# Professor Paul Scott

p.j.scott@hud.ac.uk | 01484 473953

## Biography

Professor Paul Scott has an honours degree in Mathematics and an MSc in Statistics and also a PhD in Statistics with a thesis entitled *Multipivital models with applications to a shape fitting problem* under the supervision of Dr Rodney Coleman at Imperial College London.

Paul Scott started his career at Taylor Hobson Ltd, Leicester: a world leader in the design and development of ultra-precision metrology instruments for surface texture and form. He spent twenty six years in the research department applying mathematical ideas and concepts to surface texture and form measuring instruments both during the development of instrumentation and post development for mathematical enhancements of the metrological capabilities of instrumentation.

Paul focused his research on why algorithms in surface and form characterisation and instrumentation are quick and stable whilst others are not. Only by going back to mathematical fundamental principles is it possible to discover core factors for determining quick and substantially stable algorithms to solve problems and even to try and generalise the global solution to wider problems. Most of the algorithms he developed, usually being the first in the field, have become the de-facto standard algorithms against which algorithms developed by others are compared.

Paul is also very active in National and International Standardisation for Geometrical Product Specification and Verification (GPS). He is a core member of the BSI Committee TDW4 and convenor of one of its sub-committees TDW4/-/9. Paul Scott is also a leading member of ISO Technical Committee TC/213 being a founder member of its strategic group AG1, a founder member of its technical review group AG2, convenor of working group WG15 on *Filtration and Extraction* and also convenor of advisory group AG12 on *Mathematics for Geometrical Product Specification*. He was project leader for twenty published ISO standards and is currently working on four new ISO documents.

In 1995 Paul became a Visiting Senior Research Fellow at the University of Birmingham, working one day a week with the surface metrology group. In 1997 the whole group moved to the University of Huddersfield and became a part of the Centre for Precision Technologies (CPT). In 2001 Paul became the Taylor Hobson Visiting Industrial Professor: working for two days a week at the CPT,

Paul Scott’s University research took a more fundamental and longer term view of mathematical metrology, asking the question:

*What mathematical tools will be required to solve metrology driven problems of the future? *

In answer to this question Paul:

- Pioneered the use of pattern analysis to define surface features for the characterisation of surface texture,
- Prove a necessary and sufficient criterion for stable measurement by considering the philosophy and structure of measurement,
- Helped establish a standardized framework and a toolbox of different geometrical filters,
- Helped in the development of a metrology driven smart information system, based on category theory, for surface texture.

In March 2010 Paul was awarded a Chair for Computational Geometry in the School of Computing and Engineering. This became the Taylor Hobson Chair for Computational Geometry in December 2011. In September 2013 Paul was awarded an EPSRC Fellowship in Manufacturing: Controlling Geometrical Variability of Products for Manufacturing (EP/K037374/1).

Outside of work Prof Scott enjoys: Astronomy, Numismatics, Archaeology, and solving Physical Mathematical Puzzles.

## Research and Scholarship

### Research Direction

The association of mathematics with measurement, particularly measurement associated with geometry, has a very long history from the Rhind Mathematical Papyrus (detailing mathematical problems in surveying to re-establish the field systems after the flood of the river Nile in ancient Egypt) to modern computational mathematics in metrology software (such as that used in co-ordinate measuring machines). Measurement provides the bridge between the real world and the virtual world of mathematical models, as used by science, by providing estimated values for the parameters used in the models.

Professor Scott has spent a career developing the mathematics for specifying and characterising geometrical products (i.e. products defined by their geometrical size, shape, and texture) through measurement of their geometry at all scales. By taking a fundamental, more philosophical approach to the mathematics of geometrical products and the realisation that all areas of mathematics have potential utility, many new concepts and ideas have been produced.

The dominant paradigm for measurement (the representational theory of measurement) is based on mapping the structure (relationships) of a ‘property’ on to a suitable numerical structure (scale). That is the mathematics of measurement is all about structure and relationships. One particular philosophy of mathematics seems particularly appropriate for the mathematics of measurement, namely ‘Categorical Structuralism’. Categorical structuralism views Mathematics as “the science of structures with Category theory (the theory of structures and relationships between structures) as the language of these structures and relationships. This has led to a new paradigm for measurement theory “measurement as an inverse problem” which is based on Category theory: in particular the concept of Adjoint Functors.

Philosophy can provide a ‘big picture’ of a subject area with mathematical foundations providing the bedrock on which to build. Together they facilitate asking the right sort of questions; they allow the development of a toolbox of new ideas and concepts in response to real world applications and problems; they permit appropriate solutions to problems of great impact and utility; they set research directions that are both fundamental and applied.

### Particular areas of Research include

- Foundations of specifying geometrical products
- Foundations of characterising geometrical products
- Stable, Robust, and fast algorithms for computational geometry
- Solving next generation real world industrial/manufacturing problems (Industrie 4.0)
- Development of National and International standards
- Statistical approaches to Uncertainty
- Philosophy of the measurement of geometry

## Publications and Other Research Outputs

### 2016

Townsend, A., Pagani, L., Scott, P. and Blunt, L. (2016) ‘Areal surface texture data extraction from x-ray computed tomography reconstructions of metal additively manufactured parts’
*Precision Engineering*
. ISSN 01416359

Qin, Y., Lu, W., Qi, Q., Liu, X., Zhong, Y., Scott, P. and Jiang, X. (2016) ‘Status, comparison, and issues of CAD model data exchange methods based on standardized neutral files and OWL file’
*Journal of Computing and Information Science in Engineering*
, 17 (1). ISSN 1530-9827

Qin, Y., Lu, W., Qi, Q., Li, T., Huang, M., Scott, P. and Jiang, X. (2016) ‘Explicitly representing the semantics of composite positional tolerance for patterns of holes’
*International Journal of Advanced Manufacturing Technology*
. ISSN 0268-3768

Pagani, L. and Scott, P. (2016) ‘Areal surface texture parameters on surface’.
*In: Dimensional Accuracy and Surface Finish in Additive Manufacturing*. North Carolina, USA: American Society for Precision Engineering.
.

Abdul-Rahman, H., Lou, S., Zeng, W., Jiang, X. and Scott, P. (2016) ‘Freeform texture representation and characterisation based on triangular mesh projection techniques’
*Measurement*
, 92, pp. 172-182. ISSN 0263-2241

Qi, Q., Scott, P., Jiang, X. and Lu, W. (2016) ‘A hierarchical category model for geometrical product specifications (GPS)’
*Procedia CIRP*
, 43, pp. 214-219. ISSN 2212-8271

Pagani, L. and Scott, P. (2016) ‘A sampling strategy based on B-wavelets decomposition’
*Procedia CIRP*
, 43, pp. 29-34. ISSN 2212-8271

Lou, S., Townsend, A., Jiang, X., Blunt, L., Zeng, W. and Paul, S. (2016) ‘On characterising surface topography of metal powder bed fusion additive manufactured parts’.
*In: euspen's 16th International Conference, 30 May - 3 June 2016*, Nottingham, UK

Lou, S., Jiang, X., Zeng, W., Hussein, A. and Paul, S. (2016) ‘Investigation of the compatibility of X-CT measurement data to surface topography analysis’.
*In: Dimensional X-ray Computed Tomography Conference 2016, 9 May 2016*, NPL, Teddington, London

### 2015

Qi, Q., Li, T., Scott, P. and Jiang, X. (2015) ‘A correlational study of areal surface texture parameters on some typical machined surfaces’
*Procedia CIRP*
, 27, pp. 149-154. ISSN 2212-8271

Lou, S., Jiang, X., Zeng, W. and Paul, S. (2015) ‘A theoretical insight into morphological operations in surface measurement by introducing the slope transform’
*Journal of Zhejiang University Science A*
, 16 (5), pp. 395-403. ISSN 1673-565X

Ding, H., Qi, Q., Scott, P. and Jiang, X. (2015) ‘An ANOVA method of evaluating the specification uncertainty in roughness measurement’.
*In: Laser Metrology and Machine Performance XI, LAMDAMAP 2015*. Huddersfield, UK: EUSPEN.
. ISBN 978-0-9566790-5-5

Lou, S., Jiang, X., Zeng, W., Abdul-Rahman, H. and Paul, S. (2015) ‘From planar surfaces based on lattices to freeform surfaces based on triangular meshes: an advanced extension of the areal motif method’.
*In: 15th International Conference on Metrology and Properties of Engineering Surfaces, 2-5 March 2015*, Charlotte, North Carolina, USA

Ding, H., Scott, P. and Jiang, X. (2015) ‘A Criterion for Comparing Measurement Results and Determining Conformity with Specifications’
*Procedia CIRP*
, 27, pp. 143-148. ISSN 2212-8271

### 2014

Qi, Q., Scott, P., Jiang, X. and Lu, W. (2014) ‘Design and implementation of an integrated surface texture information system for design, manufacture and measurement’
*Computer Aided Design*
, 57, pp. 41-53. ISSN 0010-4485

Lou, S., Jiang, X., Zeng, W. and Scott, P. (2014) ‘Slope transform: a theoretical insight into morphological operations in surface measurement’.
*In: 13th CIRP Conference on Computer Aided Tolerancing, 11-14 May 2014*, Hangzhou, China

Lou, S., Jiang, X. and Scott, P. (2014) ‘Morphological filters for functional assessment of roundness profiles’
*Measurement Science and Technology*
, 25 (6), p. 065005. ISSN 0957-0233

Ding, H., Scott, P. and Jiang, X. (2014) ‘A criterion for comparing measurement results and determining conformity with specifications’.
*In: 13th CIRP Conference on Computer Aided Tolerancing, 11th-14th May 2014*, Hangzhou, China

Lou, S., Jiang, X. and Scott, P. (2014) ‘Applications of Morphological Operations in Surface Metrology and Dimensional Metrology’
*Journal of Physics: Conference Series*
, 483, p. 012020. ISSN 1742-6596

### 2013

Ding, H., Scott, P. and Jiang, X. (2013) ‘Inverse problems of measurement with application on specification of surface profile’.
*In: Proceedings of Computing and Engineering Annual Researchers' Conference 2013 : CEARC'13*. Huddersfield: University of Huddersfield.
p. 229. ISBN 9781862181212

Lou, S., Jiang, X. and Scott, P. (2013) ‘Geometric computation theory for morphological filtering on freeform surfaces’
*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*
, 469 (2159), pp. 20130150-20130150. ISSN 1364-5021

Zeng, W., Jiang, X., Scott, P. and Li, T. (2013) ‘A New Method to Characterize the Structured Tessellation Surface’
*Procedia CIRP*
, 10, pp. 155-161. ISSN 2212-8271

Jiang, X., Abdul-Rahman, H. and Scott, P. (2013) ‘Multi-scale freeform surface texture filtering using a mesh relaxation scheme’
*Measurement Science and Technology*
, 24 (11). ISSN 0957-0233

Lou, S., Jiang, X. and Scott, P. (2013) ‘Identifying and Characterizing Micro-machining Signatures on Freeform Surfaces Using Morphological Methods’.
*In: Manufacturing the future conference 2013, 17-18 September 2013*, Cranfield University, UK
, pp. 63-64

Qi, Q., Jiang, X. and Scott, P. (2013) ‘A Knowledge Platform for Surface Texture in Advanced Manufacturing’.
*In: Manufacturing the Future Conference*. Cranfield, UK: EPSRC.
p. 60. ISBN 978-1-907413-22-3

Lou, S., Jiang, X. and Scott, P. (2013) ‘An Efficient Divide-and-Conquer Algorithm for Morphological Filters’
*Procedia CIRP*
, 10, pp. 142-147. ISSN 2212-8271

Qi, Q., Jiang, X., Scott, P. and Lu, W. (2013) ‘Surface texture specification, the more complete the better?’
*Procedia CIRP*
, 10, pp. 233-237. ISSN 2212-8271

Jiang, X., Abdul-Rahman, H. and Scott, P. (2013) ‘Lifting wavelet algorithm for freeform surface filtering
using a Gaussian prediction operator’
*International Journal of Precision Technology*
, 3 (3), pp. 244-260. ISSN 1755-2060

Qi, Q., Scott, P., Jiang, X., Lu, W. and Ding, H. (2013) ‘The Discussion of Uncertainties in Surface Texture during Design, Manufacture and Measurement’.
*In: The 11th International Symposium of Measurement Technology and Intelligent Instruments, 1st-5th July 2013*, RWTH, Aachen, Germany

Ding, H., Scott, J. and Jiang, X. (2013) ‘Relational Structure of Measurement with Application on Specification of Freeform
Surface’.
*In: Proceedings of the The 11th International Symposium on Measurement Technology and Intelligent Instruments*. Aachen and Braunschweig, Germany: Apprimus Wissenschaftsver.
. ISBN 978-3-86359-138-0

Lou, S., Jiang, X. and Scott, P. (2013) ‘Applications of Morphological Operations in Surface Metrology and Dimensional Metrology’.
*In: 14th International Conference on Metrology and Properties of Engineering Surfaces (Met & Props 2013), 17th - 21st June 2013*, Taipei, Taiwan
, pp. 327-338

Lou, S., Jiang, X., Bills, P. and Scott, P. (2013) ‘Defining True Tribological Contact Through Application of the Morphological Method to Surface Topography’
*Tribology Letters*
, 50 (2), pp. 185-193. ISSN 1023-8883

Lou, S., Zeng, W., Jiang, X. and Scott, P. (2013) ‘Robust Filtration Techniques in Geometrical Metrology and Their Comparison’
*International Journal of Automation and Computing*
, 10 (1), pp. 1-8. ISSN 1476-8186

Lou, S., Jiang, X. and Scott, P. (2013) ‘Application of the morphological alpha shape method to the extraction of topographical features from engineering surfaces’
*Measurement*
, 46 (2), pp. 1002-1008. ISSN 0263-2241

Lou, S., Jiang, X. and Scott, P. (2013) ‘Correlating motif analysis and morphological filters for surface texture analysis’
*Measurement*
, 46 (2), pp. 993-1001. ISSN 0263-2241

Lou, S., Jiang, X. and Scott, P. (2013) ‘An Efficient Divide-and-Conquer Algorithm for Morphological Filters’
*Procedia Engineering: 12th CIRP Conference on Computer Aided Tolerancing*
, 10, pp. 142-147. ISSN 1877-7058

### 2012

Qi, Q., Jiang, X., Scott, P. and Lu, W. (2012) ‘Model for a CAD-assisted designing process with focus on the definition of the surface texture specifications and quality’.
*In: Proceedings of the 37th International MATADOR Conference*. Manchester, UK: Springer.
pp. 273-276. ISBN 978-1-4471-4479-3

Lou, S., Zeng, W., Jiang, X. and Scott, P. (2012) ‘Comparison of Robust Filtration Techniques in Geometrical Metrology’.
*In: 18th International Conference on Automation and Computing (ICAC) 2012*. Leicestershire, UK: IEEE.
pp. 1-6. ISBN 978-1-4673-1722-1

Scott, P. and Forbes, A. (2012) ‘Mathematics for modern precision engineering’
*Philosophical Transactions A: Mathematical, Physical and Engineering Sciences*
, 370 (1973), pp. 4066-4088. ISSN 1364-503X

Wang, J., Jiang, X., Blunt, L., Leach, R. and Scott, P. (2012) ‘Intelligent sampling for the measurement of structured surfaces’
*Measurement Science and Technology*
, 23 (8). ISSN 0957-0233

Lou, S., Jiang, X. and Scott, P. (2012) ‘Algorithms for morphological profile filters and their comparison’
*Precision Engineering*
, 36 (3), pp. 414-423. ISSN 01416359

Blunt, L. and Scott, P. (2012) ‘Characterisation of structured geometry surfaces features on micro and nano scale surfaces’
*International Journal of Nanomanufacturing*
, 8 (5/6), pp. 359-371. ISSN 1746-9392

Wang, J., Jiang, X., Blunt, L., Leach, R. and Scott, P. (2012) ‘A boundary segmentation algorithm for extracting microscale dimensional parameters in the measurement of structured surfaces’.
*In: euspen 12th International Conference and Exhibition, 4 - 8 June 2012*, Stockholm, Sweden

Ding, H. and Scott, P. (2012) ‘Structure of Mathematical Morphology’.
*In: Proceedings of The Queen’s Diamond Jubilee Computing and Engineering Annual Researchers’ Conference 2012: CEARC’12*. Huddersfield: University of Huddersfield.
pp. 20-24. ISBN 978-1-86218-106-9

Lou, S., Jiang, X. and Scott, P. (2012) ‘An Introduction to Morphological Filters in Surface Metrology’.
*In: Proceedings of The Queen’s Diamond Jubilee Computing and Engineering Annual Researchers’ Conference 2012: CEARC’12*. Huddersfield: University of Huddersfield.
pp. 7-13. ISBN 978-1-86218-106-9

Qi, Q., Jiang, X. and Scott, P. (2012) ‘Knowledge modeling for specifications and verification in areal surface texture’
*Precision Engineering*
, 36 (2), pp. 322-333. ISSN 0141-6359

Abdul-Rahman, H., Jiang, X. and Scott, P. (2012) ‘Freeform surface filtering using the lifting wavelet transform’
*Precision Engineering*
, 37 (1), pp. 187-202. ISSN 01416359

Zeng, W., Jiang, X., Scott, P. and Blunt, L. (2012) ‘Diffusion filtration for the evaluation of MEMs surface’.
*In: ISMTII 2011, 29th June - 2nd July 2011*, Kaist, Daejeon, South Korea

### 2011

Jiang, X., Lou, S. and Scott, P. (2011) ‘Morphological method for surface metrology and dimensional metrology based on the alpha shape’
*Measurement Science and Technology*
, 23 (1), p. 015003. ISSN 0957-0233

Lou, S., Jiang, X. and Scott, P. (2011) ‘Morphological Filters Based on Motif Combination for Functional Surface Evaluation’.
*In: Proceedings of the 17th International Conference on Automation & Computing, 10 September 2011*, University of Huddersfield, Huddersfield
, pp. 133-137

Jiang, X., Zeng, W. and Scott, P. (2011) ‘Wavelet Analysis for the Extraction of Morphological Features for Orthopaedic Bearing Surfaces’.
*In: Progress in Molecular and Environmental Bioengineering - From Analysis and Modeling to Technology Applications*. London: InTech.
. ISBN 9789533072685

Zhang, X., Jiang, X. and Scott, P. (2011) ‘A Reliable Method of Minimum Zone Evaluation of
Cylindricity and Conicity from Coordinate
Measurement Data’
*Precision Engineering*
, 35 (3), pp. 484-489. ISSN 0141-6359

Wang, J., Jiang, X., Gurdak, E., Scott, P., Leach, R., Tomplins, P. and Blunt, L. (2011) ‘Numerical characterisation of biomedical titanium surface texture using novel feature parameters’
*Wear*
, 271 (7-8), pp. 1059-1065. ISSN 0043-1648

Zeng, W., Jiang, X. and Scott, P. (2011) ‘A Generalised Linear and Nonlinear Spline filter’
*Wear*
, 271 (3/4), pp. 544-547. ISSN 0043-1648

Wang, J., Jiang, X., Blunt, L., Leach, R. and Scott, P. (2011) ‘Efficiency of adaptive sampling in surface texture measurement for structured surfaces’.
*In: The 13th International Conference on Metrology and Properties of Engineering Surfaces, 12-15 April 2011*, National Physical Laboratory, Teddington, UK
, pp. 214-218

Wang, J., Jiang, X., Blunt, L., Leach, R. and Scott, P. (2011) ‘Efficiency of adaptive sampling in surface texture measurement for structured surfaces’.
*In: The 13th International Conference on Metrology and Properties of Engineering Surfaces, 12-15 April 2011*, National Physical Laboratory, Teddington, UK
, pp. 214-218

Lou, S., Jiang, X. and Scott, P. (2011) ‘Fast Algorithm for Morphological Filters’
*Journal of Physics: Conference Series*
, 311, p. 284. ISSN 1742-6596

Zhang, X., Jiang, X. and Scott, P. (2011) ‘Minimum Zone Evaluation of the Form Errors of Quadric Surfaces’
*Precision Engineering*
, 35 (2), pp. 383-389. ISSN 0141-6359

Zhang, X., Jiang, X. and Scott, P. (2011) ‘A Minimax Fitting Algorithm for Ultra-Precision Aspheric Surfaces’.
*In: The 13th International Conference on Metrology and Properties of Engineering Surfaces, 12-15 April 2011*, National Physical Laboratory, Teddington, UK

Jiang, X., Cooper, P. and Scott, P. (2011) ‘Freeform surface filtering using the diffusion equation’
*Proceedings of the Royal Society, A*
, 467 (2127), pp. 841-859. ISSN 1364-5021

Zeng, W., Jiang, X. and Scott, P. (2011) ‘Roundness filtration by using robust regression filter’
*Measurement Science and Technology*
, 22 (3), p. 035108. ISSN 0957-0233

### 2010

Lou, S., Jiang, X. and Scott, P. (2010) ‘A Fast Algorithm for Morphological Filters’.
*In: Future Technologies in Computing and Engineering: Proceedings of Computing and Engineering Annual Researchers' Conference 2010: CEARC’10*. Huddersfield: University of Huddersfield.
p. 190. ISBN 9781862180932

Lu, W., Liu, X., Jiang, X., Qi, Q. and Scott, P. (2010) ‘Categorical data modelling for Cylindricity Consistent with Geometrical Product Specifications Standard System’
*Proceedings of SPIE: Sixth International Symposium on Precision Engineering Measurements and Instrumentation*
, 75446S. ISSN 1996-756X

Qi, Q., Jiang, X., Liu, X. and Scott, P. (2010) ‘An unambiguous expression method of the surface texture’
*Measurement*
, 43 (10), pp. 1398-1403. ISSN 0263-2241

Qi, Q., Blunt, L., Scott, P. and Jiang, X. (2010) ‘Modeling of the concepts in ISO standards for profile surface texture’.
*In: Future Technologies in Computing and Engineering: Proceedings of Computing and Engineering Annual Researchers' Conference 2010: CEARC’10*. Huddersfield: University of Huddersfield.
pp. 172-176. ISBN 9781862180932

Lu, W., Jiang, X., Qi, Q. and Scott, P. (2010) ‘Modeling the integration between specifications and verification for cylindricity based on category theory’
*Measurement Science and Technology*
, 21 (11). ISSN 0957-0233

Kong, L., Cheung, B., Jiang, X., Lee, W., To, S., Blunt, L. and Scott, P. (2010) ‘Characterization of Surface Generation of Optical Microstructures Using a Pattern and Feature Parametric Analysis Method’
*Precision Engineering*
, 34 (4), pp. 755-766. ISSN 0141-6359

Zeng, W., Jiang, X. and Scott, P. (2010) ‘Fast algorithm of the Robust Gaussian Regression Filter for Areal Surface Analysis’
*Measurement Science and Technology*
, 21 (5), p. 055108. ISSN 0957-0233

Zhang, X., Jiang, X. and Scott, P. (2010) ‘Shape recognition and form error evaluation of quadric surfaces’.
*In: Measurement Systems and Process Improvement (MSPI) 2010, 19-20, Apr, 2010*, NPL, Teddington, UK

Jiang, X., Zhang, X. and Scott, P. (2010) ‘Template matching of freeform surfaces
based on orthogonal distance fitting for
precision metrology’
*Measurement Science and Technology*
, 21 (4), p. 045101. ISSN 0957-0233

Zeng, W., Jiang, X., Smith, I. and Scott, P. (2010) ‘Transient Signal Separation in Watt Balance Experiments’
*Physics Letters A*
, 374 (11-12), pp. 1301-1306. ISSN 0375-9601

Xu, Y., Xu, Z., Jiang, X. and Paul, S. (2010) ‘Developing a Knowledge-based System for Complex Geometrical Product Specification (GPS) Data Manipulation.’
*Knowledge Based Systems*
, 24 (1), pp. 10-22. ISSN 0950-7051

### 2009

Blunt, L., Jiang, X. and Scott, P. (2009) ‘Precision and Nanoscale Surface Metrology’.
*In: International Moulded Optics Conference,, 19-20th Nov 2009*, Breman Germany

Zhang, X., Jiang, X., Scott, P. and Cooper, P. (2009) ‘A Fast Point Projection Approach of NURBS surfaces’.
*In: A4A6 - Algorithms for Approximation VI 2009, 31st August - 4th September 2009*, Ambleside, UK

Zeng, W., Jiang, X. and Scott, P. (2009) ‘A Generalised Linear and Nonlinear Spline filter’.
*In: 12th International Conference on Metrology and Properties of Engineering Surfaces, 8-10 July 2009*, Rzeszów, Poland

Zeng, W., Jiang, X., Scott, P., Xiao, S. and Blunt, L. (2009) ‘A Fast Algorithm for the High Order Linear and Nonlinear Gaussian Regression filter’.
*In: Proceedings of the 9 th international conference of the european society for precision engineering and nanotechnology*. San Sebastian, Spain: euspen.
pp. 356-359. ISBN 978-0-9553082-6-0

Lu, W., Jiang, X., Scott, P. and Lan, X. (2009) ‘A Host System for Form Tolerance Specification in the
Next-generation GPS based on AutoCAD’.
*In: The 11th CIRP Conference on Computer Aided Tolerancing “Geometric Variations within Product Life-Cycle Management”, 26-27 March 2009*, Annecy, France

Zhang, X., Jiang, X. and Scott, P. (2009) ‘The Orthogonal Distance Fitting Of Parametric Surfaces For Precision Coordinate Metrology’.
*In: University of Huddersfield Research Festival, 23rd March - 2nd April 2009*, University of Huddersfield

Zhang, X., Jiang, X. and Scott, P. (2009) ‘A new free-form surface fitting method for precision coordinate metrology’
*Wear*
, 266 (5-6), pp. 543-547. ISSN 0043-1648

Scott, P (2009) ‘Feature parameters’
*Wear*
, 266 (5-6), pp. 548-551. ISSN 0043-1648

Zeng, W., Jiang, X., Scott, P. and Blunt, L. (2009) ‘New Geometrical Filtratation For Ultra-Precision And Micro,Nano Manufactured Products’.
*In: University of Huddersfield Research Festival, 23rd March - 2nd April 2009*, University of Huddersfield

### 2008

Xu, Y., Xu, Z., Jiang, X., Scott, P. and Pickering, J. (2008) ‘Evaluation on the categorical DBMS for the VirtualGPS knowledge system’.
*In: Proceedings of Computing and Engineering Annual Researchers' Conference 2008: CEARC’08*. Huddersfield: University of Huddersfield.
pp. 81-86. ISBN 978-1-86218-067-3

Zeng, W., Jiang, X., Scott, P. and Blunt, L. (2008) ‘Investigation on the noise separation in watt balance experiments’
*Key Engineering Materials*
, 381-38, pp. 619-622. ISSN 1013-9826

Zhang, X., Jiang, X. and Scott, P. (2008) ‘Orthogonal distance fitting of precision free form surfaces based on l1 norm’.
*In: Conference on Advanced Mathematical and Computational Tools in Metrology and Testing, 23 – 25 June 2008*, Paris, France

Li, T., Jiang, X., Blunt, L., Scott, P. and Xiao, S. (2008) ‘The Design and Use of F1 Softgauges for Validating Surface Metrology Software’
*Key Engineering Materials*
, 381-38, pp. 643-646. ISSN 1013-9826

Zeng, W., Jiang, X., Scott, P. and Blunt, L. (2008) ‘Morphological Component Analysis based Detection of Transient Behaviour in Environmental Vibration for the Watt Balance’.
*In: 10th International Conference of the European Society for Precision Engineering and Nanotechnology, euspen, 18th-22nd May 2008*, Kongresshaus Zurich

Jiang, X., Zeng, W., Scott, P. and Ma, J. (2008) ‘Linear feature extraction based on complex ridgelet transform’
*Wear*
, 264 (5-6), pp. 428-433. ISSN 0043-1648

Jiang, X., Scott, P. and Whitehouse, D. (2008) ‘Wavelets and their applications for surface metrology’
*CIRP Annals - Manufacturing Technology*
, 57 (1), pp. 555-558. ISSN 0007-8506

### 2007

Jiang, X., Scott, P., Whitehouse, D. and Blunt, L. (2007) ‘Paradigm shifts in surface metrology. Part I. Historical philosophy’
*Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences*
, 463 (2085), pp. 2049-2070. ISSN 1364-5021

Li, T., Jiang, X., Blunt, L., Scott, P. and Yao, S. (2007) ‘The Design and Use of F1 Softgauges for Validating Surface Metrology Software’.
*In: The 8th International Symposium on Measurement Technology and Intelligent Instruments (ISMTII-2007), 24-27 September 2007*, Tohoku University, Sendai, Japan

Li, T., Blunt, L., Jiang, X., Scott, P. and Xiao, X. (2007) ‘On the accuracy of roughness parameters’.
*In: The 11th International Conference on Metrology and Properties of Engineering Surfaces (Met & Props 2007), 17th-20th July 2007*, University of Huddersfield, Huddersfield, UK

Scott, P (2007) ‘Feature parameters’.
*In: The 11th International Conference on Metrology and Properties of Engineering Surfaces (Met & Props 2007), 17th-20th July 2007*, University of Huddersfield, Huddersfield, UK

Zhang, X., Jiang, X. and Scott, P. (2007) ‘A new free-form surface fitting method for precision coordinate metrology’.
*In: The 11th International Conference on Metrology and Properties of Engineering Surfaces (Met & Props 2007), 17th-20th July 2007*, University of Huddersfield, Huddersfield, UK

Li, T., Jiang, X., Blunt, L., Scott, P. and Xiao, S. (2007) ‘Comparison on F2 softgauges for surface
texture’.
*In: 1st European Conference on Tribology (ECOTRIB), June 12-15, 2007*, Ljubljana, Slovenia

Jiang, X., Zeng, W., Smith, I., Scott, P. and Maletras, F. (2007) ‘The detection of transient behaviour in environmental vibration for the Watt balance’
*Measurement Science and Technology*
, 18 (5), pp. 1487-1494. ISSN 0957-0233

Yan, W., Scott, P. and Jiang, X. (2007) ‘Structures of specification and verification knowledge-base in surface texture knowledge-based system’.
*In: 10th International Conference on Computer Aided Tolerancing, 21st-23rd March, 2007*, Erlangen, Germany

Blunt, L., Jiang, X., Leach, R., Harris, P. and Scott, P. (2007) ‘The development of user-friendly software measurement standards for surface topography software assessment’
*Wear*
, 264 (5-6), pp. 389-393. ISSN 0043-1648

Jiang, X., Scott, P., Whitehouse, D. and Blunt, L. (2007) ‘Paradigm shifts in surface metrology. Part II. The current shift’
*Proceedings of the Royal Society, A*
, 463 (2085), pp. 2071-2099. ISSN 1364-5021

Jiang, X., Scott, P. and Whitehouse, D. (2007) ‘Freeform surface characterisation - a fresh strategy’
*CIRP Annals - 2007*
, 56 (1), pp. 553-556. ISSN 1726-0604

Blunt, L., Jiang, X. and Scott, P. (2007) ‘A New Approach to Surface Metrology - Structured Surfaces’.
*In: Proceedings of the 7th International Conference of the European Society for Precision Engineering and Nanotechnology (euspen) - Bremen, Germany, 2007*. Bremen: euspen.
pp. 254-257. ISBN 978-0-9553082-2-2

### 2006

Wang, Y., Scott, P. and Jiang, X. (2006) ‘Category model to modeling the surface texture knowledge-base’.
*In: Proceedings of Computing and Engineering Annual Researchers' Conference 2006: CEARC’06*. Huddersfield: University of Huddersfield.
pp. 1-7.

Xiao, S., Xie, F., Blunt, L., Scott, P. and Jiang, X. (2006) ‘Feature extraction for structured surface based on surface networks and edge detection’
*Materials Science in Semiconductor Processing*
, 9 (1-3), pp. 210-214. ISSN 1369-8001

Scott, P (2006) ‘The case of surface texture parameter RSm’
*Measurement Science and Technology*
, 17 (3), pp. 559-564. ISSN 09570233

### 2005

Blunt, L., Jiang, X. and Scott, P. (2005) ‘Advances in micro and nano-scale surface metrology’
*Key Engineering Materials*
, 295-29, pp. 431-436. ISSN 1013-9826

Zeng, W., Jiang, X. and Scott, P. (2005) ‘Metrological characteristics of dual-tree complex wavelet transform for surface analysis’
*Measurement Science and Technology*
, 16 (7), pp. 1410-1417. ISSN 0957-0233

Blunt, L., Xiao, S., Jiang, X. and Scott, P. (2005) ‘Geometrical characterisation of MST and microfluidic
devices using novel surface metrology techniques’.
*In: 5th euspen International Conference, 9th-12th May 2005*, Montpellier, France

Blunt, L., Leach, R., Scott, P., Harris, P., Xiao, S., Li, T., Parkin, G. and Jiang, X. (2005) ‘Development of “softgauges” for surface profile metrology’.
*In: 5th Euspen International Conference, 9th-12th May 2005*, Montpellier, France

Zeng, W., Jiang, X., Scott, P. and Blunt, L. (2005) ‘Metrological characteristics of complex wavelet
transform for surface topography analysis’.
*In: 5th euspen International Conference, 9th-12th May 2005*, Montpellier, France

Ma, J., Jiang, X. and Scott, P. (2005) ‘Complex ridgelets for shift invariant characterizaion of surface topography with line singularities’
*Physics Letters A*
, 344, pp. 423-431. ISSN 0375-9601

Zeng, W., Jiang, X. and Scott, P. (2005) ‘Complex ridgelets for the extraction of morphological features on engineering surfaces’
*Journal Paper of Physics: Conference Series*
, 13, pp. 246-249. ISSN 1742-6588

Wang, Y., Scott, P. and Jiang, X. (2005) ‘The structure of surface texture knowledge’
*Journal of Physics: conference series*
, 13, pp. 1-4. ISSN 1742-6596

### 2004

Blunt, L., Jiang, X., Xiao, S. and Scott, P. (2004) ‘The use of interferometry and image analysis techniques for metrology of MST devices’.
*In: 8th International Symposium on Measurement and Quality Control in Production, 12th-15th October, 2004*, Erlangen, Germany

Scott, P (2004) ‘An application of surface networks in surface texture’.
*In: Topological Data Structures for Surfaces*. : Wiley.
. ISBN 9780470851517

Scott, P (2004) ‘Pattern analysis and metrology: the extraction of stable features from observable measurements’
*Proceedings of the Royal Society, A*
, 460, pp. 2845-2864. ISSN 1364-5021

### 2003

Jiang, X. and Scott, P. (2003) ‘Review of surface texture work in ISO’.
*In: 9th International Conference on Metrology and Properties of Engineering Surfaces, 10th-11th September 2003*, Halmstad University, Sweden

Scott, P (2003) ‘Recent developments in the measurement of aspheric surfaces by contact stylus instrumentation’
*Proceedings of SPIE*
, 4927, pp. 199-207. ISSN 0277-786X

Blunt, L., Jiang, X. and Scott, P. (2003) ‘Future developments in surface metrology’.
*In: Advanced Techniques for Assessment Surface Topography*. London: Kogan Page.
pp. 339-347. ISBN 1903996112

Blunt, L., Jiang, X. and Scott, P. (2003) ‘Advances in micro and nano-scale surface metrology’.
*In: ISMTII 2003, The Sixth International Symposium on Measurement Technology and Intelligent Instruments, 28 November - 1 December 2003*, Academic Building, Hong Kong University of Science and Technology, Kowloon, Hong Kong

Scott, P (2003) ‘Novel areal characterisation techniques’.
*In: Advanced Techniques for Assessment surface topography*. London: Kogan Page.
pp. 43-61. ISBN 1903996112

### 2002

Jiang, X., Blunt, L. and Scott, P. (2002) ‘Fundamental research into the filtration of surface texture in geometric product specification and verification’.
*In: 3rd CIRP International Seminar on Intelligent Computation in Manufacturing Engineering - ICME 2002, 3rd-5th July 2002*, Ischia, Italy

Scott, P., Jiang, X. and Blunt, L. (2002) ‘An overview of the relationship between approximation theory and filtration’.
*In: Algorithms for approximation IV : the proceedings of the Fourth International Symposium on Algorithms for Approximation, held at the University of Huddersfield, July 2001*. Huddersfield: University of Huddersfield.
pp. 188-196. ISBN 1862180407

### 2001

Xiao, S., Jiang, X., Blunt, L. and Scott, P. (2001) ‘Comparison study of the biorthogonal spline wavelet filtering for areal rough surfaces’
*International Journal of Machine Tools and Manufacture*
, 41 (13-14), pp. 2103-2111. ISSN 08906955

Burrows, J., Griffiths, B. and Scott, P. (2001) ‘The use of vectors for defining the three-dimensional texture and asymmetric directionality of turned specimens’
*Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture*
, 215 (2), pp. 125-134. ISSN 0954-4054

Scott, P (2001) ‘An algorithm to extract critical points from lattice height data’
*International Journal of Machine Tools and Manufacture*
, 41 (13-14), pp. 1889-1897. ISSN 0890-6955

## Esteem

- Fellow of the Royal Statistical Society, 1981-present
- Conference Chairman (Poster) of the organising committee, “11th International Conference on the Metrology and Properties of Engineering Surface”, 16–20 July 2007,University of Huddersfield, UK
- Conference Chairman (Poster) of the organising committee, The Seventh International Symposium on Measurement Technology and Intelligent Instruments, 6th to 8th Sept. 2005, University of Huddersfield, UK
- Member of the Scientific Committee, The sixth International Symposium on Measurement Technology and Intelligent Instruments, 28th Nov. to 1st Dec. 2003, Hong Kong
- Member of the International Committee, “8th International Conference on the Metrology and Properties of Engineering Surface”, September 27th –30th April 2000, University of Huddersfield, UK
- Board member of International Council of Measurement Technology and Intelligent Instruments ICOMI 2001-2007.
- The Best Paper: The 7th International Conference on Manufacturing Research (ICMR09) University of Warwick, UK, 8-10 September, 2009
- NPL World Metrology Award 1998, European Centre for Metrology, University of Birmingham (one of the members of the group)
- Queen’s award for technological achievement for the Form Talysurf 1992 (one of the major members of the development team)
- Royal Scholarship to study Mathematics at Imperial College (1976-1979)

## Research Degree Supervision

Computational geometry is the study of algorithms which can be stated in terms of geometry. Of particular interest is the development of mathematics for specifying and characterising geometrical products (i.e. products defined by their geometrical size, shape, and texture) through measurement of their geometry at all scales.

A fundamental, more philosophical approach to the mathematics of geometrical products will be taken allowing the development of a toolbox of new ideas and concepts, encapsulated in algorithms, in response to real world applications and problems. These are my main research interests, which I would like to train and supervise PhD students.

The candidate should be creative, have good scientific curiosity with a significant amount of imagination and considerable background in mathematics. Of crucial importance is that the candidate should be highly motivated to carry out the research.

The five subject areas for supervision are as follows:

**Decomposition of surfaces and profiles**

This project is in response to worldwide industrial requirements for a standardized set of tools for the specification of surface function, diagnostics of manufacturing methods, and diagnostics of functional failure for manufactured products defined by their geometrical size and shape.

The idea is to decompose perturbations from the designed surface into different ‘scales’ for further characterisation. The designed surface can belong to one of seven invariance classes of surfaces, namely: planar, spherical, cylindrical, revolute, prismatic, helical, and complex surfaces; depending on their global symmetries. This research will look at various types of decompositions from spectral decomposition, segmentation, morphological decomposition etc. useful to solve the industrial requirements stated above.

**The forensic characterisation of symmetry**

Symmetry is basic in the design of shape and pattern of geometrical products. Given a geometrical product, how can its symmetries be automatically detected. This includes both symmetries in the shape of the geometrical product and symmetries in the patterns on the surface. The research project will develop a toolbox of techniques and algorithms to specify symmetry and also to automatically detect and characterise symmetry and its perturbations. This will involve developing relevant pattern analysis and pattern recognition techniques, together with statistical concepts.

**The structure of inverse problems**

Inverse problems are ubiquitous in science (from the seismic decomposition of strata to the Fourier transform) but there appears to be no general theory defining what an inverse problem is or when the inverse problem is stable to be of practical utility. The research project will use category theory together with measurement theory to investigate and define the structure of inverse problems. Clear criteria will also be stated for when an inverse problem is stable and possible heuristics developed to make an unstable inverse problem stable.

**Partitioning algorithms**

The partitioning operation is one of the fundamental operations used to specify a geometrical product. Here the surface of a geometrical product is divided into independent surface portions for further analysis. The default partition, according to international standards, is that which divides the surface into maximal surface portions each of which belongs to one of the seven invariance classes of surfaces, (i.e. plane, sphere, cylinder, surface of revolution, prism, helix, and complex surface).

Algorithms exist that can implement the default partition, but they nearly all require a high density of sampled points on the surface to ensure an accurate estimate of the surface normal. The research project will develop partitioning algorithms that do not require such a high density of surface points. One approach is to use interpolation methods to reconstruct a continuous surface from the discrete sampled points so that the surface normal can be accurately estimated from sparsely sampled points and then use one of the existing algorithms.

**Uncertainty of surface texture**

The*Guide for the Uncertainty of Measurement*(GUM) is an international document that describes a standardised approach to define uncertainty. Unfortunately the uncertainty of surface texture parameters are notoriously difficult to calculate with any accuracy: mainly due to the unknown correlation structure in each surface. The research project will explore statistical techniques and mathematical model measurement procedures that will allow the uncertainty of surface texture parameters to be calculated with accuracy. This project will also involve practical surface texture measurement using the nano-lab facilities in the Centre for Precision Technologies.

### Previous research supervision

- PhD Industrial Supervisor: Completed
**6** - Supervision for post-doctoral researchers, Current:
**5**.

### Current opportunities

- Please contact this member of staff to discuss possible opportunities.