Odjel za matematiku

Kristian Sabo


ksabo web

Full Professor
Department of Mathematics
Josip Juraj Strossmayer University of Osijek
Trg Ljudevita Gaja 6
Osijek, HR-31000, Croatia¸

Google Scholar Profile

phone: +385-31-224-827
fax: +385-31-224-801
email:  ksabo @ mathos.hr
office:  18 (ground floor)


Research Interests

Applied and Numerical Mathematics (Curve Fitting, Parameter Estimation, Data Cluster Analysis) with applications in Agriculture, Economy, Chemistry, Politics, Electrical Engineering, Medicine, Food Industry, Mechanical Engineering.


PhD in Numerical Mathematics, Department of Mathematics, University of Zagreb, 2007
MSc in Mathematics, Department of Mathematics, University of Zagreb, 2003
BSc in Mathematics and Computer Science, Department of Mathematics, University of Osijek,  Croatia, 1999


Journal Publications

  1. R. Scitovski, K. Sabo, A combination of k-means and DBSCAN algorithm for solving the multiple generalized circle detection problem, Advances in Data Analysis and Classification 15 (2021), 83-89
    Motivated by the problem of identifying rod-shaped particles (e.g. bacilliform bacterium), in this paper we consider the multiple generalized circle detection problem. We propose a method for solving this problem that is based on center-based clustering, where cluster-centers are generalized circles. An efficient algorithm is proposed which is based on a modification of the well-known $k$-means algorithm for generalized circles as cluster-centers. In doing so, it is extremely important to have a good initial approximation. For the purpose of recognizing detected generalized circles, a verb|QAD|-indicator is proposed. Also a new verb|DBC|-index is proposed, which is specialized for such situations. The recognition process is intitiated by searching for a good initial partition using the verb|DBSCAN|-algorithm. If verb|QAD|-indicator shows that generalized circle-cluster-center does not recognize searched generalized circle for some cluster, the procedure continues searching for corresponding initial generalized circles for these clusters using the Incremental algorithm. After that, corresponding generalized circle-cluster-centers are calculated for obtained clusters. This will happen if a data point set stems from intersected or touching generalized circles. The method is illustrated and tested on different artificial data sets coming from a number of generalized circles and real images.
  2. R. Scitovski, S. Majstorović, K. Sabo, A combination of RANSAC and DBSCAN methods for solving the multiple geometrical object detection problem, Journal of Global Optimization 79/3 (2021), 669-686
    In this paper we consider the multiple geometrical object detection problem. On the basis of the set $A$ of data points coming from and scattered among a number of geometrical objects not known in advance, we should reconstruct or detect thosegeometrical objects. A new very efficient method for solving this problem based on avery popular RANSAC method using parameters from DBSCAN method is proposed.Thereby, instead of using classical indexes for recognizing the most appropriatepartition, we use parameters from DBSCAN method which define the necessaryconditions proven to be far more efficient.Especially, the method is applied to solving multiple circle detection problem. In this case, we give both the conditions for the existence of the best circle as arepresentative of the data set and the explicit formulas for the parameters of the bestcircle. In the illustrative example we consider the multiple circle detection problem for the datapoint set $A$ coming from $5$ intersected circles not known in advance. Using Wolfram Mathematica, the proposed method needed between 0.5 - 1 sec to solve this problem.
  3. D. Jukić, K. Sabo, An existence criterion for the nonlinear $ell_p-$norm fitting problem, Central European Journal of Operations Research 29 (2021), 957-966
    In this paper, we give a necessary and sufficient criterion for the existence of the $ell_p-$norm estimate for the nonlinear $ell_p-$norm fitting problem. Our criterion is based on the existence level that describes the behavior of the objective function as its argument approaches the extended boundary of the parameter space.
  4. R. Scitovski, K. Sabo, DBSCAN-like clustering method for various data densities, Pattern Analysis and Applications 23 (2020), 541-554
    In this paper, we propose a modification of the well-known DBSCAN algorithm, which recognizes clusters with various data densities in a given set of data points $A = {a^i in R^n : i = 1, ldots , m}$. First, we define the parameter $MinPts = floor ln |A| floor$ and after that, by using a standard procedure from DBSCAN algorithm, for each $a in A$ we determine radius $epsilon_a$ of the circle containing $MinPts$ elements from the set $A$. We group the set of all these radii into the most appropriate number $(t)$ of clusters by using Least Square distance-like function applying {tt SymDIRECT} or {tt SepDIRECT} algorithm. In that way we obtain parameters $epsilon_1 > · · · > epsilon_t$. Furthermore, for parameters ${MinPts, epsilon_1} we construct a partition starting with one cluster and then add new clusters for as long as the isolated groups of at least $MinPts$ data points in some circle with radius $epsilon_1$ exist. We follow a similar procedure for other parameters $epsilon_2, ldots, , epsilon_t$. After the implementation of the algorithm, a larger number of clusters appear than can be expected in the optimal partition. Along with defined criteria, some of them are merged by applying a merging process for which a detailed algorithm has been written. Compared to the standard DBSCAN algorithm, we show an obvious advantage for the case of data with various densities.
  5. S. Hamedović, M. Benšić, K. Sabo, Estimating the width of a uniform distribution under symmetric measurement errors, Journal of the Korean Statistical Society 49/3 (2020), 822-840
    In this paper we consider the problem of estimating the support of a uniform distribution under symmetric additive errors. The maximum likelihood (ML) estimator is of our primary interest, but we also analyze the method of moments (MM) estimator, when it exists. Under some regularity conditions, the ML estimator is consistent and asymptotically efficient. Errors with Student's t distribution are shown to be a good choice for robustness issues.


  • Scientifically branded Pork (Member of the scientific project entitled above. Project started on June 1, 2014. Principal investigator is professor Goran Kušec from Faculty of Agriculture in Osijek, University of Osijek. Project was supported by Croatian Science Foundation.)


Professional Activities

Editorial Board

Since 2012 member of the Editorial board of the Journal Osječki matematički list

2001-2012 Editor in Chief of the Journal Osječki matematički list



Committee Memberships
  •  Member of the Organize Committee of the 4th Croatian Congress of Mathematics, Osijek, 2008
  •  Member of the Organize Committee of the 15th International Conference on Operational Research, Croatian Operational Research Society, Osijek 2014



Journal of Computational and Applied Mathematics, Journal of Classification, Mathematical Communications,  International Journal of Applied and Mathematics and Computer Science, Croatian Operational Research Review, TEAM 2012 International Conference, Osječki matematički list


Service Activities

Since 2013 president of Osijek Mathematical Society

2001-2013 secretary of Osijek Mathematical Society


Selected Other Activities (in Croatian)


  • 2014., 2015.  Večer matematike – manifestacija popularizacije matematike u organizaciji Udruge matematičara Osijeku i Hrvatskog matematičkog društva -  Član Programskog i Organizacijskog odbora
  •  2013.-2016. Matematičke pripreme za učenike srednjih škola • Programski i Organizacijski koordinator
  • 2000.-2016. Zimska matematička škola za učenike srednjih škola  • Član Programskog i Organizacijskog odbora
  • 2000.-2016. Zimska matematička škola za učenike osnovnih škola  • Član Programskog i Organizacijskog odbora
  • 2006.-2016. Stručni kolokvij Udruge matematičara Osijek • Član Programskog i Organizacijskog odbora
  • travanj, 2014.  Geometrijska škola Stanko Bilinski, Našice:  Predavanje za nastavnike: „Funkcija udaljenosti i odgovarajuća geometrija“,  Radionica za učenike: “Neki optimizacijski problemi u geometriji“
  • travanj, 2014. Festival znanosti Sveučilišta Josipa Jurja Strossmayera u Osijeku  Predavanje: „Što su optimalne izborne (upravne) jedinice i kako ih odrediti“.  Član Programskog i Organizacijskog odbora
  • listopad, 2012. Stručni skup: Nastava matematike i izazovi moderne tehnologije u organizaciji Udruge Normala - Predavanje: „Zaglađivanje podataka: metode, pristupi i primjene“



Teaching (in Croatian)

Konzultacije: Srijeda  11:00 - 12:00

Teme zavšnih i diplomskih radova (pdf)


Zimski semestar 2017./2018.


Matematika I, Prehrambeno tehnološki fakultet

Primijenjena i Inženjerska matematika, Prehrambeno tehnološki fakultet



Ljetni semestar 2015./2016.

Grupiranje podataka: pristupi, metode i primjene,  ponedjeljak 13:00 - 17:00, RP2

Linearno programiranje, petak 8:00-12:00, RP1

Numerička analiza, srijeda 10:00-12:00, P24


Zimski semestar 2015./2016.

 Diferencijalni račun, utorak, 8:00 - 11:00, P 1

 Matematički praktikum, srijeda, 8:00-10:00


Ljetni semestar 2014./2015.

Grupiranje podataka: pristupi, metode i primjene,  ponedjeljak 13:00 - 17:00, RP2

Linearno programiranje, utorak 15:00-19:00, P3

Numerička analiza, srijeda 8:00-10:00, P24

Primjene diferencijalnog i integralnog računa II, srijeda 10:00-11:00, P2




  • Birthdate: November 23, 1975
  • Birthplace: Kula, Vojvodina, Serbia
  • Family: married with Marija, and have one daughter Paula


Udžbenik Linearno programiranje (pdf)


Uvodni sat (pptx)

Izvjesce procelnika 2017/2018 (pdf)

Diplomski sveucilisni nastavnicki studij matematike i informatike (pdf)