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«vorgelegt von Dipl.-Phys. Tobias Dierig aus Heidelberg Tag der mündl. Prüfung: 03.07.2002 Gewinnung von Tiefenkarten aus Fokusserien Gutachter: ...»

INAUGURAL - DISSERTATION

zur

Erlangung der Doktorwürde

der

Naturwissenschaftlich-Mathematischen

Gesamtfakultät

der

Ruprecht-Karls-Universität

Heidelberg

vorgelegt von

Dipl.-Phys. Tobias Dierig

aus Heidelberg

Tag der mündl. Prüfung: 03.07.2002

Gewinnung von Tiefenkarten aus

Fokusserien

Gutachter: Prof. Dr. Bernd Jähne

Prof. Dr. Josef Bille

Zusammenfassung

In der vorliegenden Arbeit werden Verfahren zur Tiefenschätzung aus Fokusserien einer genauen Analyse unterzogen. Mögliche Fehlerquellen werden ausgehend vom optischen Abbildungsprozess bis hin zu den digitalen Bildverarbeitungsalgorithmen eingehend untersucht. Anhand der zu Grunde liegenden physikalischen Prinzipien werden die FokusVerfahren mit anderen optischen 3D-Meßtechniken verglichen und entsprechend eingeordnet. Allen bisherigen Verfahren zur Tiefenschätzung aus Fokusserien ist gemein, daß der optische Aufbau aus einer speziellen skalierungsfreien, der sogenannten telezentischen Optik bestehen muß. Andernfalls sind die sonst entstehenden Skalierungseffekte in einem zusätzlichen, fehlerbehafteten Schritt zu korrigieren. Ein im Rahmen dieser Arbeit entwickeltes neuartiges Verfahren zur simultanen Tiefen- und Bewegungsschätzung räumt diese gravierenden Limitierungen erfolgreich aus. Dazu wird die Fokusserie als Diffusionsprozess mit einer linearen, partiellen Differentialgleichung beschrieben. Die diesen Prozess beschreibenden Parameter werden mittels einer Total Least Squares Methode direkt aus der Fokusserie geschätzt. Die Tiefeninformation der Szene wird aus der gemessenen Diffusionskonstante errechnet. Abschließend werden alle vorgestellten Verfahren der Tiefenbestimmung an synthetischen und realen Fokusserien erprobt.

Abstract In this thesis different techniques for estimating depth from focal series are quantitatively analyzed. Possible sources of error are scrutinized from the optical imaging process to the digital image processing algorithms. The focus techniques are compared to other optical 3D measurement techniques and classified according to the underlying physical principles.

In common to all existing methods of computing depth from focal series is their reliance on a special, non-scaling optical set-up, also termed telecentric. Otherwise inevitable effects due to the scaling have to be corrected for in an additional, erronous process. A novel technique presented in this thesis for simultaneous estimation of depth and motion sucessfully eleminates this serious limitation. In this method the focal series is modelled by a diffusion process, described by a linear partial differential equation. The parameters characterizing this process are established by a total least squares estimator directly from the focal series.

The information of depth can then be deducted from the measured constant of diffusion.

This thesis concludes with an accuracy examination of all presented techniques both on synthetic and real world data.

Inhaltsverzeichnis

–  –  –

braucht. Weiterhin wird ein PC-Eye2 Framegrabber der Firma Eltec verwendet.

B.2.2 newFokus.ws Mit diesem Workspace wurden alle Auswertungen gemacht. Er beherrscht alle hier erwähnten Algorithmen, allerdings werden alle Daten insbesondere auch die Bildsequenzen komplett im Hauptspeicher gehalten, wodurch dieser Workspace nur für kleinere Sequenzen oder für Rechnern mit viel Speicher geeignet ist.

B.2.3 newFokusInc.ws

Diese Workspace ist speziell für Rechner mit geringerer Hardwareausstattung gedacht. Er berechnet ein tiefenscharfes Bild, das Gütemaß und die Tiefenkarte inkrementell, d.h. es wird jeweils ein Bild geladen und sofort verarbeitet.

110 B.2 Workspaces Literaturverzeichnis J. L. Barron, D. J. Fleet, and S. Beauchemin. Performance of optical flow techniques.

International Journal of Computer Vision, 12(1):43–77, 1994.

M. Born and E. Wolf. Prinziples of Optics. Pergamon Press, 6 edition, 1980.

S. Chaudhuri and A. Rajagopalan. Depth From Focus: A Real Aperature Imaging Approach. Springer-Verlag, 1999.

T. Darell and K. Wohn. Depth from focusing using a pyramid architecture. Pattern Recognition Letters, 11(12):787 – 796, December 1990.

T. Dresler, G. Häusler, and V. H. Three-dimensional sensing of rough surfaces by coherence radar. Applied Optics, 31(7):919 – 925, March 1992.

J. Ens and P. Lawrence. An Investigation of Methods for Determining Depth from Focus. IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(2):97 – 108, February 1993.

A. Erhardt, G. Zinser, D. Komitowski, and J. Bille. Reconstructing 3-D light-microscopic images by digital image processing. Applied Optics, 24(2):194–200, January 1985.

O. Faugeras. Three-Dimensional Computer Vision: A Geometric Viewpoint. The MIT Press, Cambridge, MA, 1993.

D. J. Fleet. Measurement of Image Velocity. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1992.

C. S. Garbe. Heat Flow. PhD thesis, University of Heidelberg, Heidelberg, Germany, 2001.

in preparation.

P. Geißler. Depth-from-Focus zur Messung der Größenverteilung durch Wellenbrechung erzeugter Blasenpopulationen. PhD thesis, IWR, Universität Heidelberg, 1998.





–  –  –

P. Geißler and T. Dierig. Depth-From-Focus. In B. Jähne, H. Haußecker, and P. Geißler, editors, Handbook of Computer Vision and Applications, volume 2, pages 592–623.

Academic Press, 1999.

P. Grossmann. Depth from focus. Pattern Recognition Letters, 5(1):63 – 69, January 1987.

G. Häusler and E. Körner. Simple focusing criterion. Applied Optics, 23(15):2468–2469, August 1984.

G. Häusler and D. Ritter. Parallel three-dimensional sensing by color-coded triangulation.

Applied Optics, 32(35):7164 – 7169, December 1993.

H. Haußecker and D. J. Fleet. Computing optical flow with physical models of brightness variation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(6):661– 673, June 2001.

H. Haußecker, C. S. Garbe, H. Spies, and B. Jähne. A total least squares for low-level analysis of dynamic scenes and processes. In DAGM, pages 240–249, Bonn, Germany,

1999. Springer.

H. Haußecker and H. Spies. Motion. In B. Jähne, H. Haußecker, and P. Geißler, editors, Handbook of Computer Vision and Applications, volume 2, chapter 13, pages 309–396.

Academic Press, San Diego, 1999.

E. Hecht. Optik. Addison-Wesley, 2 edition, 1989.

B. Jähne. Digitale Bildverarbeitung. Springer, 4 edition, 1997.

R. A. Jarvis. A perspectie in range-finding techniques for computer vision. IEEE Transactions on Pattern Analysis and Machine Intelligence, 5:122–139, March 1983.

E. Krotkov. Focusing. International Journal of Computer Vision, 1:223 – 237, 1987.

B. D. Lucas and T. Kanade. An iterative image registration technique with an application to stereo vision. In DARPA Image Understanding Workshop, pages 121–130, 1981.

S. K. Nayar, M. Watanabe, and M. Noguchi. Real-time focus range sensor. PAMI, 18(12):

1186–1199, December 1996.

A. P. Pentland. A new sense of depth of field. IEEE Transactions on Pattern Analysis and Machine Intelligence, 9(4):523 – 531, July 1987.

A. Rajagopalan and S. Chaudhuri. A Variational Approach to Recovering Depth From Defocused Images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(10):1158 – 1164, October 1993.

LITERATURVERZEICHNIS

A. N. Rajagopalan and S. Chaudhuri. Simultaneous depth recovery and image restoration from defocused images. In CVPR’99, Fort Collins, Colorado, June 1999.

Y. Y. Schechner and N. Kiryati. Depth from defocus vs. stereo: How different really are they? International Journal of Computer Vision, 39(2):141–162, 2000.

T. Scheuermann, G. Pfundt, P. Eyerer, and B. Jähne. Oberflächenkonturvermessung mikroskopischer Objekte durch Projektion statistischer Rauschmuster. In DAGM, pages 319 – 326, 1995.

T. Scheuermann, G. Wiora, and M. Graf. Topographical Maps of Microstructures generated by Depth from Focus Techniques. In B. Jähne, H. Haußecker, and P. Geißler, editors, Handbook of Computer Vision and Applications, volume 3, pages 379 – 410. Academic Press, 1999.

T. J. Scholz. Ein Depth from Focus-Verfahren zur On-Line Bestrimmung der Zellkonzentration bei Fermentationsprozessen. PhD thesis, IWR, Universität Heidelberg, 1995.

R. Schwarte, H. Heinol, B. Buxbaum, T. Ringbeck, Z. Xu, and K. Hartmann. Principles of three-dimensional imaging techniques. In B. Jähne, H. Haußecker, and P. Geißler, editors, Handbook of Computer Vision and Applications, volume 1, pages 463–484.

Academic Press, 1999.

R. Schwarte, H. Heinol, B. Buxbaum, Z. Xu, T. Ringbeck, Z. Zhang, W. Tai, K. Hartmann, W. Kleuver, and X. Luan. Neuartige 3D-Visionsysteme auf der Basis Layout-optimierter PMD-Strukturen. Technisches Messen, pages 264 – 271, July - August 1998.

H. Spies. Analysing Dynamic Processes in Range Data Sequences. PhD thesis, University of Heidelberg, Heidelberg, Germany, July 2001.

H. Spies and B. Jähne. A general framework for image sequence analysis. In Fachtagung Informationstechnik, pages 125–132, Magdeburg, Germany, March 2001. Ottovon-Guericke-Universität Magdeburg.

M. Subbarao. Optical transfer function of a diffraction-limited system for polychromatic illumination. Applied Optics, 29(4):554–558, February 1988.

M. Subbarao and J.-K. Tyan. A perspectie in range-finding techniques for computer vision. IEEE Transactions on Pattern Analysis and Machine Intelligence, 20(8):864–870, August 1998.

S. Van Huffel and J. Vandewalle. The Total Least Squares Problem: Computational Aspects and Analysis. Society for Industrial and Applied Mathematics, Philadelphia, 1991.

114 LITERATURVERZEICHNIS Danksagung Beim Rückblick auf die Planung, die Durchführung und den Abschluß dieser Arbeit wird deutlich welche mannigfalten Hilfen ich in dieser Zeit erhalten habe.

An erster Stelle muß ich an Herrn Prof. Dr. Jähne denken und möchte ihm insbesondere dafür danken, daß er mich als Doktorand in seine Arbeitsgruppen integrierte, mich in Bereichen arbeiten ließ, die meiner Interessenlage beonders entsprachen, und daß er die Betreuung dieser Arbeit übernahm.

Herrn Prof. Dr. Bille möchte ich dafür danken, daß er sich als Zweitkorrektor zur Verfügung gestellt hat.

Die fruchtbaren Diskussionen und die zahlreichen Anregungen aus dem Kreis meiner Kollegen in der Arbeitsgruppe haben mir bei der Erstellung dieser Dissertation geholfen. Vor allem danke ich Hagen Spieß und Christoph Garbe für ihre Hilfestellung bei der Durchführung und Auswertung der Experimente.

Nicht zuletzt möchte ich mich ganz herzlich bei meiner Familie und Eva-Maria Lehmann bedanken, die mir besonders in den letzten Tagen bei der Endfassung dieser Arbeit mit Rat und Tat entscheidend geholfen haben.





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