INSTITUTE OF MATHEMATICS

INSTITUTE OF MATHEMATICSSection of applied algebra and geometry 1 professor, 3 associate professors, 6 lecturers

Section of computer graphics and geometry1 professor, 1 associate professor, 5 lecturers

Section of applied analysis1 professor, 3 associate professors, 7 lecturers

Section of stochastic and optimization methods1 professor, 2 associate professors, 4 lecturersSections

TeachingBasic mathematical courses offered at the Faculty of Mechanical Engineering including linear algebra analytic geometry calculus numerical methods constructive geometry and computer graphics differential equations infinite series probability and statisticsSpecial field of Mathematical Engineeringfor engineers with extended theoretical background based on mathematics and computer science

Other disciplines of applied mathematicsfor individual specializations of Masters degree programmes at the Faculty of Mechanical EngineeringINSTITUTE OF MATHEMATICS

ResearchINSTITUTE OF MATHEMATICSSection of applied algebra and geometryApplied linear algebra

Differential geometry and its applications

Coalgebras and their applications

Digital topology

Local algebras

Methods of commutative algebra in differential geometry

General algebraic systems and their applications in computer science

Topological structures on categories

GAR Grant GA201/00/1466 Continuous and Set-Theoretic Methods in Topological and Algebraic Structures GAR Grant GA201/03/0933 Set-Theoretic and Categorial Methods in Topological and Algebraic Structures MMT Research Plan MSM0021630518 Simulation Modelling of Mechatronic Systems

GAR Grant GA201/02/0225 (2002-2004) Elongation of Geometric structures

GAR Grant GA201/05/0523 (2005-2007) Geometric Structures on Fibred Varieties

GAR Grant GA201/04/0381 (2004-2006) Methods of Theory of NumbersProjects implementedINSTITUTE OF MATHEMATICSSection of applied algebra and geometry

CooperationMasaryk University in Brno Technische Universitt Wien (Austria)

Universitt Potsdam (Germany)

Universita degli Studi dell'Aquila (Italy)

Dalhousie University in Halifax (Canada)

Science University of Tokyo (Japan)

INSTITUTE OF MATHEMATICSSection of applied algebra and geometry

Samples of problems investigatedModelling the structuring of a digital plane using a new Alexandrov topology closed points are encircled. This topology offers a range of Jordan curves which is wider than that based on the commonly used Khalimsky topology. In particular, it lets curves bend at an angle of /4.INSTITUTE OF MATHEMATICSSection of applied algebra and geometry

Finding the minimum route on a smooth variety with respect to a given metric is among the basic variational problems. This is closely related to parallel transfer of vectors (see the figure) and eventually leads to the definition of a negative connection.INSTITUTE OF MATHEMATICSSection of applied algebra and geometrySamples of problems investigated

INSTITUTE OF MATHEMATICSSection of Applied AnalysisMathematical problems in modelling composite materials using a method of homogenization

Adapting the method of reliable solution (method of the worst scenario) for problems of homogenization with uncertain data

Quasi-periodic and random structures, generating, analysis

Developing tools of functional analysis and theory of function spaces for analysing mathematical models method of two-scale convergence

Devising numerical methods for flow calculation

Investigating qualitative properties of the solution of functional-differential equations, differential and difference equations with a lag

Theory of dynamic equations on time scales and their applications

Solution of selected problems of optimal controlResearch

GAR Grant GA201/01/0079 (2001-2003) Qualitative Theory of Solutions of Differential Equations

GAR Grant GA201/00/0557 (2000-2002) Mathematical Modelling of Some Nonlinear Problems of the Mechanics of Continuum

GAR Grant GA201/03/0570 (2003-2005) Mathematical Modelling of Some Nonlinear Problems of the Mechanics of Continuum

GA AVR Grant IAA1163401 (2004-2006) Limit Properties of the Solutions of Differential Equations

MMT R Research Plan MSM0021630518 (2005-until now) Simulation Modelling of Mechatronic Systems

INSTITUTE OF MATHEMATICSSection of Applied AnalysisProjects implemented

Universit Pierre et Marie Curie, Paris (France)

Chalmers University of Technology, Gteborg (Sweden)

Technische Universitt Hamburg-Harburg (Germany)

Universiteit Gent (Belgium)INSTITUTE OF MATHEMATICSSection of Applied AnalysisCooperation

Numerical solution corresponding to two-component periodic composite material with sixteen circular reinforcementsCorresponding numerical homogenized solution pertaining to homogeneous materialHomogenization (replacing strongly heterogeneous material by fictional material homogeneous in terms of identical macroscopic properties) second order elliptic equations in 2D with a homogeneous Dirichlet boundary conditionINSTITUTE OF MATHEMATICSSection of Applied AnalysisSamples of problems investigated

The temperature field of the piston of a Diesel engine (finite-element method)INSTITUTE OF MATHEMATICSSection of Applied AnalysisSamples of problems investigated

INSTITUTE OF MATHEMATICSSection of Stochastic and Optimization MethodsStochastic computing models for determining the reliability of systems, statistical models of forming processes, generalized regression linear models and classification qualityEstimates of discrete probability distributions under external conditions, multi-dimensional probability distributions and their propertiesMarkov homogeneous and non-homogeneous chains in qualityFuzzy probability, fuzzy random variables, and fuzzy probability distributions, reliability models of elements and systems with vague information, fuzzy clustering and time series prediction in power engineering and finance, fuzzy metric spaces and their applications to databases with vague informationReliability diagnostic supporting nuclear power station blocks controlStochastic optimization and its application in mechanical and civil engineeringOptimization algorithms and applications in technology, foundry, and water managementApplication of statistical methods in metrology, production process control, materials engineering, and medicineResearch

MMT R Research 1M06047 Centre for the Quality and Reliability of Production (CQR)MMT R Research Plan CEZ: J22/98: 261100009 Non-traditional Methods of Investigating Complex and Uncertain Systems GAR Grant GA103/05/0292 Optimizing the Design of Progressive Concrete StructuresState project FF-P114 Research and Development of an Advanced Probability Model With Accumulated Knowledge Base of an Experienced Industrial Operator With Focus on the Operation of the VVER-Type Nuclear Power PlantsIGA MZ R Grant ND 7134-3 Possibilities of Significantly Affecting the Intra-Abdominal Pressure After Operations of the Aboral and Gastrointestinal Tract By Enteral Feeding Applied through a Three-Luminal ProbeGAR Grant Project GA101/00/0170 Transferability of the Fracture Strength In Terms of Evaluating the Integrity of Components with DefectsFRV Project 1746/2002 Materials Science interactive textbookCooperation on international projects COST-APOMAT OC526, EUREKA COOP 2716, EUREKA E! 2914 FGM, NAZV EP 096000 6151INSTITUTE OF MATHEMATICSSection of Stochastic and Optimization MethodsProjects implemented

University of Malta (stochastic, dynamic and integer optimization)Molde University College (optimization algorithms)Nuclear Research Institute at Dukovany (development of a supporting diagnostic system of the states of a nuclear block)BUT FCE Institute of Concrete and Masonry Structures (optimization and reliability of progressive concrete structures)Faculty of Medicine of Masaryk University in Brno (statistical modelling of intra-abdominal pressure after operation)Cardiochronomics Brno (statistical analysis in cardiology and chronobiology in cooperation with the University of Minnesota)Institute of Physics of Material, Academy of Sciences R (stochastic modelling of fracture strength characteristics)SC&C Partner (statistical methods in quality control)Consulting in mathematical applications for the following companies: Alcan Dn, Alstom Power, Barum Continental, Celestica Czech Republic, Invensys Appliance Controls, LG Philips Displays Czech, METAL st n.L., Schneider Electric, Siemens, Kostal etc.INSTITUTE OF MATHEMATICSSection of Stochastic and Optimization MethodsCooperation

Estimates of discrete probability distributions using Hellingers and Shannons quasinorms under secondary moment conditions determined from real statistical dataINSTITUTE OF MATHEMATICSSection of Stochastic and Optimization MethodsResearch

Graf5

58.57135547.08374066.81406616.94048575.1242524

128.57135547.50590917.47184057.361397611.5671081

78.57135547.96671158.11412357.97160957.3006744

58.57135548.47120928.71425528.68987165.6411748

98.57135549.02567579.24309729.37946637.7375634

148.57135549.63618579.67094719.835112214.8175968

88.571355410.31056829.97167059.82205717.8116302

Orig.

K=0

K=1

K=2

K=3

K=4

Center of class

Frequencies

Hellinger quasi-norm estimate

List1

xffxfx^2fx^3fx^4Hellinger

1555558.57135548.57135548.57135548.57135548.57135548.57135548.5713554

2122448961927.08374067.50590917.96671158.47120929.02567579.636185710.3105682

3721631895676.81406617.47184058.11412358.71425529.24309729.67094719.9716705

45208032012806.94048577.36139767.97160958.68987169.37946639.83511229.8220571

5945225112556255.124252411.56710817.30067445.64117487.737563414.81759687.8116302

61484504302418144

7856392274419208Shannon

25513177503450218.57143088.5714298.5714298.5714298.5714298.57142668.5714266

n607.04602927.50207657.98751338.50436819.05477069.640743810.2644986

M016.80390397.48147088.12491328.71494219.23242789.65988799.9824543

M14.256.94412377.35294987.97261298.6975769.38024079.82684769.8256493

M221.955.102802111.63391247.28840655.45120798.034781614.63681237.8520771

M3125.05

M4750.35Pearson

8.57142868.57143018.57142838.57142738.57142738.57142838.5714301

7.18605247.52494017.91678938.37700818.92811159.604580810.4625178

6.84789077.44340458.0744798.70663519.28081549.71618139.930594

6.9316677.38130597.97081268.67034999.376019.8571489.8127065

5.176375311.39524887.37812686.00749917.110624515.20925067.7228748

List1

000000

000000

000000

000000

000000

000000

000000

Orig.

K=0

K=1

K=2

K=3

K=4

Stedy td

etnosti

Odhad pomoc Hellingerovy kvazinormy

List2

000000

000000

000000

000000

000000

000000

000000

Orig.

K=0

K=1

K=2

K=3

K=4

Stedy td

etnosti

Odhad pomoc Shannonovy kvazinormy

List3

000000

000000

000000

000000

000000

000000

000000

Orig.

K=0

K=1

K=2

K=3

K=4

Stedy td

etnosti

Odhad pomoc Pearsonovy kvazinormy

Graf6

58.57143087.04602926.80390396.94412375.1028021

128.5714297.50207657.48147087.352949811.6339124

78.5714297.98751338.12491327.97261297.2884065

58.5714298.50436818.71494218.6975765.4512079

98.5714299.05477069.23242789.38024078.0347816

148.57142669.64074389.65988799.826847614.6368123

88.571426610.26449869.98245439.82564937.8520771

Orig.

K=0

K=1

K=2

K=3

K=4

Center of class

Frequencies

Shannon quasi-norm estimate

List1

xffxfx^2fx^3fx^4Hellinger

1555558.57135548.57135548.57135548.57135548.57135548.57135548.5713554

2122448961927.08374067.50590917.96671158.47120929.02567579.636185710.3105682

3721631895676.81406617.47184058.11412358.71425529.24309729.67094719.9716705

45208032012806.94048577.36139767.97160958.68987169.37946639.83511229.8220571

5945225112556255.124252411.56710817.30067445.64117487.737563414.81759687.8116302

61484504302418144

7856392274419208Shannon

25513177503450218.57143088.5714298.5714298.5714298.5714298.57142668.5714266

n607.04602927.50207657.98751338.50436819.05477069.640743810.2644986

M016.80390397.48147088.12491328.71494219.23242789.65988799.9824543

M14.256.94412377.35294987.97261298.6975769.38024079.82684769.8256493

M221.955.102802111.63391247.28840655.45120798.034781614.63681237.8520771

M3125.05

M4750.35Pearson

8.57142868.57143018.57142838.57142738.57142738.57142838.5714301

7.18605247.52494017.91678938.37700818.92811159.604580810.4625178

6.84789077.44340458.0744798.70663519.28081549.71618139.930594

6.9316677.38130597.97081268.67034999.376019.8571489.8127065

5.176375311.39524887.37812686.00749917.110624515.20925067.7228748

List1

000000

000000

000000

000000

000000

000000

000000

Orig.

K=0

K=1

K=2

K=3

K=4

Stedy td

etnosti

Odhad pomoc Hellingerovy kvazinormy

List2

000000

000000

000000

000000

000000

000000

000000

Orig.

K=0

K=1

K=2

K=3

K=4

Stedy td

etnosti

Odhad pomoc Shannonovy kvazinormy

List3

000000

000000

000000

000000

000000

000000

000000

Orig.

K=0

K=1

K=2

K=3

K=4

Stedy td

etnosti

Odhad pomoc Pearsonovy kvazinormy

Program for generating fuzzy reliability characteristics of a fuzzy Weibull type B distributionINSTITUTE OF MATHEMATICSSection of Stochastic and Optimization MethodsResearch

Non-hierarchicalclustering of fuzzy objectsHierarchicalclustering of fuzzy objectsINSTITUTE OF MATHEMATICSSection of Stochastic and Optimization MethodsResearch

Predicting time-dependent energy consumption using a fuzzy model of a time seriesINSTITUTE OF MATHEMATICSSection of Stochastic and Optimization MethodsResearch

Using fuzzy sets to predict the energy consumption of the city of Olomouc as compared with other predictions using other methods: neural networks and statistical methods Approximating the test strength for determining a sufficient sample size in an experiment plan [n, U, n] to determine object reliabilitiesINSTITUTE OF MATHEMATICSSection of Stochastic and Optimization MethodsResearch

Graf4

128.12

129.08

123.59

121.37

122.6

122.29

128.53

123.45

90.53

87.9787.9787.9787.97

88.288.5681.92531687.7392

91.1390.5189.0781489.7976

93.9188.1187.40969894.7308

102.2610574.54853198.0981

105.47107.5396.420441102.2578

133.75130.63121.539886124.152

170.19166.2145.172653146.7131

158.45165.78141.982819169.7009

142.44161.66121.389229175.7557

144163.29136.422531146.4262

140.14152.09116.861061132.9312

141.92148.06101.098328146.3446

131.28152.73113.843788156.4428

125.07143.2593.267738138.8603

118.5139.63107.34565124.2249

127.66140.59121.001831119.6387

119.15135.1120.81736140.0189

119.74132.29120.911224144.2506

118.83134.1120.946861114.9181

126.8133.8129.03952107.4569

131.89140.04142.275925132.0831

126.74134.96110.971436136.6619

98.96102.0479.474037108.3589

91.9299.4881.63832990.7205

93.42100.0776.58632796.9633

92.8102.0176.79862295.7621

102.7799.6276.9620996.3117

102.49116.582.05970897.2558

110.46119.03102.568527102.2367

136.24142.13106.470749120.1918

170.66177.71123.038322147.3759

161.77177.29123.859985167.5111

165.01173.16113.696571167.9889

154.41174.79120.709587151.9584

154.01163.59111.740341145.327

154.01159.56105.553642165.5843

154.18164.23105.481438167.688

144.07154.75101.638535151.1335

120.34151.1194.298058137.3295

134.79152.09101.812973127.4965

131.28146.699.820091134.0559

124.03144.3892.586029134.6813

125.43145.61101.30291118.6196

132.86145.29101.358604119.3343

133.45151.53120.914368143.7085

126.25146.4592.149323144.2999

101.26113.5381.563187123.9679

100.06110.9776.62545112.0267

Real

Pred.BJ

Pred.NN

Pred FL

List1

RealPred.BJPred NNPred FL0Pred FL1Pred FL2MAPE BJMAPE NNMAPE FL0MAPE FL1MAPE FL2TlakTeplotaVitrCorel-AMCorel-ANCorel-AO

480.0900.1690.1940.1400.0780.743.703.000.00124-0.02644-0.11239

470.0800.1170.2120.1420.0800.713.703.00

510.743.701.90

510.763.903.30

540.724.103.40

860.764.002.90

900.754.203.30

830.774.103.70

770.743.904.70

800.744.104.50

890.714.503.70

750.744.805.80

810.735.304.90

740.766.005.50

690.737.105.10

770.778.305.30

710.749.206.90

770.737.208.80

880.725.809.00

860.775.307.60

860.765.508.30

840.765.607.40

620.745.606.10

660.725.009.30

620.725.308.00

640.744.703.90

620.764.803.70

630.753.902.60

690.704.602.00

1000.804.201.80

1460.734.002.80

1500.753.903.70

1370.783.801.10

1240.774.701.70

1110.776.305.50

1210.694.204.40

1040.798.104.60

950.778.305.20

850.747.003.10

890.726.602.60

850.746.701.80

880.755.702.60

840.765.203.40

910.723.502.70

890.732.202.90

840.741.501.70

840.741.001.80

640.761.301.90

670.781.402.30

670.761.602.50

670.761.902.50

690.752.303.20

820.772.203.00

840.761.400.90

1450.782.201.00

1520.762.301.70

1350.733.001.30

1330.774.601.60

1240.795.104.20

1040.726.103.80

1120.756.804.30

1080.746.904.40

1010.736.903.70

1010.796.901.60

910.746.903.40

910.746.702.80

920.776.503.70

880.776.501.50

970.776.602.10

940.746.201.30

820.776.403.50

620.776.203.60

680.766.103.40

600.765.904.20

690.755.804.80

680.745.503.30

790.755.502.30

1110.795.101.60

1460.735.102.90

1440.774.801.20

1310.765.102.00

1190.775.301.70

1160.765.501.90

1120.765.901.80

1190.726.201.30

1090.746.200.80

900.736.400.00

920.736.400.80

860.746.201.40

840.725.901.60

860.705.600.90

890.715.401.30

850.715.301.20

750.725.101.40

740.735.202.50

700.725.203.00

680.764.802.50

640.754.600.90

620.744.301.00

670.724.402.30

790.714.902.70

1120.754.602.70

1410.774.702.60

1430.784.802.20

1350.744.903.00

1300.746.204.30

1710.684.705.70

1060.845.306.60

1190.736.206.00

1060.797.105.10

1020.786.404.20

940.746.003.50

950.795.303.70

960.734.503.40

950.743.603.00

990.742.905.00

930.752.604.10

900.732.003.10

710.720.703.10

690.741.402.40

670.710.802.50

680.720.302.90

670.730.102.90

840.69-0.402.10

810.71-0.501.80

1060.800.003.00

1410.720.402.90

1520.750.904.90

1360.751.205.00

1300.751.904.40

1270.753.603.10

1030.745.904.60

1060.807.305.50

900.758.404.80

840.738.905.20

810.748.004.00

810.747.204.10

830.727.503.40

920.737.604.60

870.746.302.40

860.735.803.60

760.756.704.40

830.765.704.90

620.794.403.00

590.784.504.20

570.762.702.20

590.742.802.40

630.773.002.50

670.762.202.30

780.752.703.20

1000.802.203.60

920.732.003.60

940.741.501.60

840.754.303.10

770.725.403.10

850.746.303.10

680.726.504.50

800.757.004.40

800.787.203.90

640.716.503.50

800.724.701.80

830.733.301.30

820.752.700.70

950.742.601.40

880.751.800.60

900.750.700.00

690.780.300.00

650.77-0.400.80

640.74-0.500.50

640.74-0.901.00

610.74-1.300.80

650.76-1.600.00

700.74-2.200.80

760.75-2.000.00

1110.73-2.101.10

1070.73-2.300.00

980.74-1.200.70

970.73-0.300.00

930.720.200.70

840.731.601.10

830.733.801.70

840.714.801.20

790.734.700.90

850.713.901.40

920.712.101.20

930.701.001.40

920.711.300.90

880.720.501.10

980.710.100.00

900.72-0.301.00

740.73-0.301.50

770.75-0.400.00

780.76-0.401.20

750.73-0.401.40

710.75-0.401.20

840.72-0.200.80

870.750.000.60

1100.73-0.201.60

1420.760.300.60

1500.720.601.00

1490.741.100.00

1390.741.601.10

1350.742.000.60

1140.743.000.80

1260.723.801.30

1160.733.900.00

1000.754.500.70

1000.734.301.40

940.723.700.90

960.723.400.60

940.713.401.60

910.713.400.70

940.713.501.30

900.713.702.50

640.803.802.60

660.743.902.10

740.734.002.30

710.714.102.70

730.744.302.00

760.714.502.70

830.764.702.90

1180.744.802.10

1450.735.002.00

1330.785.102.20

1290.745.302.00

1310.785.602.00

1220.775.601.30

1170.766.101.90

1150.766.502.40

1130.736.603.00

1020.746.500.80

940.765.800.80

950.765.701.60

920.765.801.00

960.736.302.00

1000.726.102.00

940.735.901.80

900.745.900.00

750.755.800.00

650.775.600.70

700.755.500.00

690.755.500.00

710.765.500.00

720.715.400.00

820.735.200.00

1140.705.301.30

1500.705.301.10

1380.735.400.50

1220.745.500.00

1240.755.901.90

1200.725.806.70

1220.725.906.00

1110.736.406.10

1050.736.406.70

990.727.105.80

1080.745.805.40

990.814.904.50

1000.784.103.50

990.803.103.70

1070.773.003.10

1120.781.903.40

1070.772.102.40

790.761.401.20

720.760.900.60

730.761.901.40

730.721.900.60

830.721.800.90

820.712.300.90

900.762.300.60

1160.752.201.70

1470.702.101.70

1520.72-0.400.70

1390.740.300.00

1340.751.900.70

1170.744.002.70

1160.735.101.60

1100.715.601.10

1030.755.600.60

1050.745.801.20

1040.734.602.70

1060.723.301.70

1020.712.301.70

1110.741.502.10

1120.710.501.30

1090.720.001.20

1070.72-0.301.40

800.73-0.801.20

880.69-1.400.90

760.74-1.700.80

740.74-1.601.20

720.74-2.400.00

950.75-3.202.00

920.79-3.800.70

1030.81-3.100.50

1390.68-3.000.60

1680.75-2.500.80

1430.73-2.800.00

1420.73-2.300.70

1230.73-1.900.00

1320.73-1.300.00

780.70-0.900.80

1280.72-0.300.50

1160.750.100.00

1010.720.300.80

1010.720.201.20

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Real

Pred.BJ

Pred.NN

Pred FL

Adaptive filters for visualizing images with high dynamic content

Numerical methods of solar spectrum analysis, solar corona images (in cooperation with the pice Observatory, the Slovak Academy of Sciences, and the Ondejov Observatory)

Methods of 3D reconstruction of images from the classic, confocal, and tunnelling microscope (in cooperation with the Faculty of Medicine of Masaryk University in Plze)

Fast algorithms of computer graphics

Methods of image registration based on phase correlation and their applications

Applications of digital topology and fractal geometry in image analysis

Numerical methods of human retina analysis

Engineering applications of constructive geometry, multi-valued logic in system controlINSTITUTE OF MATHEMATICSSection of Computer Graphics and GeometryResearch

FRV project 374/2002 Multimedia support of the Structure and Composition of Foodstuffs course

FRV project 855/2005 Interactive textbook for the Structure and Composition of Foodstuffs course

FRV project 3323/2006 Electronic support of the Mathematical Maple Calculations courseINSTITUTE OF MATHEMATICSSection of Computer Graphics and GeometryProjects implemented

University of Veterinary and Pharmaceutical Sciences Brno (numerical methods of image analysis histological examination of foodstuffs)Faculty of Medicine of Masaryk University in Brno (numerical methods of analysis of the human retina)Institute of Physics at the BUT Faculty of Civil Engineering (fractal analysis of the fracture surfaces of building materials)The pice Observatory (numerical methods of solar corona analysis)Astronomic Institute of the Slovak Academy of Sciences at Tatransk Lomnica (numerical methods of image analysis) Astronomic Institute of the Czech Academy of Sciences at Ondejov (numerical methods of solar corona analysis)Biological Institute at the Faculty of Medicine of Charles University in Plze (numerical methods of confocal microscopy) INSTITUTE OF MATHEMATICSSection of Computer Graphics and GeometryCooperation

The solar corona during the total eclipse of 29th March 2006 reconstructed from 51 images and visualised by newly developed adaptive filters. The image significantly exceeds the capacities of the state-of-the-art space probesINSTITUTE OF MATHEMATICSSection of Computer Graphics and GeometrySamples of problems investigated

Dopplergramme of a part of the solar chromosphere obtained by analyzing a series of images of the H-alpha absorption line.

INSTITUTE OF MATHEMATICSSection of Computer Graphics and GeometrySamples of problems investigated

A new exact numerical method for determining the absorption of the light radiated by the solar photosphere in the hydrogen H-alpha lineINSTITUTE OF MATHEMATICSSection of Computer Graphics and GeometrySamples of problems investigated

New numerical methods for analyzing pictures of human retinaINSTITUTE OF MATHEMATICSSection of Computer Graphics and GeometrySamples of problems investigated

Numerical methods for identifying and analyzing bone splinters in meat foodstuff productsINSTITUTE OF MATHEMATICSSection of Computer Graphics and GeometrySamples of problems investigated

software reconstructionphotograph of a real objectNumerical methods developed for processing optical sections obtained form devices with narrow sharpness band.Using software tools based on state-of-the-art numerical methods of image analysis, not only a sharp image can be obtained but also a 3D object almost undistinguishable from the real one. INSTITUTE OF MATHEMATICSSection of Computer Graphics and GeometrySamples of problems investigated

The new methods of processing transparent optical sections from a confocal microscope facilitate a detailed study of the cell morphology and provide a virtual tour of their interiorsINSTITUTE OF MATHEMATICSSection of Computer Graphics and GeometrySamples of problems investigated

Using measure-theory-based algorithms, the fractal dimension of microscopic samples can be determined with increasing precisionINSTITUTE OF MATHEMATICSSection of Computer Graphics and GeometrySamples of problems investigated

INSTITUTE OF MATHEMATICSThank you for your attention

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INSTITUTE OF MATHEMATICS