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Recognition
Society
Recoyn~tion. Vol. 26, No. 3. pp 409 418. 1993
m Great Britain
@ 1993 Pattern
RECOVERING
DYNAMIC INFORMATION
HANDWRITING
FROM STATIC
G. BOCCIGNONE,
A. CHIANESE,L. P. CoRDnLLAt and A. MARCELLI
Dipartimento di Informatica e Sistemistica, University of Naples “Federico II”, Via Claudio, 21,80125 Naples,
Italy
Abstract--It
is generally agreed that the advantage of on-line character recognition methods with respect
to off-line ones mostly relies on the availability of dynamic information.
This mainly concerns the order in
which the strokes forming characters have been drawn. In this paper we present and discuss a method which
attempts, in the off-line case, to recover part of the lost script dynamics. The method makes it possible to
reconstruct
one of the most likely trajectories followed by the writer while drawing characters. It is based
on a suitable implementation
of good continuity
criteria which take into account direction, length and
width of the strokes making up characters. The algorithm either subdivides or unfolds the digital ribbon
forming isolated characters as well as groups of connected characters, by solving the ambiguities which arise
at every joint. Experimental
results are reported and discussed.
OCR
Skeleton
Handprint
shape fidelity
1.
Handwriting
Off-line recognition
INTRODUCTION
In many image processing applications (OCR, storage,
analysis and transmission of line drawings, text and
map processing, etc.), the digital representation of the
objects of interest in the image can be considered as
being made of ribbons evolving and intersecting in a
two-dimensional (2D) space.
In the case of handwritten characters, this assumption implies thinking of the writing process as a complex human movement of trajectory formation, which
sequentially structures a ribbon shape as a function of
time. In this framework, space oriented models have
been proposed to interpret handwriting as a mechanism
capable of generating smooth trajectories by composing
basic curve elements.(“*)
In general, a distinction is made in the literature
between on-line and off-line script, depending on
the type of information available for the purpose of
machine recognition. (3.4) For instance, dynamic information about the order in which the line pieces
making up the characters (strokes) are drawn by the
writer is available and exploited in the on-line case,
whereas only the static result of the writing process is
available in the off-line case. Therefore, it is agreed that
the advantage of on-line over off-line systems mostly
depends on the possibility to capture temporal or dynamic information. This information or at least part of
it would be very useful also in the static case.
In this paper we present and discuss a method which
attempts, in the off-line case, to recover part of the lost
script dynamics, exploiting only information available
t Author to whom all correspondence
should be addressed.
Dynamic
information
Thinning
at the visual level. For instance, given a character like
the simple one in Fig. 1, the problem we want to solve
is that of recovering the order in which the strokes
making up the character were drawn. In the given
example, the most likely order is the one indicated by
the sequence of arrows.
The complexity of the task is evident if we consider
that the figures we are dealing with are represented by
self-intersecting and joining 2D digital ribbons. At
each joint a complex decision about trajectory direction
is necessary in order to unfold or divide the ribbon.
The basic assumption underlying our method is that
subsequently drawn ribbon strokes share more similar
features than strokes which, although joining, are not
temporally subsequent.
The method we propose has been developed in
the framework of a handwritten character recognition
system with the purpose of recovering information
useful to obtain more effective decompositions and
descriptions ofcharacters in terms of meaningful parts.
It has been shown to be effective both in the case of
isolated handprinted characters and in the case of
connected sequences of characters (handwritten words).
Problems arising especially in this second case will be
discussed in the following sections.
In the analog plane, a character, as well as a handwritten word, can be seen as a set of complex curves
(in particular a single one) and can then be described
for instance in terms of a set of functions ai(
where
aj is the direction of the tangent to the ith curve at every
point, and li is a curvilinear coordinate along the curve.
The fact that movements made by humans for
drawing characters can be described as piecewise continuous trajectories,“‘*“) implies continuity condi409
410
G. BOCCIGNONE
et al.
2. PRELIMINARYRIBBONREPRESENTATION
Fig. 1. A handwritten character. The arrows show the most
likely order in which the lines have been drawn.
tions on each curve piece forming a character. Thus,
given two curve pieces that join at a point P identified
by curvilinear coordinates I, and 1, on the two pieces,
the likelihood that they were drawn one after the other
increases as the difference a,(l,) - a,([,) decreases.
In order to extend the general criterion illustrated
above also to the case of the digital ribbons representing
characters, it appears convenient to transform the
ribbon into a digital line (skeleton) through a thinning
process. However, since in the analog case stroke
thickness is a feature that in some cases can help to
take a decision about the order in which connected
strokes have been drawn, we use a thinning transformation which associates local thickness information
to skeleton points.
In our work we made two basic assumptions:
(1) Variations in direction, speed and pressure of the
writing movement affect direction and width of the
lines drawn and hence the shape of the written characters. It has to be noted that whilst changes in writing
movement direction always result in curvature variations along the ribbon, pressure variations may or may
not originate different ribbon widths, according to the
quality of the paper and to the writing instrument.‘@
(2) The former shape features can automatically be
detected at the visual level: ribbon stroke direction and
width are sufftcient, in the large majority of cases,
for taking a trajectory decision in the neighborhood
of a crossing point, if proper criteria of good continuity
are used.
In Section 2 we illustrate the process that, starting
from the bit map of a ribbon, makes it possible to
substitute the latter with a labeled curve that adequately
preserves the information held by the ribbon and
constitutes a compact and convenient representation
of it. In Sections 3 and 4, a method for transforming
the labeled curve into a set of simple curves, by
dividing or unfolding the former at every joint, will be
outlined and experimental results discussed.
According to the considerations illustrated above
and to previous work on elongated figure description
and ribbon modelling,‘7s) we chose the skeleton as the
most convenient initial representation of a ribbon. In
order to preserve information about ribbon thickness,
the skeletonization algorithms computing the Medial
Axis Transform (MAT) of a figure(‘) must be used. In
particular, we have experimented with algorithms that
convert an 8-connected figure into an 8-connected
digital curve having unit width throughout and outlining a generalized axis of symmetry of the figure
(e.g. references (1411)). This kind of transformation is
information-preserving,
and hence reversible, since it
associates to every skeleton pixel a label specifying the
distance of the pixel from the background.
The MAT of characters is a digital curve that is not
necessarily simple, i.e. it can be made of parts that join
or cross (Fig. 2). In the following, MAT pixels will be
termed end points (EP), normal points (NP) or branch
points (BP), depending on whether the number of
MAT pixels in their 3 x 3 neighborhood is one, two or
greater than two.
Unfortunately,
thinning algorithms,
including
medial axis transformation, although appealing techniques for representing ribbon-like figures in a compact
way, exhibit a number of unwanted features that require their output to be further processed before it
can be used.
In our case, a first problem is that of computing the
direction of the digital lines merging at a line joint, so
as to evaluate the smoothness of the transition from
one line piece to the other. This cannot be reliably done
on the digital skeleton looking at a small window
around the junction pixels. A solution is to approximate
the MAT with a piecewise continuous curve. Note that
some sort of approximation is in any case generally
necessary in order to use the skeleton of a figure for
description and recognition purposes.
A second, more complex problem is that thinning
techniques typically give rise to lines whose shape does
not always faithfully reflect that of the original figure,
even in the case of ribbon-like figures. These shape distortions depend on the limited locality of the criteria
according to which skeleton pixels are selected, while
they are independent of the metric used in the digital
plane for thinning. Since they are mainly located in
correspondence to line joints, they can dramatically
affect the possibility of reliably applying good continuity criteria. It is absolutely necessary to avoid or
correct such distortions in order to obtain significant
results, as it can be easily seen from the examples given
in the figures of this paper.
As for the first problem, we adopted a polygonal
approximation. The procedure reduces the digital line
to a polyline made of k generally connected segments
Ei, i = 1,. . . , k, bounded by h vertices Vj. A great
many algorithms have been proposed in the literature
for approximating a digital curve with a polygonal
411
Recovering dynamic information from static handwriting
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Fig, 2, A digital ribbon and its g-connected
MAT. Every pixel of the skeleton is labeled according to its
I-distance from background.
line. The main results of the polygonal approximation
relevant to our purposes are:
 the reduction
of the noise introduced by both
digitization and thinning processes;
 the reduction ofthe amount of data to be processed;
 the possibility of describing the MAT in terms of
angles and sides.
However, in order not to destroy possibly important
information about the shape of the curves representing
characters, the approximation has to guarantee that
significant curve inflections are preserved. To this end,
we consider only non-collinear points as candidate
vertices” 2,and adopt a low value for the approximation
tolerance. This choice does not prevent us from obtaining a significant reduction of the number of skeleton
points, but suggests the choice of a merging technique
to perform the approximation, since it is less computationally expensive with respect to splitting techniques when the number of sides of the polygon is not
particularly small.(1z~‘3)
The approximation of the MAT is performed by
following all its branches according to a breadth first
strategy, while locating the vertices of the approximating polygonal. Tracing is started from the most left EP
of every connected set of pixels or, in the absence of
end points, from the top left point. If the most left EP
has an x-distance from the top left NP greater than a
threshold depending on the type of script, the latter
point is taken as the starting point; this may be the case
with some connected sequences of letters. These choices
have been suggested from the simple observation that
writing using the latin alphabet normally develops
from left to right and that characters are most frequently
drawn starting from their left side. This behavior is
quite general, independent of the type of character
(handprinted or cursive written) and of aspects such as
culture and nationality. It is clear however that no
choice is absolutely unquestionable.
Whatever the
choice, a number of counterexamples could be found.
We made a choice that is in accordance with a simple
heuristics and, to our experience, leads to maximize the
positive results.
On the other hand, our approach is aimed not to
recover the “true” order and direction in which all the
strokes making up a character were drawn, but to
properly connect or separate contiguous line pieces at
junctions. We believe in fact, that recovering the right
information about which are the line pieces presumably
included between a pen-down and a pen-up, even
independently of the direction in which they were
traced by the writer, is an already interesting result
which can be profitably used in the framework of a
handwritten character recognition system.C1”~15)
It may be possible to locate with higher reliability
the starting point of the line tracing, by making more
G. BOCCIGNONEet al.
412
complex hypotheses on the handwriting process and
assuming suitable information from the gray level
image, as very recently proposed in reference (16).
The output data structure of the approximation
procedure is a directed graph whose nodes are the
vertices Vi of the polygonal and the arcs represent its
sides.
The following information
node:
is associated to each
(1) number of the vertex in the tracing order;
(2) X, Y coordinates of the vertex;
(3) 8-distance of the vertex from the background
(label);
(4) number and list of both father nodes and son
nodes;
(5) number of components the node belongs to.
In addition, the algorithm gives two arrays whose
generic elements, length[i, j] and width[i, j], respectively represent the length and the average width of the
side between two subsequent vertices Vi and Vj. In the
following, we will call PMAT the polygonally approximated MAT.
Since the decision about dividing or unfolding the
ribbon at each branch point is taken by using good
continuity criteria, it is important that the PMAT is
not affected by significant shape distortions that, by
modifying the geometry of the polygonal, would cause
a wrong decision to be taken. As already said, thinning
techniques typically give rise to distorted representations
of ribbon shape. Most typical distortions are:
(1) Spurious whiskers generated in the presence of
insignificant protrusions, noise or convexities of the
ribbon edge.
(2) Spurious BPS generated because of the splitting
of an ideal single branch point at ribbon crossings.
Consequently, a spurious branch not corresponding to
an actual ribbon stroke but to a virtual one is generated.
(3) Spurious inflections at the junction of strokes.
(4) Conjoint effects of types (2) and (3).
Figures 3(a) and (b) show the MAT and the PMAT
of a character, respectively. It can be noted that shape
distortions are mostly generated in correspondence of
branch points, where the continuity criteria have to be
checked. It is therefore fundamental to avoid or eliminate distortions for any method based on good
continuity criteria to be effective. We have shown in
reference (17) how the information held by the labeled
MAT is sufficient for locating and correcting such distortions. The algorithms proposed (which will not be
discussed here), exploit information about labels of the
vertices and relative direction and length of PMAT
sides. In this way it is possible to recognize and
eliminate spurious whiskers, to merge split BPS, and
to correct anomalous inflections of the MAT. Figure 3(c)shows the PMAT of a character after having corrected the shape distortions of types (l)-(3) introduced
by thinning.
b)
3. DIVIDING
Fig. 3. (a) The bit map of a character and its MAT (superimposed). For the clarity of the picture, MAT pixels are not
labeled. (b) The PMAT superimposed on the bit map. (c)The
PMAT
after correcting
shape distortions
(CPMAT).
AND UNFOLDING
THE RIBBON
Once the corrected PMAT of the ribbon (CPMAT)
has been obtained, the segments joining at each BP are
considered, in order to group or split them to form sets
of connected simple curves. The goal is to reconstruct
the stroke sequence of the ribbon according to the
Recovering dynamic information from static handwriting
most feasible sequence that could have been followed
by the writer in drawing the character.
Following the basic philosophy of our approach, at
each joint, pairs of merging lines exhibiting the most
similar features should be kept together.
The main feature we consider in implementing good
continuity criteria is the direction of the lines at the
joint. Two joining curve pieces are considered
as
having been drawn successively if their union is a
smooth curve: the smoother the curve, the more likely
this will be. Because of the polygonal approximation
of the MAT, the segments actually merging at a BP are
assumed to represent the local direction of character
strokes: longer segments will represent more significant
strokes. Since the smoothness of the curve is measured
by the difference between the direction of the segments
joining at a BP, the more the segments are aligned, the
higher the probability
that they belong to the same
stroke. If one of the considered segments is too short
in comparison
with the length of the neighboring
segments, the subsequent one is considered, so as to
take a more reliable decision about stroke direction.
The other two features we adopt to evaluate the
degree of similarity between segments joining at a BP
are segment length and width. By using these features,
for every pair of segments joining at a BP, a good
continuity score G = A(r) + L(a) + W(6) is computed,
where:
LYis the angle between the segments;
u is the ratio between the length of the shortest
and the longest segment of the pair;
 6 is the absolute
value of the difference between
the average widths of the two segments.


The meaning of G is that the likelihood that two
segments belong to the same stroke is considered
a linear combination
of functions. We included L(O)
among them, because we found experimental evidence
that this is one of the criteria used by man, especially
in the case of handprintings.
Depending on writing
characteristics, however, this function may be of minor
importance.
The functions A, L and W have been empirically
evaluated, as illustrated in Section 4, and each of them
b)
4
Fig. 4. A handwritten numeral. The results of the various phases of the process are shown. The last picture
of the set shows the polygonals assumed to represent the characters and the order assigned to their vertices.
The first digit of the label assigned to the vertices identities a component
as found by the procedure.
Fn 26-3-c
413
G.
414
B O C CIG N O N E
e t a l.
d)
Fig. 5. An example
of results obtained
with handwritten
words.
Recovering dynamic information from static handwriting
415
Fig. 6. Some handprinted characters and the tinal polygonals representing them.
provides as output a value ranging from 0 to 1 which
represents the normalized probability that, according
to each of the three similarity criteria adopted (i.e.
direction, length and width similarity), independently
considered, a pair of segments is merged.
The dividing and unfolding procedure is continued
for every BP of the CPMAT of a character by taking
into account the number k of segments joining at the
BP and the value of the score G assigned to each pair
of such segments. The two most common cases are
k = 3 and 4.
Fork = 3, the pair of segments with the highest score
G is kept together and the third segment is cut at the
BP. This is compatible with knowledge about the
handwriting process and namely with the hypothesis
that during writing the number of pen-up and pendown is minimized.
Fork = 4, the pair of segments with the highest score
G is kept together and either unfolded with respect to
the remaining pair or divided from it, according to the
case. The latter is also considered united, without
further calculations being made for the moment. The
rationale behind this behavior is that at the intersection
among four segments, two types of decision can be
taken: either two segments lying on opposite sides of
the junction or two segments on the same side are kept
together. In the former case, the most simple hypotheses
on the handwriting process lead to the conclusion that
we are in the presence of a crossing. In the latter case,
exemplified by a K-junction, the less compromising
decision about the pair of remaining segments, on the
basis of the presently available information, is that of
keeping them together for the moment and deciding
in the following, on the basis of more global information,
whether they are actually part of a single stroke or
must be split.
Any other solution does not seem in accordance
with the possible hypotheses on the writing process.
Some examples of characters and short words processed according to our method are shown in Figs 446.
4. EXPERIMENTALRESULTS
The experimental work has been carried out by
using a data set of 10,000 handwritten characters
produced by 20 writers. Each writer was requested to
till in a set of forms with predefined square boxes of
size 0.25 x 0.25 in. The writers were only requested
to write characters inside the boxes, without imposing
either any character model or constraints on the
writing instrument. Upper and lower case letters and
numerals were allowed. The character set was uniformly
distributed over the various classes and included both
handprinted and cursive letters. Each writer was also
requested to write a few cursive words, but the results
obtained with this material were only used for qualitative evaluations.
Each form was digitized using a flat-bed scanner
with a resolution of 300 dpi. The data set was divided
into training and test sets, comprising l/3 and 2/3 of
the characters, respectively.
416
G . B~CCIGNONE
90
95
100 105110
115120
et al.
125 130 135 140145
150155160
165 170 175 180
Fig. 7. The plot of ,4(a). The curve represents the normalized probability that a pair of segments joining at
a BP are merged as a function of the value of the angle a between them.
In order to quantitatively
evaluate the trend of
the functions A, L and W used to implement good
The computational cost of the whole process, excluding medial axis transformation, ranges from 10 to
continuity criteria, the training set was considered and
20% of the time needed for computing the MAT,
six parameters were evaluated for every pair of seg- depending on the character considered. Some of the
ments joining at a BP: CC,
c and 6 defined in the previous
partial times are, in fact, more or less independent
section, and three boolean variables v,(a), v*(a), ~~(6) of the character, but others, like time for correctspecifying whether, according to the opinion of a ing distortions, depend on its shape. In any case the
human observer, the pair of segments should be split
average time computed over a set of characters disor merged into the same stroke, taking into account CC, tributed among the various classes with the typical
c and 6 independently. The value false was assigned to
frequency occurring in a text page, was nearer to the
lower bound.
vi if the segments were not to be merged together.
The histograms of A(a), L(o) and W(6) were then
5. DISCUSSION
computed. In particular, c(was uniformly sampled with
a 5” resolution in the range 90”180”, ~7spanned in the
The method illustrated in the previous sections
range O-l and 6 assumed discrete values from 1 to 5, allows the reconstruction of one of the possible trajecthe latter being the maximum value observed in the
tories followed by the writer, and thus to recover
whole data set. The function A was defined as
part of the lost dynamic information, starting from
static handwriting. It is mainly based on a shape
44 = N,(4lCN,(4 + N,b)l
preserving representation of the lines making up handwhere N,(E) is the number of times vi(~) was true and
written characters and on the implementation
of
N,(a) the number of times vr(c() was false.
a set of suitable good continuity rules.
By using a linear regression, a curve was fitted to
It has to be noted however, that at the connection
these points, obtaining the trend of A shown in Fig. 7. between subsequent characters in a word, cases may
As can be seen, for CI< 1lo” the probability of merging
occur where good continuity criteria alone do not
two segments is equal to 0, whilst for c(> 160” the
always lead to the expected conclusions about the way
probability is 1.
of coupling strokes at a junction. This happens esThe functions L and W were defined analogously to
pecially when some line piece is retraced. Better results
A. In the case of the considered training set, the
could only be obtained by incorporating in thesystem
histogram of L showed a linear trend for 0.2 < Q < 0.9,
some more knowledge about the handwriting process.
while W showed a linear trend for 1 < 6 < 5.
The convenience of doing this depends on the characBy running the programs on the test set, about
teristics of the recognition system which follows.
97% of correct results were obtained. The errors were
As the experiments illustrated in the paper have
essentially found in correspondence either to shape
shown, in the large majority of cases, our method
distortions of the PMAT not properly corrected or to
makes it possible to properly connect, at junctions,
situations where G assumed very similar values for the
pieces of curve which have been drawn successively to
different pairs of segments joining at the BP.
each other, but does not always guarantee that the
Recovering
dynamic
information
recovered
drawing
direction is the one actually followed
by the writer: it could be the opposite one. This is not
a problem if information about drawing direction is
only partially exploited by the recognition system, as
in the case of the system we are developing.(14) On the
other hand, the drawing direction is in many cases
writer dependent and, to ascertain it in questionable
cases, it would be necessary to search for special clues
on the gray level image of the script, as recently
suggested in reference (16). Some of these techniques
could be integrated in our method, if so desired.
With respect to other approaches using good continuity criteria applied to the skeleton of characters
(e.g. reference (18)) the distinctive features of our method are:
(1) To outline that the shape distortions introduced
by thinning techniques at the intersection among strokes
can heavily compromise the possibility of successfully
applying good continuity criteria and thus to carry
out a technique for correcting such distortions before
further processing.
(2) To evaluate the smoothness of the digital lines
by deriving information from a very wide neighborhood of the skeleton branch points and not simply
from their nearest neighbors. This is obtained by
polygonally approximating the skeleton and by suitably using information about the direction of the sides
of the polygonal (see Section 3).
(3) To use, among good continuity criteria, not only
the information about stroke direction, but also some
more information useful to evaluate the homogeneity
between contiguous stroke pieces, such as information
about their thickness and relative length.
(4) To have experimentally evaluated the form of
the functions A, Land W used to implement good continuity criteria, so as to take advantage of the knowledge of the human behavior.
The proposed method not only allows more reliable
decompositions and descriptions of characters but,
because of its generality, it can also be useful for processing and interpreting other important ribbon like
shapes such as maps and engineering drawings.
6. SUMMARY
In this paper a method for recovering part of the
dynamic information in the case of off-line character
recognition has been presented. The method makes it
possible to reconstruct one of the possible trajectories
followed when drawing characters. In fact, from a
static point of view, characters and more generally
handwritten script appear as a set of self-intersecting
and joining 2D ribbons. Therefore, a crucial point in
order to accomplish the task, is that of dividing or
unfolding the ribbon at every joint.
First of all, the ribbon is substituted by a reliable
representation, which we have called CPMAT. On the
basis of suitable good continuity criteria, any connected sequence of segments making up the CPMAT is
unfolded or divided into components, according to the
417
from static handwriting
case. In the former case, every crossing is changed into
an “overlap” and the CPMAT is transformed into a
simple curve. In the latter case, at a junction where a
pen-up (pen-down) reasonably occurred during writing,
the CPMAT is “separated” into components. Part of
the lost dynamic information is then restored, allowing
a more effective description of characters for recognition purposes. Experimental results are reported and
discussed.
REFERENCES
1. P. Morass0 and F. A. Mussa Ivaldi, Trajectory formation
and handwriting:
a computational
model, Biol. Cybern.
45, 131-142(1982).
2. H. L. H. M. Teulings and A. J. W. M. Thomassen, Computer aided analysis of handwriting
movements,
Visible
Language 13(3), 218-231 (1979).
3. C. C. Tappert, C. Y. Suen and T. Wakahara,
State of the
art in on-line handwriting
recognition,
IEEE Trans.
Pattern Analvsis Mach. Intell. PAMI-1218). I 787-808
(1990).
’
4. M. R. Bozinovic and S. N. Srihari, Off-line cursive script
word recognition,
IEEE Trans. Pattern Analysis Mach.
Intell. PAMI-11(l),
68-83 (1989).
5. P. Viviani and C. A. Tazzuolo, Space-time invariance in
learned motor skills, Tutorials in Motor Behauiour, G. E.
Stelmach and J. Requin, eds, pp. 525-533. North-Holland,
Amsterdam (1980).
6. M. Ammar, Y. Yoshida and T. Fukumura, A new elfective
approach for o&line verification of signatures by using
pressure features, Proc. 8th lnt. Conf on Pattern Recognition,
Paris, France, pp. 566-569 (1986).
of shape, Comput.
7. A. Rosenfeld, Axial representations
Vision Graphics Image Process. 33, 156-I 73 (1986).
8. J. Ponce, On characterizing
ribbons and linding skewed
symmetries, Comput. Vision Graphics Image Process. 52,
328-340 (1990).
9. A. Rosenfeld and A. C. Kak, Digital Picture Processing.
Academic Press, New York (1977).
IO. C. Arcelli, L. P. Cordella and S. Levialdi, From local
maxima to connected skeletons, IEEE Trans. Pattern
Analvsis Mach. Intell. PAMI-S(2).
~ 134-143 (1981).
11. C. Arcelli and G. Sanniti di Baja, A thinning algorithm
based on prominence detection, Pattern Recognition 13,
225-235 (1981).
12. L. P. Cordella and A. Di Paolo, Algorithms for extraction
of morphological
features, Proc. 2nd Int. Conf on Visual
Psycophysics and Medical Imaging, Bruxelles, pp. 131138 (1981).
13. T. Pavlidis, Structural Pattern Recognition. Springer,
New York (1982).
14. A. Chianese, L. P. Cordella, M. De Santo and M. Vento,
Classifying character shapes, Visual Form: Analysis and
Recognition, C. Arcelli et al., eds, pp. 155-164. Plenum
Press, New York (1992).
15. H. Nishida and S. Mori, Algebraic description
of curve
structure,
IEEE Trans. Pattern Analysis Mach. Intell.
PAMI-14(5), 516-533 (1992).
16. D. S. Doermann and A. Rosenfeld, Recovery of temporal
information
from static images of handwriting,
Proc.
IEEE Comput. Sot. Co@ on Computer Vision and Pattern
Recognition, Urbana, pp. 162-168 (1992).
17. G. Boccignone,
A. Chianese,
L. P. Cordella
and A.
Marcelli, Using skeletons for OCR, Progress in Image
Analysis and Processing, V. Cantoni et al., eds, pp. 2755
282. World Scientific, Singapore (1990).
18. V. Govindaraiu
and S. N. Srihari. Seoaratina
handwritten text from overlapping nontextual contours, Proc. Int.
Workshop on Frontiers in Handwriting Recognition, Bonas,
France, pp. Ill-119(1991).
II
L
418
G. BOCCION~NE
et al.
About the Author-GIusEPPE BOCCIGNONE
was born on 30 July 1959. He received the laurea degree in
physics from the University of Turin, Italy, in 1985. In 1986 he joined Olivetti Corporate Research, Ivrea,
Italy. From 1990 to 1992, he was chief researcher of the Computer Vision Lab at C.R.I.A.I., Naples, Italy.
He is currently at Research Labs of Bull HN Information Systems, Milano, Italy, leading projects on
biomedical images. Since 1987 his main research interests have been in the field of medical image processing,
optical character recognition, texture analysis and shape description.
CHIANESEwas born in Naples, Italy, in 1954. He graduated in electronic
engineering in 1980 at University of Naples and is presently Associate Professor of Computer Science at
the same University. He has worked on computer networks, parallel architectures, computer vision, optical
character recognition and more recently, concurrent object oriented programming.
About the Author-AwELo
Ahout the Author-Lum
P. CORDELLA
was born in Milano, Italy, on 26 November 1938. He is Professor
of Computer Science at the Faculty of Engineering of the University of Naples, Italy. He has been active in
the held of image processing and pattern recognition since 1972. His present research interests are in the
field of optical character recognition, shape analysis, document and map processing, parallel computer
architectures for vision.
About the Author-Ammo
MARCELLIwas born on 20 March 1957. He received the Iaurea degree in
electronic engineering in 1983 and the Ph.D. in electronics and computer engineering in 1987, both from
University of Naples. Currently he is Associate Researcher at the Faculty of Engineering of the University
of Naples, Italy. His research interests are in optical character recognition, texture analysis, shape description
and expert systems.