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«Affine Multi-View Modelling for Close Range Object Measurement A thesis submitted to the University College London for the degree of Doctor of ...»

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Affine Multi-View Modelling for Close Range

Object Measurement

A thesis submitted to the University College London for the

degree of Doctor of Philosophy (Ph.D.)

Margarita Rova

Department of Civil, Environmental and Geomatic Engineering

London, 2010

Declaration of authorship

I, Margarita Rova, confirm that the work presented in this thesis is my own. Where

information has been derived from other sources, I confirm that this has been indicated in the


Signed ……………………………… Date ………………………………

-2Acknowledgements During this Ph.D. work I was supervised by Prof. Stuart Robson. I would like to thank you Stuart, for your support and guidance with regards to algorithm development as well as for reading this thesis. For your influence in my personal development over the last four years - I am grateful to you. Further mention goes to Prof. Michael Cooper who acted as an advisor during the critical stages of setting up this research topic as well as towards the thesis completion.

I also would like to thank my examiners Prof. Jon Mills and Prof. Paul Cross for reading the initial version of the Ph.D. thesis and for their critical comments regarding the scientific as well as the English language part of this text.

It is true that a Ph.D. is a highly difficult process. The people I had the privilege to meet within this course have given me invaluable support and, in many ways, guidance along the way. My fellow Ph.D. colleagues and friends Joe (for being a breath of fresh air during the hardest of times), Mojtaba, Toby, Tip, Andrew, Anna, Artemis, Chris, Nikos, Byron, Peter, Steve as well as the Post-docs Dr. Ant Sibthorpe and Dr. Joao Oliveira - thank you. I would also like to single out Prof. Marek Ziebart for his inspirational input and support. Additional thanks goes to my flatmates and friends in both London and Athens for their resilience especially in dealing with my moody moments, Niki in particular.

This thesis is dedicated to my parents Yiannis and Eleni and my sisters Melita, Marina and Elena for their faith in my pursuit of a Ph.D. research. I am grateful to Prof. Elli Petsa who is held responsible for firstly inspiring my interest in the area of photogrammetry and urged my further studies in the Univesity College London.

Lastly, I would like to acknowledge the Greek State Scholarships Foundation (IKY) for their financial contribution in this Ph.D. work.

-3Abstract In photogrammetry, sensor modelling with 3D point estimation is a fundamental topic of research. Perspective frame cameras offer the mathematical basis for close range modelling approaches. The norm is to employ robust bundle adjustments for simultaneous parameter estimation and 3D object measurement. In 2D to 3D modelling strategies image resolution, scale, sampling and geometric distortion are prior factors. Non-conventional image geometries that implement uncalibrated cameras are established in computer vision approaches; these aim for fast solutions at the expense of precision. The projective camera is defined in homogeneous terms and linear algorithms are employed. An attractive sensor model disembodied from projective distortions is the affine. Affine modelling has been studied in the contexts of geometry recovery, feature detection and texturing in vision, however multi-view approaches for precise object measurement are not yet widely available.

This project investigates affine multi-view modelling from a photogrammetric standpoint. A new affine bundle adjustment system has been developed for pointbased data observed in close range image networks. The system allows calibration, orientation and 3D point estimation. It is processed as a least squares solution with high redundancy providing statistical analysis. Starting values are recovered from a combination of implicit perspective and explicit affine approaches. System development focuses on retrieval of orientation parameters, 3D point coordinates and internal calibration with definition of system datum, sensor scale and radial lens distortion. Algorithm development is supported with method description by simulation. Initialization and implementation are evaluated with the statistical indicators, algorithm convergence and correlation of parameters. Object space is assessed with evaluation of the 3D point correlation coefficients and error ellipsoids.

Sensor scale is checked with comparison of camera systems utilizing quality and accuracy metrics. For independent method evaluation, testing is implemented over a perspective bundle adjustment tool with similar indicators. Test datasets are initialized from precise reference image networks. Real affine image networks are acquired with an optical system (~1M pixel CCD cameras with 0.16x telecentric lens). Analysis of tests ascertains that the affine method results in an RMS image misclosure at a subpixel level and precisions of a few tenths of microns in object space.


Σηε θσηνγξακκεηξία ν πξνζαλαηνιηζκόο ηεο θάκεξαο θαη ν πξνζδηνξηζκόο

ηξηζδηάζηαησλ ζεκείσλ απνηειεί ζεκειηώδεο εξεπλεηηθό ζέκα. Πξννπηηθέο θάκεξεο

πξνζθέξνπλ ηε καζεκαηηθή βάζε ησλ αιγόξηζκσλ πνπ εθαξκόδνληαη ζε επίγεηεο

εθαξκνγέο. Νόξκα απνηειεί ε εθαξκνγή ζπζηεκάησλ ζπλόξζσζεο ηεο δέζκεο γηα

ηνλ ηαπηόρξνλν πξνζδηνξηζκό ησλ παξακέηξσλ πξνζαλαηνιηζκνύ θαη ηξηζδηάζηαηεο

κέηξεζεο ζεκείσλ. Σε ζηξαηεγηθέο πνπ βαζίδνληαη ζηε δηδηάζηαηε πξνο ηε

ηξηζδηάζηαηε αληηζηνηρία ε αλάιπζε ηεο εηθόλαο, ε θιίκαθα ηνπ ζέλζνξα, ε

δεηγκαηνιεςία επηθαλείαο θαζώο θαη ε γεσκεηξηθή δηαζηξνθή απνηεινύλ βαζηθνύο

παξάγνληεο. Με ζπκβαηηθέο εηθνλνιεπηηθέο γεσκεηξίεο πνπ εθαξκόδνληαη ζε κεβαζκνλνκεκέλεο θάκεξεο είλαη εδξαησκέλεο ζε εθαξκνγέο ηεο όξαζεο ππνινγηζηώλ;

απηέο απνζθνπνύλ ζε επηιύζεηο πςειήο ηαρύηεηαο επηβαξύλνληαο ηνλ παξάγνληα ηεο

αθξίβεηαο. Η πξνβνιηθή θάκεξα πξνζδηνξίδεηαη ζε ζπζηήκαηα νκνγελώλ

ζπληεηαγκέλσλ όπνπ εθαξκόδνληαη γξακκηθνί αιγόξηζκνη. Έλαο ζέλζνξαο

ηδηαίηεξνπ ελδηαθέξνληνο είλαη ν αθηληθόο, ν νπνίνο είλαη απαιιαγκέλνο από

πξνβνιηθέο δηαζηξνθέο. Αθηληθέο κέζνδνη έρνπλ κειεηεζεί ζην πιαίζην ηεο

αλαθαηαζθεπήο γεσκεηξίαο, εμαγσγήο ζεκείσλ θαη ηεο δεκηνπξγίαο πθώλ ζηελ

όξαζε ππνινγηζηώλ; σζηόζν πνιπ-εηθνληθέο κέζνδνη γηα κέηξεζε αληηθεηκέλσλ κε

πςειή αθξίβεηα δελ είλαη αθόκα επξέσο δηαζέζηκεο.

Απηή ε κειέηε εξεπλά ην αθηληθό πνιπ-εηθνληθό πξόβιεκα από ηελ

θσηνγξακκεηξηθή ζθνπηά. Έλα λέν αθηληθό ζύζηεκα ζπλόξζσζεο ηεο δέζκεο έρεη

αλαπηπρζεί γηα δεδνκέλα κέηξεζεο ζεκείσλ πνπ παξαηεξνύληαη ζε επίγεηα δίθηπα

εηθόλσλ. Τν ζύζηεκα επηηξέπεη βαζκνλόκεζε, πξνζαλαηνιηζκό θαη ππνινγηζκό

ζεκείσλ ζην ρώξν ηνπ αληηθεηκέλνπ. Επεμεξγάδεηαη σο ειαρηζηνηεηξαγσληθή

επίιπζε κε πςειή πεξίζζεηα παξέρνληαο ζηαηηζηηθή αλάιπζε. Αξρηθέο ηηκέο

αλαθηώληαη κέζσ ζπλδπαζκνύ έκκεζσλ πξννπηηθώλ θαη άκεζσλ αθηληθώλ ξνπηηλώλ.

Η αλάπηπμε ηνπ ζπζηήκαηνο εζηηάδεη ζηνλ ππνινγηζκό ησλ παξακέηξσλ

πξνζαλαηνιηζκνύ, ζπληεηαγκέλσλ ζεκείσλ αληηθεηκέλνπ θαη εζσηεξηθήο

βαζκνλόκεζεο κε ηε δπλαηόηεηα λα πξνζδηνξίδεηαη ην ζύζηεκα αλαθνξάο

(εμσηεξηθέο ή εζσηεξηθέο δεζκεύζεηο), ηεο θιίκαθαο ηνπ ζέλζνξα θαη ηεο αθηηληθήο

δηαζηξνθήο. Η αλάπηπμε ηνπ αιγόξηζκνπ ππνζηεξίδεηαη κε πεξηγξαθή ηεο κεζόδνπ

κε δεδνκέλα πξνζνκνίσζεο. Υπνινγηζκόο αξρηθώλ ηηκώλ θαη εθαξκνγή ηνπ

-5αιγόξηζκνπ εθηηκώληαη κε ζηαηηζηηθνύο δείθηεο, ζύγθιηζε ηνπ αιγόξηζκνπ θαη

ζπζρέηηζε ησλ παξακέηξσλ. Ο ρώξνο ηνπ αληηθεηκέλνπ ειέγρεηαη κε αμηνιόγεζε ησλ

ζπληειεζηώλ ζπζρέηηζεο γηα ηα ζεκεία ηνπ ρώξνπ θαη ησλ ειιεηςνεηδώλ ζθάικαηνο.

Η θιίκαθα ηνπ ζέλζνξα ειέγρεηαη κε ζύγθξηζε ζπζηεκάησλ θάκεξαο κε κέηξα

εζσηεξηθήο θαη εμσηεξηθήο αθξίβεηαο. Γηα ηελ αλεμάξηεηε αμηνιόγεζε ηεο κεζόδνπ,

έιεγρνο εθαξκόδεηαη κε ζπκβαηηθό ζύζηεκα κεζόδνπ ηεο δέζκεο κε παξόκνηνπο

δείθηεο. Ο ππνινγηζκόο ησλ αξρηθώλ ηηκώλ ησλ πεηξακαηηθώλ δεδνκέλσλ έρεη

πξνέιζεη από αθξηβή δίθηπα εηθόλαο αλαθνξάο. Αιεζή αθηληθά δίθηπα εηθόλσλ

ιακβάλνληαη κε έλα νπηηθό ζύζηεκα (~1Μ pixel CCD θάκεξεο νπιηδόκελεο κε 0.16x

ηειεθεληξηθό θαθό). Αλάιπζε ησλ ειέγρσλ επηβεβαηώλεη όηη ην αθηληθό κνληέιν

απνδίδεη απνηειέζκαηα κε RMS ζθάικα εηθόλαο ππνςεθηδηθήο ηάμεο θαη αθξίβεηαο

ηεο ηάμεο ησλ κεξηθώλ δεθάδσλ κηθξώλ ζην ρώξν ηνπ αληηθεηκέλνπ.

-6Contents Declaration of authorship

3. Digital close range image formation

3.3.2. Point-based measurement method

4.4.1. Background methods Prior to the iterative process Model assessment

6.7.1. Bundle adjustment results

- 13 List of figures Figure 1.1: Thesis outline.

- 14 Figure 4.4: Representation of a close range image network.

associated brightness histograms.

- 15 Figure 6.16: Normalized span of model parameters (full). CPE - Iter. 3-2.......... - 176 Figure 6.17: Precisions of model parameters. CPE - Iter.3.

network geometry. CPE (ρ0.7).


- 16 Figure 6.48: Point data distribution - dataset B2


- 17 List of tables Table 3.1: Synoptic specifications for CCD-based close range camera systems.... - 54 Table 3.2: Nominal specifications of employed optical systems.

- 21 Introduction

Photogrammetry is primarily focused on camera calibration, orientation and object reconstruction. Since its origin, perspective-based imaging sensors have been widely utilized particularly in industrial, archaeological and medical applications. In principle, the main aim of photogrammetric processing is accuracy. The norm is to apply robust bundle adjustment tools for both parameter estimation and object reconstruction. A similar sensor-based discipline is computer vision which is generally open in variant imaging geometries focusing on the implementation of uncalibrated cameras and automation. The projective camera is defined in homogeneous terms and linear algorithms are employed. Current state of the art is system automation and often fusion of intensity and range imaging sensors. Thus, integration of photogrammetry and computer vision approaches is a fact, particularly when considering their significant overlap in close range applications.

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