### Petar Taler

School of Applied Mathematics and Informatics

Josip Juraj Strossmayer University of Osijek

Josip Juraj Strossmayer University of Osijek

### Research Interests

- Parallel Computing on GPUs
- Clustering of large Data Sets
- Distributed Computing

### Degrees

- PhD in Electrical Engineering (Computer Science and Telecommunications), Faculty of Electrical Engineering, University of Osijek, Croatia, 2019.

(thesis: Statistical area estimation of an object captured with additive error, in Croatian) - MSc in Electrical Engineering (Computer Science and Telecommunications), Faculty of Electrical Engineering, University of Osijek, Croatia, 2010.
- BSc in Electrical Engineering (Electronics), Faculty of Electrical Engineering, University of Osijek, Croatia, 2002.

### Publications

Journal Publications

- S. Hamedović, M. Benšić, K. Sabo, P. Taler, Estimating the size of an object captured with error, Central European Journal of Operations Research
**26**/3 (2018), 771-781In many applications we are faced with the problem of estimating object dimensions from a noisy image. Some devices like a fluorescent microscope, X-ray or ultrasound machines, etc., produce imperfect images. Image noise comes from a variety of sources. It can be produced by the physical processes of imaging, or may be caused by the presence of some unwanted structures (e.g. soft tissue captured in images of bones ). In the proposed models we suppose that the data are drawn from uniform distribution on the object of interest, but contaminated by an additive error. Here we use two one-dimensional parametric models to construct confidence intervals and statistical tests pertaining to the object size and suggest the possibility of application in two-dimensional problems. Normal and Laplace distributions are used as error distributions. Finally, we illustrate ability of the R-programs we created for these problems on a real-world example. - M. Benšić, P. Taler, S. Hamedović, E.K. Nyarko, K. Sabo, LeArEst: Length and Area Estimation from Data Measured with Additive Error, The R Journal
**9**/2 (2017), 461-473This paper describes an R package LeArEst that can be used for estimating object dimensions from a noisy image. The package is based on the simple parametric model for data that are drawn from uniform distribution contaminated by an additive error. Our package is able to estimate the length of the object of interest on a given straight line that intersects it as well as to estimate the object area if it is elliptically shaped. The input data may be a numerical vector as well as an image in JPEG format. In this paper, background statistical models and methods for the package are summarized, and algorithms and key functions implemented are described. Also, examples that demonstrate its usage are provided. - P. Taler, K. Sabo, Color image segmentation based on intensity and hue clustering - a comparison of LS and LAD approaches, Croatian Operational Research Review
**5**/2 (2014), 378-385Motivated by the method for color image segmentation based on intensity and hue clustering proposed in [26] we give some theoretical explanations for this method that directly follows from the natural connection between the maximum likelihood approach and Least Squares or Least Absolute Deviations clustering optimality criteria. The method is tested and illustrated on a few typical situations, such as the presence of outliers among the data. - T. Marošević, K. Sabo, P. Taler, A mathematical model for uniform distribution voters per constituencies, Croatian Operational Research Review
**4**(2013), 63-64This paper presents two different approaches on the basis of which it is possible to generate constituencies. The first one is based on cluster analysis by means of which one can get compact constituencies having an approximately equal number of voters. An optimal number of constituencies can be obtained by using this method. The second approach is based on partitioning the country to several areas with respect to territorial integrity of bigger administrative units. Natural units obtained in this way will represent constituencies which do not necessarily have to have an approximately equal number of voters. Each constituency is associated with a number of representatives that is proportional to its number of voters, so the problem is reduced to the integer approximation problem. Finally, these two approaches are combined and applied on the Republic of Croatia. - K. Sabo, R. Scitovski, P. Taler, Ravnomjerna raspodjela broja birača po izbornim jedinicama na bazi matematičkog modela, Hrvatska i komparativna javna uprava
**14**(2012), 229-249U ovom radu predložen je matematički model, na osnovi kojeg je moguće definirati maksimalno kompaktne i dobro razdijeljene izborne jedinice, koje se po broju birača međusobno mogu razlikovati najviše za 5%. Model se temelji na primjeni klaster analize uz poštivanje zakonom propisanih pravila prema kojem izborne jedinice trebaju imati približno jednak broj birača. Metoda je ilustrirana na primjeru dostupnih podataka iz 2007. godine te tako dobivenu raspodjelu izbornih jedinica ne treba shvatiti kao konačni prijedlog rješenja, već isključivo kao prikaz mogućnosti koje nudi ova metodologija. Prema trenutno važećem zakonu izbori se u Republici Hrvatskoj provode u 10 izbornih jedinica. U radu je predloženo nekoliko pristupa poznatih iz literature na osnovi kojih je moguće definirati primjereni broj izbornih jedinica, koje zadržavaju svojstvo maksimalne unutrašnje kompaktnosti i dobre razdijeljenosti.

Refereed Proceedings

- M. Benšić, P. Taler, E.K. Nyarko, Statistical estimation of the object’s area from the image contaminated with additive noise, 15th Iberian Conference on Information Systems and Technologies (CISTI), Seville, Spain, 2020, 1-6Area estimation of circular or ellipsoidal object on an image is a current issue in computer vision. Several methods that address this problem have been previously presented, but it turned out that they do not give satisfactory results when dealing with noisy images. As part of the research presented in this paper, a statistical model for estimating the width of uniform distribution for data contaminated with additive error was applied in order to approach the mentioned problem in an innovative manner. Initially, a method for length estimation of intersection of an object with an arbitrary line has been developed. It is possible to estimate the set of object’s edge points using this method. Further, a circle or an ellipse is fitted in that set of points and its area is calculated, which approximates the area of the object itself. It is also possible to estimate the area of a circular or ellipsoidal object represented by a set of points in the plane.The presented method was implemented and publicly released as a package for the programming language R. The method has been extensively tested on the problem of estimating the area of objects recorded using RGB-D camera. Different noise levels were added to the captured images, and estimation results were compared with the ones obtained by several established methods. The test results showed that the method presented in this paper gives qualitatively the best results of area estimation when dealing with noisy images.
- P. Taler, S. Hamedović, M. Benšić, E.K. Nyarko, LeArEst - The Software for Border and Area Estimation of Data Measured with Additive Error, 59th International Symposium ELMAR-2017, Zadar, 2017, 259-263This paper proposes a solution to the problem of estimating object dimensions from a noisy image. Image noise can be produced by the physical processes of imaging, or can be caused by the presence of some unwanted structures (e.g. soft tissue captured in X-ray images of bones). We suppose that the data are drawn from uniform distribution on the object of interest, but contaminated by an additive error having normal or Laplace distribution. The software for border estimation of an object registered in such manner has been developed, and brief description of its key functions is given. The software is able to estimate the borders of an object on a given line that intersects it, as well as to estimate its area. Its input data may be numerical data, as well as images in JPEG format.
- D. Matijević, G. Martinović, P. Taler, DISTRIBUTER - The Distributed System for Efficient Execution of Parallel Programs, 33rd International Convention on Information and Communication Technology, Electronics and Microelectronics (MIPRO), Opatija, 2010

Others

- P. Taler, Computer error in calculating function value, Osječki matematički list
**6**(2007), 107-114U članku se promatraju problemi koji nastaju prilikom izračunavanja vrijednosti nekih funkcija u aritmetici s pomičnim zarezom. Analizirano je nekoliko karakterističnih primjera i dan postupak kako umanjiti pogreške koje nastaju prilikom izračunavanja vrijednosti funkcija.

Software

- M. Benšić, K. Sabo, P. Taler, S. Hamedović, LeArEst softverski paket za R (2017)Package provides methods for estimating borders of uniform distribution on the interval (one-dimensional) and on the elliptical domain (two-dimensional) under measurement errors. For one-dimensional case, it also estimates the length of underlying uniform domain and tests the hypothesized length against two-sided or one-sided alternatives. For two-dimensional case, it estimates the area of underlying uniform domain. It works with numerical inputs as well as with pictures in JPG format.