Grey-Scale Measurements in Multi-Dimensional Digitized Images. Lucas J. van Vliet

Transcriptie

1 Grey-Scale Measurements in Multi-Dimensional Digitized Images Lucas J. van Vliet

2

3 Grey-Scale Measurements in Multi-Dimensional Digitized Images proefschrift Ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magnificus, prof. ir. K.F. Wakker, in het openbaar te verdedigen ten overstaan van een commissie aangewezen door het College van Dekanen op dinsdag 5 oktober 1993 te uur door Lucas Jozef van Vliet geboren te Schiedam, natuurkundig ingenieur.

4 Dit proefschrift is goedgekeurd door de promotor Prof. dr. I.T. Young. Dr. P.W. Verbeek heeft als toegevoegd promotor in hoge mate bijgedragen aan het tot stand komen van dit proefschrift. Samenstelling promotiecommissie Rector Magnificus, Prof. dr. I.T. Young, Dr. P.W. Verbeek, Prof. dr. ir. E. Backer, Prof. dr. ir. A. van den Bos, Dr. T.J. Jovin, Prof. dr. J.J. Koenderink, Prof. dr. ir. A.W.M. Smeulders, voorzitter Technische Universiteit Delft, promotor Technische Universiteit Delft, toegevoegd promotor Technische Universiteit Delft Technische Universiteit Delft Max Planck Institute Gottingen, germany Universiteit van Utrecht Universiteit van Amsterdam This research was partially supported by The Netherlands Foundation for Biomedical Research NWO-MW (grant ), The Netherlands Project Team for Computer Science Research SPIN (Project Three-Dimensional Image Analysis) and Imagenetics (Naperville IL, USA). Published and distributed by: Delft University Press Stevinweg CN Delft The Netherlands Telephone Fax ISBN / CIP Copyright 1993 by L.J. van Vliet All rights reserved No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without permission from the publisher: Delft University Press, Stevinweg 1, 2628 CN Delft, The Netherlands. Printed in The Netherlands.

5 Aan Tineke Aan mijn ouders

6

7 Table of Contents Part I: Introduction to Grey-Scale Measurements 1. General Introduction Analog to Digital Point Measurements Object Measurements From Binary to Grey-Scale Measurements Scope of this Thesis From Analog Objects to Digital Images Image Formation: Introduction to Fourier Optics Image Registration: The CCD Camera Image Sampling: Aliasing Free Measurements Image Synthesis: Bandlimited Test Images Image Filtering Nonlinear Grey Scaling Functions Part II: Point Measurements 3. Edge Localization by Second Derivative Filters Introduction Second Derivative Filters Step-Edge Objects Slope-Edge Objects Spherical Objects in 3D and Higher Dimensions vii

8 VIII TABLE OF CONTENTS 3.6. Sampling Experiments Conclusions Edge Localization by MoG Filters: Multiple-of-Gaussians Introduction Gaussian Filters Weights of Gaussians Widths of Gaussians Error analysis Experiments Conclusions Isophote Curvature Introduction Theory Isophote curvature in 2D Isophote curvatures in 3D Experiments Conclusions Part III: Object Measurements: Σsamples = grey-volume 6. 2D Area and 3D Volume Introduction D Area as Grey-Volume Erf-Clipping of PLUS: CP method Experiments Conclusions D Length and 3D Area Introduction Edge Length as Grey-Volume

9 TABLE OF CONTENTS IX 7.3. Isophote Edge Length Continuous Edge Length from a Sampled Image Curved-Edge Displacement by Gaussian Filters Zero crossing of Laplacian Edge Length Extension to 3D Methods Experiments Conclusions Euler Number and 3D Length Introduction Length Estimation through Grey-Volume Measurement Object Enumeration and the Euler Number Effects of Low-pass Filtering Experiments Conclusions Bending Energy of Rods and Plates Introduction Bending energy Measurement of bending energy Experiments Conclusions Part IV: Conclusions 10. Conclusions Point Measurements Object Measurements Appendix I: Stack of Pillboxes Appendix II: Gaussian Stack Shape Appendix III: Stack of Pillballs I Appendix IV: Stack of Pillballs II

10 X TABLE OF CONTENTS Appendix V: Stack of Pillballs III Appendix VI: Pillball FT Appendix VII: Gaussian Edge Slope Appendix VIII: Bending Energy of Parametric Curves/Surfaces Appendix IX: Second Order Rotation Invariance References Summary Samenvatting Dankwoord Curriculum Vitae & Bibliography