
Federation, and currently in the Dorodnicyn
Computing Centre of the Russian Academy of
Sciences, Moscow, Russian Federation.
The final goal of this research is automated
image mining. The main instrument is the
Descriptive Approach to Image Analysis (Gurevich,
1989; 1991), which provides: 1) specialization of
Zhuravlev’s Algebra (Zhuravlev, 1998) for an image
recognition case; 2) standardization of image
analysis and recognition problems representations;
3) standardization of a descriptive language for
image analysis and recognition procedures; 4) means
to apply common mathematical apparatus for
operations over image analysis and recognition
algorithms, and over image models (Gurevich and
Yashina, 2004).
Taking as a strategic goal the automated image
mining it is necessary to provide image analysis
professionals and final users with the following
opportunities:
 automated design, test and adaptation of
techniques and algorithms for image recognition,
estimation and understanding;
 automated selection of techniques and algorithms
for image recognition, estimation and
understanding;
 automated testing of the raw data quality and
suitability for solving the image recognition
problem;
 standard technological schemes for image
recognition, estimation, understanding and
retrieval.
We shall outline the goals of theoretical
development in the framework of the Descriptive
Approach (and image analysis algebraization)
(“What for”), the tool to achieve this goal (“How”),
state of the art in the field (prospective trends),
necessary steps to finalize the Descriptive Approach
(“What to Do or What to be Done”) and the global
problem of an image reduction to a recognizable
form. It will be shown also how and where to link
theoretical results in the foundations of image
223
Gurevich I. (2007).
THE DESCRIPTIVE TECHNIQUES FOR IMAGE ANALYSIS AND RECOGNITION.
In Proceedings of the Second International Conference on Computer Vision Theory and Applications, pages 223-229
DOI: 10.5220/0002071302230229
Copyright
c
 SciTePress

analysis with the techniques used to solve
application problems.
The structure of the paper is as follows:
1. What for
2. How
 The Tool - Descriptive Approach
3. State of the Art:
 Plurality and Fusion
 Multialgorithmic Classifiers
 Multimodel Representations
4. What to Do or What to be Done. Basic Steps:
 Step 1. Mathematical Settings of an Image
Recognition Problem
 Step 2. Image Models
 Step 3. Multimodel Representation of Images
 Step 4. Image Equivalence
 Step 5. Image Metrics
 Step 6. Descriptive Image Algebras
5. Conclusion
 Image Reduction to a Recognizable Form
2 WHAT FOR?
The image analysis and recognition techniques and
tools are destined for solving of the following basic
classes of applied image analysis problems:
1. Image matching for classification with an image,
a set of images and a series of images.
2. Searching an image for some
regularity/irregularity/object/token/fragment/prim
itive of arbitrary or prescribed type/form.
3. Clusterization of an image set.
4. Image segmentation (for homogeneous regions,
groups of objects, selection of features).
5. Automatic selection of image primitives, specific
objects, feature objects, logical and spatial
relations.
6. Image reduction to a recognizable form.
7. Reconstruction and Restoration of missed frames
in an image series and of images by fragments,
primitives, generative procedures and context.
8. Image analysis problem decomposition and
synthesis.
The most important – critical points of an
applied image analysis problem solving are as
follows:
 CPI. Precise setting of a problem (Step 1).
 CPII. Correct and “computable” representation
of raw and processed data for each algorithm
at each stage of processing (Step 2, Step 5).
 CPIII. Automated selection of an algorithm
(Step 1, Step 3, Step 6):
− CPIII-1. Decomposition of the solution process
for main stages (Step 1, Step 6);
− CPIII-2. Indication of the points of potential
improvement of the solution (“branching
points”) (Step 1, Step 6);
− CPIII-3. Collection and application of problem
solving experience (Step 3, Knowledge Base);
− CPIII-4. Selection for each problem solution
stage of basic algorithms, basic operations and
basic models (operands) (Step 6);
− CPIII-5. Classification of the basic elements
(Step 3, thesaurus).
 CPIV. Performance evaluation at each step of
processing and of the solution (Step 2, Step 4,
Step 6).
− CPIV-1. Analysis, estimation and utilization of
the raw data specificity (Step 2);
− CPIV-2. Diversification of mathematical tools
used for performance evaluation (Step 6);
− CPIV-3. Reduction of raw data to the real
requirements of the selected algorithms (Step
4).
The further development of the Descriptive
Approach should provide necessary means for
implementing of these steps. After each Critical
Points in the brackets are indicated the
corresponding “next steps” (the description of the
steps see below).
So, the success of image mining in a whole is
connected with overcoming of the Critical Points in
a following way:
 automated design, test and adaptation of
techniques and algorithms for image
recognition, estimation and understanding
(CPIV);
 automated selection of techniques and
algorithms for image recognition, estimation
and understanding (CPIII);
 automated testing of the raw data quality and
suitability for solving the image recognition
problem (CPII);
 standard technological schemes for image
recognition, estimation, understanding and
retrieval (CPI).
3 HOW?
Mathematical fundamentals for image processing
and image analysis procedures are constructed in the
framework of the Descriptive Approach to Image
Analysis, which provides:
 specialization of Zhuravlev’s Algebra for an
image recognition case (CP1);
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 standardization of image analysis and
recognition problems representation (CP1);
 standardization of a descriptive language for
image analysis and recognition procedures
(CP2);
 means to apply common mathematical
apparatus for operations over image analysis
and recognition algorithms, and over image
models (CPIV).
 The Descriptive Approach is based on:
 descriptive model of image recognition
procedures (CPI);
 image reduction to a recognizable form (CPII);
 image models (CPII);
 algebraization of image mining (CPIII, CPIV);
 generative principle and bases of transforms
and models.
The preliminary condition of algebraization of
image mining is development of formal systems for
image representation and transformation satisfying
to the following conditions: a) each object is a
hierarchical structure constructed by a set of
operations of image algebra (Gurevich and Yashina,
2003) applied to the set of elements of images; b)
the objects are points, sets, models, operations,
morphisms; c) each transform is a hierarchical
structure constructed by a set of operations of image
algebra on the set of basic transforms.
The Descriptive Approach provides construction
and application of two types of such formal systems
- special versions of algebras - image algebras
(CPIII, CPIV) (Ritter and Wilson, 2001) and
descriptive image algebras (CPIII, CPIV) (Gurevich
and Yashina, November 2003; 2003; Gurevich and
Zhuravlev 2002).
Exploitation of the Generative principle and
bases of transforms and models provides for
decomposition of a problem into primitive tasks,
establishing of the correspondence between basic
primitive tasks and basic primitive transforms and
combining of basic algorithms and models.
The corner-stone of the Descriptive Approach is
a model of image recognition procedures (Figure 1).
Figure 1: Descriptive model of image recognition
procedures.
4 STATE OF THE ART
The current trends in image recognition are
connected with plurality and fusion of image
recognition and image data, use of multiple
classifiers and of multiple model representations of
the images under processing. The classical and
modern versions of image recognition schema are
represented in Figure 2 and Figure 3.
5 WHAT TO DO OR WHAT TO
BE DONE
In this section we shall outline the basic “next steps”
necessary to finalize the Descriptive Approach and
indicate what is done and what to be done for each
of the steps. These steps are as follows:
 Step 1. Mathematical Settings of an Image
Recognition Problem (CPI, CPIII-1, CPIII-2);
 Step 2. Image Models (CPII, CPIV-1);
 Step 3. Multiple Model Representation of
Images CPIII-3, CPIII-5);
 Step 4. Image Equivalence (CPIV-3);
 Step 5. Image Metrics (CPII);
 Step 6. Descriptive Image Algebras (CPIII-1,
CPIII-2, CPIII-4, CPIV-2).
5.1 Step 1. Mathematical Settings of an
Image Recognition Problem
Done:
 CPIII-1 - Descriptive Model of Image
Recognition Procedures;
 CPIII-1 - Mathematical Setting of an Image
Recognition Problem. Image Equivalence
Case.
To Be Done:
 CPIII-2 - Establishing of interrelations and
mutual correspondence between image
recognition problem classes and image
equivalence classes;
 CPI - New mathematical settings of an image
recognition problem connected with image
equivalency;
 CPI - New mathematical settings of an image
recognition problem connected with an image
multiple model representation and image data
fusion.
THE DESCRIPTIVE TECHNIQUES FOR IMAGE ANALYSIS AND RECOGNITION
225

Figure 2: Image recognition. Classical case.
Figure 3: Image recognition. General case (multiple classifiers and model plurality).
5.2 Step 2. Image Models
Done:
 CPII - Main types of image models were
introduced and defined;
 CPII - It was shown which types of image
models are generated by the main versions of
descriptive image algebras with one ring.
To Be Done:
 CPIV-1 - Creation of image models catalogue;
 CPIV-1 - Selection and study of basic
operations on image models for different types
of image models (including construction of
bases of operations);
 CPIV-1 - Use of information properties of
images in image models;
 CPIV-1 - Study of multiple model
representations of images.
5.3 Step 3. Multiple Model
Representation of Images
Done:
 CPIII-3 - Generating Descriptive Tree (GDT) -
a new data structure for generation plural
models of an image is introduced.
To Be Done:
 CPIII-5 - to define and to specify GDT;
 CPIII-5 - to set up image recognition problem
using GDT;
 CPIII-5 - to define descriptive image algebra
using GDT;
 CPIII-5 - to construct a descriptive model of
image recognition procedures based on GDT
using;
 CPIII-5 - to select image feature sets for
construction of P-GDT;
 CPIII-5 - to select image transform sets for
construction of T-GDT;
 CPIII-5 - to define and study of criteria for
selection of GDT-primitives.
 An example of GDT is shown in Figure 4.
5.4 Step 4. Image Equivalence
Done:
There were introduced several types of image
equivalence:
 image equivalence based on the groups of
transformations;
 image equivalence directed at the image
recognition task;
 image equivalence with respect to a metric.
To Be Done:
 CPIV-3 - to study image equivalence based on
information properties of an image;
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 CPIV-3 - to define and construct image
equivalence classes using template
(generative) images and transform groups;
 CPIV-3 - to establish and to study links
between image equivalence and image
invariance;
 CPIV-3 - to establish and to study links
between image equivalence and appropriate
types of image models;
 CPIV-3 - to establish and to study links
between image equivalence classes and sets of
basic image transforms.
5.5 Step 5. Image Metrics
To Be Done:
 CPII - to study, to classify, to define
competence domains of pattern recognition
and image analysis metrics;
 CPII - to select workable pattern recognition
and image analysis metrics;
 CPII - to construct and to study new image
analysis-oriented metrics;
 CPII - to define an optimal image recognition-
oriented metric;
 CPII - to construct new image recognition
algorithms on the base of metrics generating
specific image equivalence classes.
5.6 Step 6. Descriptive Image Algebras
Done:
 CPIII-1 - Descriptive Image Algebras (DIA)
with a single ring were defined and studied
(basic DIA);
 CPIII-2 - it was shown which types of image
models are generated by main versions of DIA
with a single ring (Table 1);
 CPIII-4 - the technique for defining and testing
of the necessary and sufficient conditions for
generating DIA with a single ring by a set of
image processing operations were suggested;
 the necessary and sufficient conditions for
generating basic DIA with a single ring were
formulated;
 CPIV-2 - the hierarchical classification of
image algebras was suggested (Figure 5);
 it was proved that the Ritter’s algebra could be
used for construction DIA without a “template
object”.
To Be Done:
 CPIII-1 - to study DIA with a single ring,
whose elements are image models;
 CPIII-2 - to study DIA with several rings (super
algebras);
 CPIII-2 - to define and study of DIA operation
bases;
 CPIII-4 - to construct standardized algebraic
schemes for solving image analysis and
estimation problems on the DIA base;
 CPIV-2 - to generate DIA using equivalence
and invariance properties in an explicit form;
 to demonstrate efficiency of using DIA in
applied problems.
Figure 4: Generating Descriptive Trees.
THE DESCRIPTIVE TECHNIQUES FOR IMAGE ANALYSIS AND RECOGNITION
227

6 CONCLUSIONS
In principle, the success of image analysis and
recognition problem solution depends mainly on the
success of image reduction to a recognizable form,
which could be accepted by an appropriate image
analysis/recognition algorithm. All above mentioned
steps contribute to the development techniques for
this kind of image reduction/image modeling. It
appeared that an image reduction to a recognizable
form is a critical issue for image analysis
applications, in particular for qualified decision
making on the base of image mining. The main tasks
and problems of an image reduction to a
recognizable form are listed below:
1. Formal Description of Images: 1) study and
construction of image models (Step 2); 2) study
and construction of multiple model image
representations (Step 3); 3) study and
construction of metrics (Step 5).
2. Description of Image Classes Reducible to a
Recognizable Form: 1) introduction of new
mathematical settings of an image recognition
problem (Step 1); 2) establishing and study of
links between multiple model representation of
images and image metrics (Steps 3, 5); 3) study
and use of image equivalencies (Step 4).
3. Development, Study and Application of an
Algebraic Language for Description of the
Procedures of an Image Reduction to a
Recognizable Form (Step 6).
After passing through the above mentioned steps
it would be possible to formulate the axiomatics of
the descriptive (mathematical) theory of image
analysis.
Table 1: Generation of image models by DIA.
Figure 5: Hierarchy of algebras.
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228

ACKNOWLEDGEMENTS
The paper was partially supported by the Russian
Foundation for Basic Research, Grants No. 04-07-
90187
and 05-01-00784 and by the grant
“Descriptive Algebras with One Ring Over Image
Models” (the Program of the Basic Research
“Algebraic and Combinatorial Techniques of
Mathematical Cybernetics” of the Department of
Mathematical Sciences of the Russian Academy of
Sciences).
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