Vol. 7 (1998):
Abstracts of Papers
Nos. 1/2: Special Issue: Proc.
5th GKPO'98 Conference,
No. 3,
No. 4: Special Issue on Medical Image Analysis.
Special issue:
Proc. 5th International Conference on Computer Graphics and Image Processing (GKPO'98),
Borki, Poland, May 1822, 1998.
 Wojdala A., Gruszewski M., Dudkiewicz K., Donotek M.:
Realtime depthoffield algorithm for virtual studio.
MGV vol. 7, nos. 1/2, 1998, pp. 514.
[Paper nominated
for the Best Paper Award.]

Since the beginning of realistic image synthesis, depth of
field was considered an important, though computationally
expensive factor enhancing the realism of computer generated
images. Introduction of virtual reality techniques created
the demand for this effect to be at least interactive. This
paper describes physicallybased, realtime depth of field
algorithm, addressing the needs of even more demanding
application  virtual TV studio.
 Reginski M., Stepien C.:
The method of animation of a growing spruce with seasonal
model changes.
MGV vol. 7, nos. 1/2, 1998, pp. 1526.

This paper describes an algorithm which generates a model of
a tree in different moments of it's life. The algorithm, in
opposition to those already known, enables to get the model
in time period shorter than a year. Therefore it is possible
to make an animation of a growing tree including seasonal
changes in its appearance. A morphing method was used as a
base of this animation. Necessary transformations of a
sequence of models are presented in order to adapt these
models to the standard of the morphing method.
Key words: botanical tree, animation, morphing,
simulation of the growing process.
 Kobus K.:
Fast animation of turbulent fog.
MGV vol. 7, nos. 1/2, 1998, pp. 2740.

This paper presents a method of fast animation of turbulent fog
phenomena. The high realism and interactive
frame rates are achieved due to use of spectral theory of turbulence
and visualisation in post processing.
 Wcislo R., Kitowski J., Moscinski J.:
Animation of group of elastic objects based on distributed
physical simulation.
MGV vol. 7, nos. 1/2, 1998, pp. 4148.

The paper presents the overview of a
computer system for performing animations of a set of solids and
(optionally) a liquid medium. The animation is driven by the
simulation based on physical laws to ensure the maximum reality.
Key words: multibody animation, molecular dynamics,
cellular automata, distributed simulation.
 Olenski R., Radziszewski P.:
Realtime rendering and animation of mirages.
MGV vol. 7, nos. 1/2, 1998, pp. 4964.

The document presents a method that can be used to visualize a mirage
phenomenon using a "conventional" polygonal renderer. An algorithm of
the calculation of the scene reflection in the mirage is shown, with
its major parts: preselection of the mirage surfaces, mirage polygons
and scene polygons and calculation of the modified viewing frustum.
Approaches to the mirage animation are also discussed. Method
presented here allows for faster rendering process, in comparison to
wellknown raytracing methods, and thus can be easier used in
applications that require fast image generation times, e.g. in flight
simulators.
 Kasprzak J., Raczkowski J.:
Modelling a wind field effecting a smoke.
MGV vol. 7, nos. 1/2, 1998, pp. 6574.

The visual simulation of natural phenomena is a challenge problem
in computer graphics. In the paper a simplified method of the wind field
modelling is presented. The method is based on a discrete volume space
where vectors of the field are defined. The wind field is used
for animation of smoke. The smoke density is transferred between
voxels in space due to wind vectors in subsequent frames.
Key words: modelling natural phenomena, animation,
discrete volume space, wind, smoke.
 Karpouzis K., Votsis G., Tsapatsoulis N., Kollias S.:
Compact 3D model generation based on 2D views of human faces:
application to face recognition.
MGV vol. 7, nos. 1/2, 1998, pp. 7585.

A face recognition and syntheticnatural hybrid coding
tool involving frontal and profile views is presented in this paper.
The tool utilizes the above mentioned 2D images  upon which certain
protuberant points are automatically detected  and adapts a generic
3D head model (polygon mesh) according to the predetermined information
gained by the available views. This mesh provides shape information
which  combined with texture information  is important for
the robustness of a recognition system. The main advantage
of the proposed approach is its ability to overcome constraints
raised from arbitrary variations in scale, rotation and orientation,
which are dominant deterioration factors in the identification task.
Besides the face recognition aspect, applications which involve
geometry transmission, such as teleconferencing, can take advantage
of the proposed algorithm's ability to parametrically describe
a complex organic model, such as a human head.
During the texture map creation process, issues related to
the luminance differences and rotation variance between
the available views, are successfully dealt with.
Regarding the adaptation of the polygon topology of the 3D model,
we apply a set of localized transformations, in order to preserve
the continuity of the human head surface. Besides this,
the problem of the minimum organic model representation required
is addressed. The aspect under which this issue is verged upon,
is that of the solution of a tradeoff problem between
low computational complexity and high approximation quality.
Key words: 3D face modeling, automated feature extraction,
geometry compression.
 Bartkowiak M., Domanski M.:
An efficient technique for highcompression
of chrominance data.
MGV vol. 7, nos. 1/2, 1998, pp. 8797.
[Paper nominated
for the Best Paper Award.]

The paper describes an
original technique to encode chrominance. We assume that the
luminance is encoded entirely independently from chrominance.
Nevertheless the chrominance coder and decoder use the
reconstructed luminance in order to exploit the mutual
correlation between the luminance and the chrominance
components. The experimental results prove usefulness of the
technique for image coding with high compression ratios.
Key words: color, chrominance, video coding,
very low bitrate.
 Jozwik A., Chmielewski L., Sklodowski M., Cudny W.:
A parallel net of (1NN, kNN) classifiers for optical
inspection of surface defects in ferrites.
MGV vol. 7, nos. 1/2, 1998, pp. 99112.

The challenging task of optical inspection of
surface defects in ferrite cores has been successfully
approached with a set of methods. In this paper the attention is
paid to the k Nearest Neighbours classifier developed for the
system. A parallel net of twodecision classifiers is presented.
The combination of the 1NN and kNN rules reduces the
training time. A great part of computations is restricted to the
class overlap area. The classification quality is significantly
improved if a separate feature selection for each of the
component classifiers is done. A dramatic improvement of
classification speed obtained by reference patterns sets
reduction for component classifiers is vital, as in the considered
task the classifier is used for recognition of pixels. The
proposed modifications of the classifier are of general
usefulness for pattern recognition. The presented quality
inspection system can be applied to various defect detection
tasks.
Key words: statistical pattern recognition,
nonparametric methods, kNN rules, parallel classifiers,
quality inspection, ferrite cores.
 Doulamis N., Doulamis A., Kollias S.:
A dynamically trained neural network for machine vision
applications.
MGV vol. 7, nos. 1/2, 1998, pp. 113123.

A dynamically trained neural
network is proposed in this paper proper for adapting the
network performance to non stationary image or video inputs.
The scheme includes, on one hand, a retrieval mechanism
which selects the most appropriate network from the system memory
and, on the other hand, a weight perturbation procedure
which adapts the network weights to the current condition.
If no suitable network exists in memory,
new weights and network structure are created and then
stored for future use. Experimental results are provided
indicating the good performance of the proposed system
to computer and machine vision applications.
Key words: neural networks, image processing,
adaptive training, non stationary inputs.
 Furtak J.:
Camera calibration utilising controlled translation.
MGV vol. 7, nos. 1/2, 1998, pp. 125134.

This paper presents camera calibration algorithm based on the same
landmarks observed by camera in different locations. The
basic idea of algorithm is recurrent using of intermediary results.
This feature makes the knowledge accumulation during calibration
process possible. Algorithm was verified experimentally. The
experiment realisation method and received results are described.
 Kulikowski J.L.:
Computeraided analysis of serial images.
MGV vol. 7, nos. 1/2, 1998, pp. 135149.

A concept and basic procedures of computer analysis of
serial images (ASI) stored in image databases (IDB) is described.
An ASI is considered as a series of computer
procedures recognising some relations among imagerecords
stored in IDB. The relations can be described both on some vectors
of parameters assigned to the records and on the images themselves.
Three basic groups of relations are considered: similarity, ordering
and some higherorder relations described as hyperrelations of the
MATCH  and SPREADtype. Special attention also has been paid
to the semiordering of imagerecords based on the concept of
semiordered linear vector spaces (Kantorovitsh spaces);
this is considered as a general method of multiaspect evaluation
of imagerecords. Some concepts of ASI described in the paper
have been realised in the system APOS, compatible with a standard
library of image processing procedures and an IDB management system.
APOS has been designed mainly for biomedical applications.
Key words: image processing, image databases,
serial images, relations, hyperrelations, semiordered vector spaces.
 Tanács A., Palágyi K., Kuba A.:
Medical image registration based on
interactively identified anatomical landmark points.
MGV vol. 7, nos. 1/2, 1998, pp. 151158.

Registration is a recently emerged task in medical
image processing used to match two independently acquired images.
To register images, the geometrical relationship
between them is to be determined.
Matching all the geometric data available for a
patient provides better diagnostic capability, better
understanding of data, and improves
surgical and therapy planning and evaluation.
Registration of images taken from different modalities
(i.e., multimodality registration) is regarded as a rather
difficult problem.
This paper describes a method for solving 2D/2D and
3D/3D registration using interactively defined point landmarks.
We have implemented this robust and effective method.
The SIR (Simple Image Registration) software system runs on
IMB PCs under Windows operating system.
Key words: medical imaging, registration problem,
reslicing, image fusion.
 Østergaard L.R, Lind J., Larsen O.V., Nielsen H.,
Bartholdy N.J., Haase J.:
System for 3D localisation of malformations
in the human brain.
MGV vol. 7, nos. 1/2, 1998, pp. 159167.

A 3D localisation system for preoperative planning is presented.
The developed localisation system is able to estimate the 3D position
of a target, e.g. an AVM (ArterioVenous Malformation), based on a
set of digital Xray images. Distortion correction and camera
calibration is performed in order to obtain accurate 3D estimates.
The system is tested on a plexiglass
phantom with embedded steel pellets offering 126 test points with
known 3D positions. The test has shown that the
system is able to estimate 3D positions with a mean error
of 0.33 mm and a maximum error of 1.18 mm. The required accuracy is
0.6 mm and the test showed that more than 90% of the 3D position
estimates fulfil this requirement.
Key words: Digital Xray imaging, distortion correction,
camera calibration, preoperative planning.
 Punys J., Puniene J.:
Statistical approach for boundary extraction
in echocardiographic images.
MGV vol. 7, nos. 1/2, 1998, pp. 169178.

The technique for defining an initial endocardial boundary
in 2D ultrasound heart images is developed. The model
of a boundary is constructed on a set of connected vertices.
The position of vertices is evaluated by applying the matched
detector technique. The parameters of the detector weigth function
are adapted for eliminating undesirable deformation effects
caused by the papillary muscles. Then the endocardial boundary
is modified on the basis of criterion on which the geometrically
deformable model can be constructed. Results of applying
the algorithm for endocardial boundary estimation
to medical images are presented.
 Thurfjell L., Ranefall P., Bengtsson E.:
A deformable atlas of the chest based on the visible man.
MGV vol. 7, nos. 1/2, 1998, pp. 179186.

This paper describes the creation of a 3D computerised anatomical
atlas of the chest based on data from the Visible Human project
at the National Library of Medicine. A pixelwise box classifier
was used to segment different organs in the chest colour
and CT images of the male cadaver and a chest atlas containing
surface descriptions of the segmented organs was created.
The structures in the atlas can be visualised using
fast surface rendering. The atlas can also be deformed to fit
the anatomy of another individual. This is illustrated
by an application example where the atlas is matched
to MRI data from a healthy volunteer.
 Belikova T.P., Stenina I.I., Yashunskaya N.I.:
Image interpretation based on image processing
and knowledgeguided data analysis.
MGV vol. 7, nos. 1/2, 1998, pp. 187196.

A series of methods has been developed to promote medical
image analysis and interpretation in complex diagnostic
tasks. Image processing methods were used for better
representation of informative features for the expert's
analysis. Then the expert's descriptions of processed image
were collected in a database to find discriminative features
and create classification decision rules. Created threshold
rules were interpreted by physicians as a syndromelike
construction conventional for medicine. We proposed some
statistics that were helpful for measuring some
discriminative features directly in the image to realize
unbiased expertindependent part of image descriptions.
Developed methods were applied for early peripheral lung
cancer diagnosis and helped to improve the efficacy of image
interpretation for physicians of different qualifications.
Key words: image processing,
knowledgeguided image analysis, uncertain data interpretation,
computeraided image diagnosis.
 Hashoti E.:
Graphical and nongraphical information integration,
data base application development using AutoCAD.
MGV vol. 7, nos. 1/2, 1998, pp. 197203.

This research paper will analyze our ideas about different issues
on integration of two different types of information: graphical
and nongraphical. Although many GIS packages are available
in the world's software market, still it is quite difficult
to choose among this variety of numerous software, both
satisfying cost and quality requirements. Most of many
specific cases require approaching this argument without
risking additional and maybe unnecessary investments. By
choosing common tools and software, we offer to present our
study which focuses and samples the Immovable Properties
graphical and nongraphical manipulation.
Key words: AutoCAD extended data,
onedirectional linkage, external data identification.
 Nieniewski M.:
Experiments with morphological Markov random fields.
MGV vol. 7, nos. 1/2, 1998, pp. 205220.

The paper presents results of experiments with morphological Markov Random
Fields (MRFs). The use of MRFs allows one to include a prior knowledge
about an image via the probability model into the processing of the image.
At the same time, when generating random textures, one notes that
various textures are possible, for which the models still
have to be invented. The morphological MRFs offer a method for enlarging
the set of probability models. However, it is not obvious what the
effects of changing the model and its parameters will be. The paper
presents results of systematic experiments with the generalized
Ising model as well as generalized Potts model. In this way
a deeper insight into the properties of the morphological MRFs
is obtained.
 Lumini A.,
Maio D.:
Image generation by Petri nets.
MGV vol. 7, nos. 1/2, 1998, pp. 221232.
[The Best Paper Award recipient.]

This paper presents a new approach to computer image generation.
The basic idea is to translate the evolution of a Petri net
into a graphic output. In particular, we focus on three methods
for image generation which exhibit a certain analogy with fractals.
Some experimental results are reported together with a brief
investigation on the relationships between generated
images and their corresponding Petri nets.
Key words: image generation, Petri nets, fractals.
 Ihle T., Fuchs S.:
Marching open stars  single pass segmentation
of 3D pseudomanifolds.
MGV vol. 7, nos. 1/2, 1998, pp. 233244.

We present an approach for segmentation of 3D voxel data based on
algebraic topology. The framework leads to a single pass algorithm for
constructing symbolic descriptions of volumetric data. Unlike previous
algorithms, segmentation is not limited to extracting isosurfaces,
i.e. 2D~manifolds, enabling the processing of image sequences. Due to
the anchoring on algebraic topology, the correctness of the algorithm
can be proven.
Key words: topology, 3D segmentation.
 Iones A., Zhukov S., Krupkin A.:
Building optimal bounding volumes for realtime
3D visualization.
MGV vol. 7, nos. 1/2, 1998, pp. 245258.

Bounding volume hierarchies are widely employed in many areas of
Computer Graphics. Usually they are used as crude approximations of
scene geometry to speed up timeconsuming computations such as
visibility tests for frustum culling, ray shooting, etc. A number of
bounding volume types have been discussed by various researchers.
They include bounding spheres, axisaligned and oriented
bounding boxes (OBBs), and others. Although it is practically
possible to use any of these bounding volumes, some types
prove to be particularly useful in certain applications.
E.g., Gottschalk et al. used OBBs to implement a very effective
exact collision detection scheme.
In this paper we address the problem of efficient bounding volume
selection, the solution of which allows us to significantly
accelerate such operations as visibility tests for frustum culling
and ray shooting. We prove that minimal surface area (minimal
perimeter in 2D) oriented bounding box is optimal among all the
oriented bounding boxes with respect to the three operations stated
above. Then, we develop a number of algorithms to create optimal
oriented bounding boxes and their approximations and finally discuss
the results of our practical implementation.
Key words: computational geometry, bounding volumes,
frustum culling, ray shooting, realtime graphics.
 Moscinska K.:
Markov random fields and constrained optimization
for textured image segmentation.
MGV vol. 7, nos. 1/2, 1998, pp. 259268.

Classical methods of image segmentation, like discontinuity detection
or region growing concepts, are not satisfactory in case of textured
images. The alternative is the application of stochastic models
like Markov Random Fields (MRF) for image modelling and segmentation.
Stochastic models may be described in terms of energy function that
should be minimized during a relaxation procedure. Instead
of doublystochastic model, in which both the intensity and
the label process are modelled by a MRF, we apply MRF for region
geometry modelling, whereas image intensity is modelled by the set
of deterministic features. Local texture properties are evaluated
using local linear transforms or results from the first order histogram.
We measure the disparity between spatial features on the basis
of the KolmogorovSmirnov statistics. Stochastic relaxation algorithm
is applied for the minimization of the global energy function.
The forbidden label configurations introduce constraints
into the minimization process. Simulation results for the texture
segmentation task are given. The examples presented in the paper
confirm the usefulness of proposed models and the efficiency
of the designed algorithms. Parallel implementation
of the constrained optimization can be considered due
to the local computation.
Key words: Markov Random Field, texture,
image segmentation, stochastic relaxation, constrained optimization.
 Sluzek A.:
Momentbased contour segmentation using
multiple segmentation primitives.
MGV vol. 7, nos. 1/2, 1998, pp. 269279.

The paper presents a new technique
of segmenting digital contours using multiple segmentation
primitives. Therefore, segmentation results are a combination of line
segments, arcs, corners, etc., depending on how well these shapes
match the original contour. In the first step, the prospective
instances of all available segmentation primitives are detected
within the input digital contour. This is done by using features
based on moments and moment invariants adapted for digital contours.
Then, the detected instances are ranked according to how accurately
they fit the corresponding fragment of the contour. Finally, the
toprank segmentation primitives are selected one by one until the
whole contour is approximated. The algorithm has relatively low
computational complexity, and it allows parallel implementation.
Moreover, the algorithm is not sensitive to the performance of edge
detectors so that similar results are produced no matter what edge
detector has extracted contours from the original image. Therefore,
if the quality of cameracaptured images is satisfactorily high, the
algorithm can analyse them without any preprocessing required
(except, of course, edge detection).
Key words: contour images, segmentation,
shape primitives, moment invariants.
 Palenichka R.M., Ivasenko I.B.:
Structureadaptive evaluation of additive noise level
in images.
MGV vol. 7, nos. 1/2, 1998, pp. 281290.

In the paper the problem of noise estimation is considered.
The distinctive feature of the presented structural image model
is the separate modeling of the object's planar shape as well as
the image intensity function which is defined within
the support regions of objects and for the background itself.
For the intensity function model of the original
image a piecewise polynomial model is assumed.
Key words: noise estimation, piecewice polynomial model,
sequentional differentiation, trimmed mean filter.
 Kozera R.:
An overview of the shapefromshading problem.
MGV vol. 7, nos. 1/2, 1998, pp. 291312.

In this paper, we discuss the problem of recovering the shape
of a smooth lambertian surface illuminated by one (two, three)
distant point lightsource(s). We show that the system of three (two) firstorder nonlinear partial differential equations corresponding
to the case of three (two) point lightsource photometric stereo
has a unique (generically unique) solution. In the case of one point
lightsource, we discuss the existence and uniqueness
of solutions to the corresponding eikonal equation.
In connection with uniqueness, we consider circularlysymmetric
eikonal equations forwhich there exist circularlysymmetric
and noncircularly symmetric smooth solutions. In addition,
we briefly discuss a number of shape reconstruction algorithms
based on a single (multiple) image analysis.
 Skomorowski M.:
Parsing of random graphs for scene analysis.
MGV vol. 7, nos. 1/2, 1998, pp. 313323.

Further results of research into parsing of random graphs
for recognition of distorted scenes are presented.
An efficient topdown parallel parsing algorithm
for analysis of distorted scenes is proposed.
The proposed approach involves parsing of graph grammars.
To take into account all variations of a distorted scene under
study, a probabilistic description of the scene is needed.
The random graph approach is proposed here for such a description.
Key words: scene analysis, graph grammars, graph parsing,
random graphs.
 Dabkowska M., Mokrzycki W.S.:
A facedependent view model of convex polyhedra.
MGV vol. 7, nos. 1/2, 1998, pp. 325334.

This paper relates to the view model of convex polyhedra
construction in the perspective projection, using the view sphere concept.
Such models are devoted to visual identification systems. In particular,
a new concept of featuredependent choice of the view points and their
dislocations on the view sphere is presented. And also a new method
and an algorithm of determining oneview areas on the sphere is described.
Key words: visual identification of objects,
view model database, view sphere, view points,
strategy of view points selection, oneview areas on the sphere.
 Grabska E., Gurba M., Strug B.:
Designing Aalto lamps by means of attributed
graph grammars.
MGV vol. 7, nos. 1/2, 1998, pp. 335343.

This paper concerns with computer aided design. Design process
is illustrated by means of designing lamps in the framework
of graph transformations. The theoretical concepts are implemented
and examples of designed artifacts are presented.
Key words: graph transformation, design,
aesthetics, rendering.
 Grabska E., Hliniak G.:
Graphic prints design using graph grammars.
MGV vol. 7, nos. 1/2, 1998, pp. 345353.

The syntactic and semantic aspects of graphic prints design process
are considered. The syntactic structures of prints are represented
by graphs. Hence, graph grammars are tools for generation
of graph representations of Escher's prints.
The possible ways of a realisation of those representations
are specified by a realisation scheme which maps
graphs into graphic prints. The implementation of Escher's prints
is also discussed.
Key words: graph, graphical model, graph grammar,
graphic print.
 Iwanowski M.:
An attempt to segmentation of semiographic characters
of printed Japanese script for recognition by GedNLC grammars.
MGV vol. 7, nos. 1/2, 1998, pp. 355365.

In the paper three methods of an automated segmentation of kanji
graphs are described. The first two of them yield divisions at the
level close to the traditional components of kanji} graphs.
But a too large number of kanji graphs which do not lend themselves
to division makes one assign to these methods an auxiliary role
in the system under construction.
The third method divides a kanji graph into segments which
approximately correspond to fragments of traditional strokes.
Hence almost every kanji graph lends itself to division into
segments, and the description thus obtained can be used
for their recognition by GedNLC grammars.
Key words: kanji graph, segmentation,
measure of distance.
 Kowalczyk N.:
TREPHL: visual programming in threedimensional
environments.
MGV vol. 7, nos. 1/2, 1998, pp. 367381.

In this paper we propose a new visual programming language called
TREPHL intended for application in a threedimensional environment.
The main purpose of the language would be automation of repetitive
tasks by endusers not trained as programmers. Other possible uses
for the language may be solving domainspecific problems and creating
prototypes.
The design of the language profits from the following assumptions:
paradigm of objectorientation, readytouse components supplied by
operating systems and application programs as basic program blocks,
construction metaphor for building programs from bricks shaped to
emphasize the possible attachments between objects and hydraulic
metaphor for representing the flow of data and control as pipes
connecting objects.
 Klopotek M.A.:
Structure and motion from multiframes.
MGV vol. 7, nos. 1/2, 1998, pp. 383396.

The paper gives an overview of the problems and methods of
recovery of structure and motion parameters of rigid bodies
from multiframes.
 Hassanien A.E., Nakajima M.:
An efficient crossdissolve transformation with elastic body
spline warping interpolation for facial image morphing.
MGV vol. 7, nos. 1/2, 1998, pp. 397406.
[Paper nominated
for the Best Paper Award.]

In this paper, we propose a new image morphing algorithm which
uses elastic body spline to generate a warp function that interpolates
scattered data points. The spline is based on a Partial
Differential Equation of Navier that describes the equilibrium
displacement of the elastic body subjected to forces.
The spline maps can be expressed as the linear
combination of an affine transformation and Navier interpolation
spline. The proposed algorithm generates a smooth warp that
reflects the feature point correspondence. It is efficient in time
complexity and smoothed interpolated morphed images with only a
remarkable small number of feature points specified. It allows each
feature point to be mapped to the corresponding feature point in the
warped image. Once the images warped to align the positions of feature
and their shapes, the inbetween facial animation from given
two facial images can be defined by cross dissolving the positions
of correspondence features and their shapes and colors.
We describe an efficient cross dissolve algorithm for generating
the inbetween image.
Key words: image morphing, image warping,
elastic body spline and feature specification.
 Lebiedz J.:
Integer midpoint Bézier curve scanconversion
algorithm.
MGV vol. 7, nos. 1/2, 1998, pp. 407415.

By much the same midpoint methodology as is employed in algorithms
which generate a quantized representation of a straight
line or a circle, incremental algorithms using only integer operations
(addition/subtraction and sign testing) can generate a close approximation of
more complicated curves given by implicit equation F(x,y)=0. The equations
F(x,y)=0 for parabolic and cubic Bézier curves are derived and integer
midpoint algorithms for these curves are presented.
Key words: Bézier curves, discrete curves,
scan conversion, raster graphics.
 Malgouyres R., Lenoir A.:
Topology preservation within digital surfaces.
MGV vol. 7, nos. 1/2, 1998, pp. 417425.

Given two connected subsets Y in X of the set of the surfels
of a connected digital surface, we propose three equivalent way
to express that Y is homotopic to X.
The first characterization is based on sequential
deletion of simple surfels. This characterization enables us
to define thinning algorithms within a digital Jordan surface.
The second characterization is based on the Euler Characteristics
of sets of surfels. This characterization enables us, given
two connected sets Y in X of surfels, to decide whether Y
is nhomotopic to X. The third characterization is based
on the (digital) fundamental group.
 Kiciak P.:
Rendering rational curves on raster devices.
MGV vol. 7, nos. 1/2, 1998, pp. 427436.

We present a very fast and accurate procedure of rendering
rational Bézier curves on a raster device. The method uses
a homographic reparameterization of the curve to obtain the numerator
and denominator represented in the monomial basis and uses
the Horner scheme to compute them.
The fixed point arithmetics used in the implementation
is accompanied by a rounding error analysis that guarantees
the accuracy of the curve image.
Key words: rational Bézier curves,
fixed point arithmetics.
 Putz B.:
Remarks on NURBS representation.
MGV vol. 7, nos. 1/2, 1998, pp. 437443.

The paper presents two different knot vectors used in literature for
NURBS representation. Bspline and Bézier representation
are also easily presented as subsets of NURBS representation,
with connection to knot vectors and existing standards.
Key words: NURBS, Bspline,
Bézier curves and surfaces, knot vector, knot sequence.
 Hrytskiv Z., Voloshynovskiy S.:
Nonlinear adaptiveparametric image restoration.
MGV vol. 7, nos. 1/2, 1998, pp. 445454.

In this paper the problem of restoration of defocused
images corrupted by mixed noise is considered. To enhance the noise
immunity of restoration algorithm based on iterative method with adaptive
regularization and parametric constrains on the solution the prefiltering
is proposed to be carried out. To avoid double image blurring on the
prefiltering stage the simultaneous suppression of gaussian and impulse
noises is performed according to the local image structure using adaptive
nonlinear filter.
Key words: noise removal and filtering,
adaptive image restoration, regularization, iterative algorithm.
 Starovoitov V., Samal D.:
Experimental study of color image similarity.
MGV vol. 7, nos. 1/2, 1998, pp. 455462.

A new idea for lowlevel comparison of color images is presented
and tested experimentally. The developed method allows to compare
two color images of the same size and color range.
A modified chessboard metric was used as a measure of local
dissimilarity between the pixels of compared images followed by
the calculating of global dissimilarity value.
Providing the dissimilarity value is lower than some value,
we can say that two digital images are similar and present
the same scene.
Key words: digital color image, distance,
lowlevel image processing, image comparison.
 Okun O.:
Euclidean distance transform with the reduced number
of multiplications.
MGV vol. 7, nos. 1/2, 1998, pp. 463474.

A new method of the Euclidean distance map generation is developed
which reduces the number of multiplication operations needed
to compute distances. This method belongs to a class of the ordered
propagation distance transforms using masks whose shape depends
on a direction of the distance value propagation.
To obtain Euclidean distances, we apply two nonEuclidean transforms
(city block and chessboard) simultaneously so that our approach
is faster than the standard algorithms because it uses only additions
instead of multiplication operations when labelling the distance map.
Experiments confirm correctness of our method and memory requirements
for it do not exceed those for other transforms using ordered
propagation.
Key words: distance transform, ordered propagation,
Euclidean distance, city block distance, chessboard distance.
 SzirmayKalos L., Fóris T., Purgathofer W.:
Nondiffuse, randomwalk radiosity algorithm with linear
basis functions.
MGV vol. 7, nos. 1/2, 1998, pp. 475484.

This paper presents an efficient method to solve the general
rendering equation, using a combined finite element and quasirandom
walk approach. Applying point collocation method, the surfaces
are decomposed into planar patches where the directional distribution
of the radiance is assumed to be a linear combination of the distributions
at the vertices. The direction dependent radiance function
of the vertices is then computed by random or quasirandom walk.
Key words: rendering equation,
quasimonte carlo quadrature, radiosity, pointcollocation method.
 Toumit J.Y., Emptoz H.:
From the segmentation to the complete
reading of a mathematical document.
MGV vol. 7, nos. 1/2, 1998, pp. 485504.

Automatic reading of scholar manuals is an important problem for the editors;
we are presently working in this context on the conversion of mathematical
manuals into electronic documents. No research on the entire mathematical
document seem to have been achieved until now, there has been only studies
on the formulas themselves. We therefore present the problem of reading
such documents. Those documents contain two types of information
of different natures: the text and the mathematical objects.
To perform a better treatment on the text itself, we are leaded
to separate those two types of information; in this article,
we pay a particular attention to this treatment which can be considered
as a multilanguage segmentation problem. Classical methods do not provide
satisfactory results and we needed to introduce a new segmentation
approach; it fills the document's surface using "propagation" methods
around particularily specific points of the text or of the mathematical
objects. We also analysed the constraints relative to the documents
we have to deal with; in this context, we need to use the graylevel
image without binarizing it. A method for segmenting words
and characters using this graylevel image is presented
and we then introduce tetrarization which leads to more reliable
images than binarized images.
Key words: automatic reading, mathematical formulas,
multilingual segmentation, grayscale image processing.
 Bres S., Emptoz H.:
Local and global orientations on images.
MGV vol. 7, nos. 1/2, 1998, pp. 505513.

This paper presents a new method of anisotropy inspection and
quantification in digital images. It allows to detect the measure the
occurrence of each directions of an image. The human visual system is
usually very powerful for anisotropy detection, because it performs
this analysis at different levels. Local information (from details)
and more global information (from spatial distribution of patterns)
are simultaneously present for the treatment. We show that our method
is able to perform the anisotropy feature analysis using this global
approach, unlike classic methods of directions analysis. Moreover,
our method directly processes grey level images, uses the inner part
of the patterns instead of their contours and is able to inspect all
the directions of a picture. These specifications overcome most of
the limitations of usual methods.
 Betsos G., Heger R.:
A desktop virtual reality system for automated
assembly planning.
MGV vol. 7, nos. 1/2, 1998, pp. 515531.

This paper describes the basic components of a system, that automates
the assembly planning of industrial products. The system makes use of
the technique of Virtual Reality (VR) in order to simulate the manual
assembly of products in an intuitive way. The end user can interact
with three dimensional objects inside a virtual environment and
assemble them in a variety of ways. He can subsequently use a browser
to view the precedence graphs of the actions performed inside the VR
environment. With the aid of these graphs, he can choose the optimal
assembly sequence. All the components of the system are controlled
using a Graphical User Interface (GUI) developed using the Tcl/Tk
scripting language.
 Neumann L., Neumann A., Prikryl J., Purgathofer W.:
The constant radiance term.
MGV vol. 7, no. 3, 1998, pp. 535549.

This paper describes a fundamental improvement for all
rendering methods that evaluate the rendering equation in any
complexity. The "Constant Radiance Term" accelerates the
computation of multiple interreflections in arbitrary
nondiffuse environments. It is an extension of the
constant radiosity step introduced earlier for solving radiosity
problems and does not require geometrical nor visibility information.
A constant radiance portion is extracted from the solution in every
surface point and every direction. The residuum problem can be
solved faster or with reduced variance by all known methods that
consider nondiffuse light interreflections, like different versions
of distribution ray tracing, deterministic and stochastic radiosity
methods, and hybrid solutions. The constant radiance value is chosen
in such a way that the total selfemitted power of the residuum
problem is zero so that after the extraction of the constant part
there are places with positive selfemittance and places with
negative self emittance.
The achieved acceleration can be significant for environments with many
bright coloured surfaces. Using a decomposition into separate
positive and negative problems it is possible to apply this
technique even when using turnkey rendering software.
 Li W., Ke Q., Huang X., Zheng N.:
Light field rendering of dynamic scene.
MGV vol. 7, no. 3, 1998, pp. 551563.

Image based rendering has displayed advantage in speed over
traditional geometry based rendering algorithms. With the
four dimensional light field descriptions, static scene can
be generated with interactive rate on ordinary computer. The
limitation of the scheme is that it can only handle static
scene and fixed illumination. This paper raises the idea to
decompose the light field into sublightfields that do not
change as scene changes. It expands the advantage of light
field rendering to dynamic scenes where the position and
orientation of objects, lights and viewpoint can be modified
arbitrarily.
The sublightfields include: ambient light field and spot
light field. The latter is actually an eightdimensional
space. Because diffuse reflection is independent on view
direction, this paper presents a fourdimensional
representation of spot light field. Considering the linearity
of diffuse reflection to different spot lights, the spot
light fields of an object can be represented by the
reflection light field to a purecolor light with unit
intensity, to decrease storage and preprocessing. Owing to
the coherency in their data structures, data of the
corresponding point in the ambient light field, diffuse light
field and depth field are combined into a 5dimensional
vector which can be compressed efficiently with vector
quantization. The algorithm given in this paper accurately
computes typical characteristics of dynamic scene such as
changes in surface color and shadow.
Key words: ambient light field, spot light field,
diffuse light field, depth field.
 Flasinski M., Skomorowski M.:
Parsing of random graph languages for automated inspection
in statisticalbased quality assurance systems.
MGV vol. 7, no. 3, 1998, pp. 565623.

Basic requirements for an automated visual inspection in intelligent
SPCoriented quality assurance systems are discussed. Extensions of
feature IEgraphs representing solids in CAD to a stochastic
model of manufacturing processes are proposed. An efficient random
graph language analysis based on parsable ETPL(k) graph grammars
is presented as a tool for intelligent reasoning in high layer modules
of automated inspection systems. The first applications of the model
are shown.
Key words: graph parsing, graph grammar,
syntactic pattern recognition, visual inspection.
 Rosin P.L.:
Grouping curved lines.
MGV vol. 7, no. 3, 1998, pp. 625644.

This paper examines the problem of automatically grouping image
curves. In contrast, most previous work has been restricted to points
and straight lines. Some of the computational aspects of the groupings,
namely continuation, parallelism, and proximity are analysed,
and the issues of neighbourhoods, combinatorics, and multiple scales
are discussed.
Key words: illusory contours, automatic curve grouping,
segmentation and completion of curves,
multi, natural and single scales of curves.
 Abuzova I.V., Ignatiev V.M., Kotov V.V., Larkin E.V.:
The method of multiframe image filtering.
MGV vol. 7, no. 3, 1998, pp. 645654.

Features of so called multiframe images are described.
Methods and algorithms of multiframe images processing, such as
reduction to the base frame and filtering of an outcome threedimension
signal, are considered. Results of experimental researches are given.
Key words: image, frame, multiframe, Fourier spectrum,
Haar spectrum, filtering.
 Bartkowiak A., Szustalewicz A.:
Watching steps of a grand tour implementation.
MGV vol. 7, no. 3, 1998, pp. 655680.

Bartkowiak and Szustalewicz (1997), have proposed
an implementation of the grand tour algorithm
designed specially to detect outliers in multivariate data.
The algorithm works by performing a sequence of rotations
and projections onto a specific 2Dplane. This is equivalent
to perform a series of rotations yielding transformed coordinates
of the data:
X^{tr} = X A, with A being the rotation
matrix, while X and X^{tr} denote
the data matrices before and after the rotation, respectively.
A superimposed concentration ellipse indicates the outstanding points.
We complement the paper by considering some details
and variants of the implementation of the grand tour algorithm.
In particular we watch the trajectories of the projected points.
Our concern is the denseness of the watched projections.
We look at the trajectories of the projected points visible in the
projection plane and the frequencies of their appearing in various
sectors of that plane.
In the Appendix we present the derivation of the formula for
the rotation matrix A employed in each step of the algorithm
for obtaining the transformed data coordinates.
Key words: dynamic graphics, grand tour,
rotation, projection, uniform distribution.
 Yadohisa H.:
Visualization of proximity data by multidimensional scaling
with residual from space reduction.
MGV vol. 7, no. 3, 1998, pp. 681686.

New multidimensional scaling method for representing a twoway
proximity data is proposed.
Given an n x n data matrix D of proximity measures between n objects,
a configuration of objects, optimum in a sense, is determined
by applying some suitable multidimensional scaling method
as a set of coordinates X. A residual matrix is defined here as
a reducedspace difference of D and the inter object distance matrix
composed from X.
The main purpose of this paper is to propose a graphical method
for representing the residual caused from space reduction.
Key words: asymmetry, data visualization,
(dis)similarity, graphical representation, MDS.
 Smolka B.:
An application of random Markov field in selected problems
of lowlevel image processing (in Polish). [Dissertation Abstract]
MGV vol. 7, no. 3, 1998, pp. 688.
Special Issue on Medical Image Analysis.
Special Issue Editor: Juliusz L. Kulikowski.
 Kim J., Gillies D.:
Automatic morphometric analysis of neural cells.
MGV vol. 7, no. 4, 1998, pp. 693709.

Studies of developing neural cells are widely used in fundamental research
into the mechanisms of nervous diseases, such as multiple sclerosis.
These studies normally require researchers to estimate the populations
of different classes of cells in microscope images of either tissue
or cultures. The estimation process is carried out by human visual
inspection, and is time consuming and subjective in nature. As an attack
on this problem, we have been investigating the use of computer vision
to classify and count the neural cells automatically. We apply various
image processing techniques to reduce the neural cells in an image
to a skeleton form. Then various measures such as the fractal dimension
and 2^{nd} moment are applied to classify cells according
to their spatial growth characteristics seen during their
development. The measures are then combined using a bayesian classifier,
and a decision is taken as to which class a cell belongs.
Our initial studies were aimed at classifying the different development
stages of the cells knowns as oligodendrocytes. The results were
encouraging with better then 80% agreement between the computer
analysis and human judgement.
Key words: Sholl coefficient, fractal dimension,
2^{nd} moment, profile, bayesian classifier, oligodendrocytes.
 Pietka D., Dulewicz A., Jaszczak P., Nechay A.:
Extending DIPS software package for research and routine
investigations of biomedical images.
MGV vol. 7, no. 4, 1998, pp. 711723.

The paper introduces DIPS (Digital Image Procesing System), a new,
original software package, developed to meet specific requirements
of image analysis in scientific environment. Without going deeply into
programming details, key features of the system are highlighted:
flexibility when designing new picture processing schemes and simplicity
when performing routine tasks.
Key words: image processing software,
microscopic image acquisition, object extraction, morphometry,
cytopathology, histopathology, cells and smears classification.
 Rakotomalala V., Macaire L., Postaire JG., Valette M.:
Identification of retinal vessels by color image analysis.
MGV vol. 7, no. 4, 1998, pp. 725742.

A recursive edge tracking of the retinal blood vessel is presented
in order to achieve a bidimensionnal reconstruction of the retinal
vasculature. First, color edge detection is applied on the original
angiographic images. Second, from interactive selection of starting points
near the papilla, the tracking of the two contours of a vessel
is processed. The algorithm validates the next connected pixels
to the current ones which satisfy the tracking hypotheses. Problems
induced by the curvature of the vessel and the discontinuity
of the detected edges will be dealed with. Third, during the tracking,
the algorithm looks for branchings along the major vessel beeing
tracked. Another recursive tracking procedure is then performed
from these branch points until the end of the vessel is reached.
Contour and the color of the vessel's body are associated in order
to get more accurate extraction.The reconstructed vascular
structures will be used as landmarks for the followup of a new
retinopathy called CytoMegaloVirus retinitis found on patients with
acquired immune deficiency syndrome (AIDS).
Key words: color image processing, color gradient,
blood vessel reconstruction, edge tracking, color region/edge cooperation.
 Nikiel S., Kirby G.H.:
Fractal palettes for medical imaging.
MGV vol. 7, no. 4, 1998, pp. 743750.

A fractal colour model used for medical imaging is discussed in this paper.
Presented method should lead to better understanding of displays of complex
and ambiguous medical data sets. A simple technique for generation
of fractal palettes with different 'irregularity' is presented together
with sample images. The method was tested with real life datasets.
Obtained results show that the fractal colour model can be used as
an additional interactive tool for medical visualisation purposes.
This tool is especially useful in enhancing detail visibility within
uncertain regions of computer tomography, magnetic resonance and Xray
mammography images.
Key words: data display, medical imaging, fractals.
 Khouas L., Clarysse P., Friboulet D., Odet C.:
Fast 2D vector field visualization using a 2D texture
synthesis based on an autoregressive filter. Application
to cardiac imaging.
MGV vol. 7, no. 4, 1998, pp. 751764.

This paper presents a new technique for vector field visualization
and its application to the motion estimation of the heart.
Our approach is based on the principle of filtering a texture
over the data to visualize. For this purpose, we have first developed
a texture model that allows 2D synthesis of furlike texture.
The technique is based on a non stationary two dimensional
AutoRegressive synthesis (2D AR). The texture generator
allows a local control of orientation and length
of the synthesized texture (the orientation and length
of filaments). We have experimented the use of this texture
model to represent 2D vector fields. We use orientation,
length and color attributes of our furlike texture
to visualize local orientation and magnitude of a 2D vector
field. The visual representations produced seem satisfying
since complete information about local orientation is easily
perceived. In addition, due to the AR formulation,
the obtained technique is computationally efficient.
In particular, the application of this technique to the
visualization of the myocardial motion has proven very useful.
Key words: furlike texture, AR texture modeling,
texture synthesis, 2D vector field visualization,
computeraided diagnosis, cardiac motion analysis.
 Mari M., Smits P.C., Kies P., Chmielewski L.:
Interactive object detection using a fuzzy
image segmentation approach.
MGV vol. 7, no. 4, 1998, pp. 765780.

In this paper the attention is focused on the processing of digital
images, in particular on the segmentation of medical images.
A new 3D fuzzy segmentation technique is presented to outline
the advantages of a relatively simple software tool that may help
the user to find contours of the objects of interest in images.
The proposed technique is based on a seed growing approach, which takes
into account both contextual and topological information in the image.
The uncertainty of the image is considered through the use of fuzzy measures,
well suited to represent the characteristics of a medical image.
The result is a set of possible contours for the volume of interest
at different certainty values. They may be viewed as alternative contours
of the same object. If the method is used interactively, the user has
the possibility to scroll very quickly through the different contours
to select the most appropriate one for a specific application, according
to his own knowledge.
Quantitative and qualitative results have been presented for a set
of standard test and real images, showing the peculiarities of the proposed
approach. The main applications are suggested in diagnosis (volume
determination of tumours) as well as in therapy (oncological treatment
planning).
Key words: image processing, fuzzy connectedness,
optimal path, isoregion, MR imaging.
 Bogus P., Massone A.M., Masulli F., Schenone A.:
Interactive graphical system for segmentation of multimodal
medical volumes using fuzzy clustering.
MGV vol. 7, no. 4, 1998, pp. 781791.

The paper presents a computerized interactive graphical system
for multimodal medical volumes segmentation. We present a new generation
of the system obtaining by applying fuzzy methods in clustering.
We give an outline of fuzzy cmeans algorithm and we report the results
obtained by using it to multimodal medical volumes segmentation.
Key words: multimodal medical volumes, fuzzy clustering,
segmentation, medical application.
 Csébfalvi B., SzirmayKalos L.:
Interactive volume rotation.
MGV vol. 7, no. 4, 1998, pp. 793806.

In this paper a new volume rendering method is presented which provides
realtime rotation without using any acceleration hardware. The algorithm
is based on the efficient handling of empty voxels, where according
to the opacity values a 3D binary mask is generated indicating the locations
of the nontransparent voxels. Ray casting is performed on this binary mask
which is rotated rapidly by shearwarp factorization and an incremental
alignment technique. The location of a nonzero bit hit by a ray is mapped
onto the corresponding voxel location in the original classified volume,
in order to get the opacity and color values in the given sample point.
The technique proposed for rotating and sampling the binary mask exploits
only the standard ALU operations providing interactive frame rates even
on low cost machines.
Key words: volume rendering, ray casting,
shearwarp factorization.
 Peckar W., Schnörr C., Rohr K., Stiehl H.S., Spetzger U.:
Linear and incremental estimation of elastic deformations
in medical registration using prescribed displacements.
MGV vol. 7, no. 4, 1998, pp. 807829.

We propose an approach for estimation of elastic deformations
in medical registration. Compared to standard registration methods
based on elasticity theory, our estimation scheme does not contain
parameters of the deformation model (elastic constants). Rather,
the computed elastic deformation is uniquely defined through
incorporation of prescribed displacements on boundary structures
in the source and target image. Under the assumption of correctness
of input data, our estimation scheme provides the exact correspondence
of structures to be registered due to the constraints. Furthermore,
to cope with largemagnitude deformations, we propose an incremental
model based on successive linearizations of the nonlinear elastic
equilibrium equation. To illustrate the performance of our approach,
we show experimental results for 2D and 3D synthetic as well as
real medical images and provide timing information for sequential
and parallel realizations.
Key words: nonrigid medical image registration,
elastic deformations, finite element method.
 Belov D.I., Sadykhov R.H.:
New approach to hiddensurface elimination
of 3D medical images.
MGV vol. 7, no. 4, 1998, pp. 831840.

This article presents a new algorithm for hiddensegment elimination
on the plane. A condition of equivalence of two solutions of
hiddensegment elimination problems is presented. On the basis
of the results a new approach to efficient solution of hiddensurface
elimination problem for investigated 3D medical images is suggested.
Key words: hiddensurface elimination,
hiddensegment elimination, layermodel.
 Belikova T.P., Stenina I.I., Yashunskaya N.I.:
Image processing and knowledgeguided data analysis
for medical diagnostics support.
MGV vol. 7, no. 4, 1998, pp. 841858.

A series of methods has been developed to support medical image analysis.
Optimal filtering was applied for better imaging of informative features
(diagnostically important details and structures). Several models of image
background were tested to design an optimal filter, which is the best
by expert criteria. Descriptions of processed images were made in terms
of emphasized informative features, collected in the database, and used
to find a decision rule, which presented an effective solution of medical
tasks in easily interpretable form. Developed methods allowed to explicit
some elements of human visual task structure into several simpler subtasks.
It shows the approaches to effective learning the physicians and to automated
computing some informative features directly in the image to realize
expertindependent part of image analysis and description. The methods
were tested in the task of early peripheral lung cancer diagnosis and gave
an essential improvement of diagnostic accuracy for the physicians
of different qualifications.
Key words: image processing, knowledgeguided image analysis,
uncertain data interpretation, computeraided image diagnosis.
 Cerezo E., Serón F.J., Soria A.:
PCRT3D: an interactive threedimensional radiation
treatment planning system based on volume rendering
for lowend platforms.
MGV vol. 7, no. 4, 1998, pp. 859878.

The objective of radiation therapy is to concentrate a prescribed
radiation dose accurately within a target volume in the patient.
Computer assisted radiation treatment planning provides a tool
to find the optimum configuration of radiation beams for the treatment
of an individual patient. It involves interesting 3D techniques
that demand highend visualisation and computational abilities,
pushing the limits of available technology.
PCRT3D is a therapyplanning tool that runs under WINDOWS NT
and is an updated and improved version of the PCRTv3.2 tool
that is being used in more than 30 Spanish hospitals. All the
visualisation part of the application has been developed
in the Advanced Computer Graphics Group of the University
of Zaragoza (Spain). Based on volume rendering, anatomical
and dose information can be mixed and observed in 3D
and on every desired plane. Some of its major features are a simple
and intuitive interface, strict manipulation of the input data
coming from the scanner to avoid artifacts showing up and special
render algorithms to achieve interactivity. The creation of new images
by means of morphing between images, beameyeview and digitally
reconstructed radiographs also figure among its capabilities.
Key words: 3D visualisation, volume rendering, morphing,
3dimensional treatment planning.
 Martin R.R., Anguh M.M.:
Estimating wound volumes from scanner data.
MGV vol. 7, no. 4, 1998, pp. 879889.

This paper considers how data from combined 3D depth maps and colour images
can be used to estimate the volume of a wound  a procedure which may be
important to its successful treatment. The colour image is used to segment
the data into wound and nonwound areas. We then use the area of good skin
surrounding the wound to fit a hypothetical surface going across the wound,
telling us where the skin surface would have been without a wound. Finally,
data in the wound area is used to estimate the depth of the wound relative
to this hypothetical surface, from which the volume of the wound
can be computed. The main new contribution of this paper lies
in the surface fitting method described. At present only a methodology
is given, as practical tests have not been carried out.
Key words: surface fitting, wound volume, volume estimation,
depth map, image, scanner.
 Revievers' index
 Authors' index
 Contents of volume 7, 1998
Maintained by Zenon Kulpa
Last updated Oct 26, 1999