The computational forensics is an area of research where scientists provide solution of
forensic problems by using algorithmic, modeling, computer simulation, and computerbased
analysis. One of the very well known problem is making of the face sketch of
criminal on the basis of onlooker(s) statement. In this work we are focusing on the
problem of identification of image of face. The identification of criminal face is always
conducted in a recursive way, the sketch expert have images of different parts of face e.g.
images of different types of nose. The sketch expert will ask the witness, it should be
much bigger or smaller than presented images, and the witness responded to questions But in proposed system we are trying to give more liberty to the onlooker. In proposed
system onlooker has to input the statements into the system and there will be a face sketch
of criminal as an output.
1. Motivation
The onlooker has to give statements about different parts of face of criminal like forehead,
eyes, nose, and chin etc. e.g. "His nose was small and chin was long" is used for sketch
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making. These statements are full of uncertainty. The key reason of applying the proposed
technique is what seems to be a big nose to some witness might not be a big nose to
another witness. Or, we can say it is really hard to infer the perception of different human
brains precisely. So we need a system that can convert imprecise face description, into a
complete face. This objective may be achieved by using the concept of Sketching With
Words (SWW).
SWW is inspired by the concept of Fuzzy Geometry (f-geometry) and Computing With
Word technique (CWW), both have been given by Zadeh.
The f-geometry of Zadeh is based on fuzzy valid (f-valid) reasoning. The f-geometry may
provide a framework for estimating the components of the face on the basis of the
onlooker(s) statements. The statements are preprocessed and converted in to Generalized
Constraint Language (GCL).
The perception in the onlooker(s) statements are mapped into membership value by using
possiblistic constraint.
Sometimes it is either impossible or bit costlier to identify exact solution of any problem.
For example in computational forensics exact identification of imprecise images of finger
prints, shoe prints, and face-sketch drawn by experts on the basis of onlooker(s) statement
is either impossible or bit costlier. When precise reasoning is infeasible, excessively costly
or unneeded, then the mode of reasoning which is admissible is f-valid reasoning.
Since face sketch experts have to drawn the face of criminal with free hand. The precise
interpretation of onlooker's perception based natural language statements is either
impossible or bit costlier. Hence it is impossible to draw exact face. There are fair chances
of escaping of criminal from the clutches of law and trapping of innocents. So in the
above said situation we have to rely on the f-valid reasoning. The f-valid reasoning falls in
the province of Unprecisiated Fuzzy Logic (FLu.). Extended Fuzzy Logic (FLe) is the
result of adding Unprecisiated Fuzzy Logic in Fuzzy Logic (FL) [5][6][9]. The f-validity
is a measure of the degree of belongingness of any f-objects with respect to corresponding
crisp geometric objects. In f- geometry the measure of similarity among the f-objects is fsimilarity.
L. A. Zadeh has explored the concept of f-geometry in order to have a better
understanding of FLu.
2 Overview of Proposed System
In Figure 1 schematic diagram of proposed system is shown. Since, the geometric objects
are the basic components of face. Hence in proposed system we have estimated the fvalidity
of different parts of the face by using f-geometry. The parts of face are stored in a
centralized database along with the membership value.
As the input natural language statement is supplied. First we have preprocess these
statements then converted in GCL. Afterwards the concept of possibilistic constraint is
used to estimate the membership of different components of face. On the basis of the
membership value components of face is retrieved from database. After processing all the
statements and retrieving parts of face, we have combined them to make a complete face
All these f-objects are transformed of their respective crisp objects in Euclidian Geometry.
The face sketch of the criminal may be one of the crucial evidence in catching the
criminal. Face sketch is drawn by the sketch expert on the basis of onlooker's statement,
which is description of different human face parts like forehead, eyes, nose, and chin.
These statements are full of uncertainties e.g. 'His eyes were not fairly small'. Since the
precise interpretation of these natural language statements is a very difficult task. So we
need a system that can convert imprecise face description, into a complete face. Sketching
With Words (SWW) is a methodology in which the objects of computation are fuzzy
geometric objects. Therefore, in this work we have applied the SWW technique to design
a system that can simulate a face sketch expert. SWW is inspired by Computing With
Words (CWW) and fuzzy geometry. There are two major imperatives for computing with
words. First, computing with words is a necessity when the available information is too
imprecise to justify the use of numbers; and second, when there is a tolerance for
imprecision which can be exploited to achieve tractability, robustness, low solution cost
and better rapport with reality.Generalized Constraint Language (GCL) is used to estimate
the possiblistic constraint in natural language statement. Since the onlooker has to
granulate face into granule label. Hence the concept of fuzzy granule is also applied for
face recognition. Different types of face are generated after applying 'fairly' and 'very'
linguistic hedges on face components.A system that can draw the sketch of the face can be divided into two phases. First phase
to prepare a database of different parts of face. These parts must be represented with son
types of measurement according to size and shapes. Since the onlooker(s) statement are ii
natural language. Hence the second stage is to compute the words of natural languaj
statement, then fetch the different parts of face according to desire degree of belongingness.
3 Computing With Words
The CWW provides a framework for computational theory of perceptions. The
computational theory of perceptions have an important bearing on how humans make -
and machines might make - perception-based rational decisions in an environment of
imprecision, uncertainty and partial truth.
In CWW, the initial data sets (IDS) are translated into terminal data set (TDS). IDS and
TDS are assumed to consist of perception based natural language statements. These
propositions are translated, respectively, into antecedent and consequent constraints.
Consequent constraints are derived from antecedent constraints through the use of rules of
constraint propagation.
In this work, there is a requirement of translation of initial data set into antecedent
constraint only. So we have discussed only this translation.
3.1 Representation of natural language statement into GCL
In GCL the natural language statement is expressed as a generalized constraint in the form
of X isr R
Where R is a constrained fuzzy relation, X is the constraining variable relation; 'isr' is a
variable copula in which r is a variable whose value defines the way in which R constrains
X. Among the basic types of constraints are: possibilistic, veristic, probabilistic, random
set, pawlak set, fuzzy graph and usuality. In this work we are using only possibilistic
constraint which will discussed in detail later on.
In GCL, 'X is R' is the representation of different natural language statementin the form
of P-» X is R
Nose is Large.
Eyes are Small
Forehead is medium
As a simple illustration, consider the proposition
P = Nose is not fairly Small
In this case, the constrained variable is the Nose, which may be expressed as
X = Size(Nose) = Part[ Name=Nose ].
The constraining relation, R, is given by R = (Size2)' which implies that the linguistic
hedges'fairly' interpreted as a squaring operation, and the negation as the operation of
complementation. Equivalently, R may be expressed as 3.2 Possibilistic constraint
When the value of copula r is blank in X isr R .X is R abbreviated to X "ezar". And R
constrains X by playing the role of the possibility distribution of X. More specifically, if X
takes values in a universe of discourse, U = { u },
then Poss{ X = u } =TIx (u)= |IR(U),
where ^R is the membership function of R, and ITx is the possibility distribution of X,
that is, the fuzzy set of its possible values.
X isr R is given by IIx ( u )= ^R(U),
In the following example we have explore the concept of possibility distribution in a fuzzy
set.
We have a set of possible values that may be taken by X are (0,1,3,4).
The possibility distribution is given as
rix =1/0+1/1+0.8/4 + 0.7/3
Poss(X=3) = 0.7.
For instance ' 0.7/3' means the possibility of that the value of X is 3 is 0.7.
3.3 Possibility distribution with hedges
In proposed work Linguistic hedges,, are defined as unary operators on fuzzy sets.
Thelinguistic hedge very defined as Concentration (CON) operation and fairly is defined
by as Dilation (DIL) operation.
The 'very' hedges strengthens the positive meaning of true, while fairly weakens its
positive meaning. So we have used a parametric representation of linguistic hedges of
fuzzy logic.
The basic linguistic truth expressions associated with respective parameters as follows,
3.5 Fuzzy Granule
In this section we have discussed the basics of fuzzy granule as well as its application in
recognition of different types of face components. The concept of fuzzy granule has been
applied because fuzziness of granules , their attributes and their values are
characteristic of ways in which human perceptions are formed , organized and
manipulated. The concept of granule is used when there is no well define boundary. The
size of different types of nose is not a crisp value but granule of size between 2 to 5
inches.
The different types of nose are represented by term set. The totality of values of a
linguistic variable constitutes its term-set, which in principle could have an infinite
number of elements. For example, the term- set of the linguistic variable nose might read
as T(nose) = small + not small+ very small + not very small + . . . + large +not large+
very large +not very large +....+ medium+ not medium + . . .,
In which + is used to denote the union rather than the arithmetic sum. Similarly, the termset
of the linguistic variable as well as fuzzy granule of others component of face may be
constituted.
Above two imperatives are suitable for the stated problem, because statement of onlooker
is not exact and the resultant face sketch may have some imprecision.
Next section the membership of different face parts are estimated by f-geometry.
3.6 Sketching With Words
Sketching With Words is an emerging research area. We have applied SWW technique for
the estimation of perceptions in geometric shapes by using triangular membership
function. The f-geometry is a tool that is useful in sketching the different types of
geometric shapes on the basis of perceptions based natural language statements. Sketching
With Words may provide a scientific basis for human face recognition system by
simulating the forensic sketch expert in the discipline of computational forensic. Because,
the geometric objects are the basics of any shape found in an image. For that, we have
estimated the fuzzy validity, then, those fuzzy images are stored along with the possible
descriptions in natural language. In proposed system we have associated f-objects with
natural language statements by using the concept of CWW.
3.7 Proposed System
It is really hard" to meet human decision making capability. The situation will be more
complex if we are mapping sketch from perceptions of some group of persons. The
procedure we have followed for drawing of face sketch is consists of two stages. First is a
narration of description face by onlooker's on the basis of perception, second stage is
sketching of face by expert on the basis of his/her level of understanding. Due to the
complexity of system, the proposed system has following assumptions.
The size and shape of face components are having variety of nature. The
development is at preliminary stage, it is not possible to include all types of
component with their degree of flexibility. So we are taking a limited number of
standards and well define shapes (f-objects) into account like f-circle, f-semicircle,
and f-triangle.
i. All the components are supposed to be f-objects off-geometry.
ii. Scaling of these f-objects do not affect the membership values. Similar System is
applicable for different size of face.
The simulation of queries and estimation of membership values of different parts is done
on C#.Net and Mat-Lab 2009 respectively.
The descriptions in natural language are the keywords. For that, a very large database
containing several types of eyes, nose, forehead, chin, and lips is established. The
description of face of criminal, which are natural language statements is given as given as
input. As an output a complete facial image of criminal will be produced. In this work we
have not focused on the different issue of related to database like size of database
scalability etc.
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where 'b' is a real number. The value of b=8 inches, because it is the largest number and
has been used for normalizing rest of the component of face.
In Table 1, the size of different parts of face is given. Where the variables xi, X2, X3, and
X4 are taken from Figure 3 , variable^' is the largest value. The values of xi, X2, and X3
are used for small, medium, and large, constraints respectively.
The shape of foreheads, eyes, nose, lips and chins are considered as f-semicircle, f-circle,
f-triangle, f-circle and f-triangle respectively. We are considering three types of sizes
small, medium, and large. The size of different parts of face is shown in Table 1 with
small, medium, and large constraints.
As shown in Figure 5 the value of variable X4 is 8 inches which is the length of face. All
the parts of face are normalized by X4.
Large Nose:- The length of the large triangular nose is (X3) considered as 4 inches.
Sample of Input Statements
"He has a very small nose. He has small eyes. He has small chin. He has large lips. He has
not medium forehead."
First of all, we preprocessed the input query by (i) stop word removal and (ii) stemmer
algorithm. The stop word removal eliminates quite often repeated words which may have
a very little meaning to play a vital role in the query. Usually, they are articles, pronouns,
supporting verb and prepositions, like a, an, the, for, he, is, etc. But, it has least effect on
the semantics of the word. Conversely, some may disagree that stop word is very much
context dependent.
Second step is stemming of keywords. Stemmer is needed to be deployed, because, the
queries arriving to propose system is usually not in GCL, but, mostly in natural language.
So, the stemmer converts a word to its canonical form. Although, it has no major effect on
the semantics of the word, like cats, catty, cat like words usually refers to a pet animal cat.
By this way, the user need not worry about the specific terms while performing a query.
As the porter 'stemmer algorithm' that we removes the suffixes of the query. This
algorithm is usually followed for the English language. But, this is not the same with other
languages, which removes prefixes of the word.
After preprocessing the statement is converted into GCL. i.e. in the form of X isr R.
hedges of fuzzy logic on 'small' and 'large' constraint are shown in Figure 5, and 6
respectively.
In Fig. 7 the size of small forehead is 2 inches. When we have applied complement
operator, then the size of 'not small forehead' is more than to 2 inches. Moreover when
'fairly' operator is applied on small forehead, the size of 'fairly small forehead' is much
higher than to 2 inches. The size of forehead after applying 'fairly' linguistic hedges with
small constraint should be less that to 2 inches.
Figure 9 Size of different parts of face after applying linguistic hedges on small
constraint
This is strengthening the positive meaning of truth. It means the size of fairly small
forehead stirring towards higher value. The variation in similar fashion in the size of other
parts of face after applying 'fairly' hedges with small constraint can be seen in Figure 9.
To remove the above mentioned discrepancy we have applied the concept of a parametric
representation of linguistic hedges of fuzzy logic that has been introduced previously.
Linguistics hedges 'fairly' with small constraint generate forehead, which is less than to 2
inches. Hence the size of 'fairly small forehead' is more, than to 2 inches. The size of
'not fairly small forehead' is much higher than to 2 inches. Variations in the size of
Variations in the size of large foreheads after applying hedges and complement operator
are shown in Figure. 11.
In Figure 11, the size of large forehead is 5.4 inches. When we have applied complement
operator then the size of 'not' large forehead' is much less than to 5.4 inches. Linguistics
hedges 'very' generate forehead of 3.65 inches. Hence the size of 'very large forehead' is
less than to 5.4 inches. The size of very large forehead should be more than to 5.4 inches.
Hence the application of 'very' linguistic hedges weakens its positive meaning of large
forehead. It is showing that the size of large forehead is shrinking after applying 'very'
hedges. Similarly the size of other parts of face after applying 'very' linguistics hedges
with large constraint can be seen in Figure 9. To remove above discrepancy parametric
representation of linguistic hedges of fuzzy logic is applied, that has been already
introduced.
The linguistics hedges 'very' generate forehead of 7.02 inches. Hence the size of 'very
large forehead' is more than to 5.4 inches. The size of 'not very large forehead' is much
less than to 5.4 inches. Variations in the size of large forehead as per above discussion is
given in Figure 12. Similarly the size of other parts of face after applying 'very'
linguistics hedges with large constraint can be seen in Figure 12.
In Figl3 the size of medium forehead is 4.8 inches. When we have applied complement
operator that reduces from 4.8 inches. In same fashion size of other components are going
to reduce from the original size after applying complement operator on medium
constraint.
3.9 Different Queries and Outputs
For avoiding the complexity in proposed system, we are leaving the transforming of
different synonyms as future work. All the synonyms of small, medium, and large
constraints have supposed to be producing same membership value with the respective
linguistic hedges.
For example if we have an onlooker's a statement ' he has long nose' or ' he has a
large nose' will produced same membership value. In similar fashion 'broad forehead'
or 'large forehead' will be treated as same constraint.
Input Query Statement
Query Statement 1
He has large forehead. His eyes are large. He has a large nose. He has large lips. He has a
large chin.
3.10 Summary
In proposed work the concept of f-geometry, CWW, Fuzzy Granule, Pdssibilistic
Constraints, and GCL are used. These concepts are applied for the recognition of face on
the basis of perceptions. Various fuzzy objects are used for describing different parts of
face. This system sets out to draw the face sketch of criminal on the basis of perceptions
based verbal description of the onlooker. The shapes of foreheads, eyes, noses, lips, and
chins are considered as f-semicircle, f-circle, f-triangle, f-circle and f- semicircle
respectively. The role of SWW is very important. The SWW is in its initial stages of
development. In time, SWW may come to play an important role in the conception, design
and utilization of intelligent systems of face recognition. Possibilistic constraints with
linguistic hedges 'very 'and 'fairly' are used. We have estimated membership values of
different components of face with large and small constraints. In traditional approach
'fairly' hedges increases the size of different parts which strengths the positive meaning of
truth. Whereas 'very' hedges have weaken positive meaning of truth i.e. 'very' hedges
reducing the size of different parts with large constraint. Parametric representation of
linguistic hedges for fuzzy logic removes the shortcomings of unary operator. This
approach has produced more realistic results. In future the system can be made more
realistic by combining possibliistic constraints with probabilistic constraints. There is lot
of space for improvement and enhancement in proposed work. For example other types of
shapes as well as sizes can be used as face components. For avoiding the complexity in
proposed system, we are leaving the transforming of different synonyms as future
work.The proposed work is not just restricted to face sketch recognition, but can be
implemented for inexact modeling, biometrics, many fields where there is possibilities of
uncertainty and other areas of intelligent image processing..

CLAIMS
1. We claim that the proposed system may come to play an important role in the
conception, design and utilization of intelligent systems of face recognition of
criminals,
2. We claim that Sketching With Words concept is applied for the recognition of
face on the basis of perceptions.
3. We claim that Various fuzzy objects are used for describing different parts of face
foreheads, eyes, noses, lips, and chins.
4. We claim that Parametric representation of linguistic hedges for fuzzy logic
removes the shortcomings of unary operator.