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Die vorliegende Arbeit besch¨aftigt sich mit kontrastbasierten Methoden zur Extraktion der dreidimensionalen Information aus den oben beschriebenen Schnittbildserien, ein Prozess der Oberfl¨achenextraktion genannt wird. Es werden zw¨olf verschiedene mathematische Operatoren zur Kontrastmessung auf ihre Tauglichkeit fur die holographische Gesichtsvermessung hin untersucht, unter anderem der neu entwickelte ¨ XSML-Operator, welcher die besten Ergebnisse erzielt. Neben der Wahl des Fokuskriteriums wird auch die Wahl der Gr¨oße der lokalen Pixelumgebung, welche fur die Kontrastmessung verwendet wird, diskutiert. ¨ W¨ahlt man eine feste Umgebungsgr¨oße, stellt dies immer einen Kompromiss zwischen lateraler Aufl¨osung und Robustheit gegenuber Rauschen dar. Ein adaptiver Ansatz, basierend auf einem neu entwickeltem Ent- ¨ scheidungskriterium, passt automatisch die Umgebungsgr¨oße lokal an die Beschaffenheit der Daten an und erm¨oglicht somit eine optimale laterale Aufl¨osung bei minimaler B
Art: Abschlussarbeiten
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Summary
For planning, simulation and documentation of interventions in maxillofacial surgery high resolved soft tissue information of the human face in upright position is needed. This information can be gained by holographic methods, which allow a recording of the whole face in an extremely short time period, so that no movement artifacts occur. The hologram is recorded with a single laser pulse of 35 ns duration and stored in a photosensitive material. After automated wet-chemical processing, the hologram is optically reconstructed with a cw-laser. During the optical reconstruction, a light field, which is a one-to-one three- dimensional representation of the recorded face, emerges at its original position and is digitized into a set of two-dimensional projections. Digital image processing merges these projections into a three-dimensional computer model. Besides the topometric information, a high resolved, pixel precise texture is also extracted from the holographic reconstruction and used for the texturing of the computer models.
This thesis concentrates on contrast based methods for extracting the three-dimensional information from the described set of two-dimensional projections, a process called surface extraction. Twelve different ma- thematical operators for contrast measurement are evaluated with regard to their suitability for holographic facial measurement, amongst others the newly developed XSML operator, which performs best. Besides the choice of the focus criterion, also the local pixel neighborhood used for contrast measurement is investigated. Choosing a fixed neighborhood size one always has to compromise between achievable lateral resolution and robustness against noise. A multi-scale approach based on a novel decision criterion automatically adapts the neighborhood size locally to the constitution of the data and enables an optimal lateral resolution with minimal user interaction.
All evaluations of new methods are done qualitatively by appraising the results with regard to holographic reconstructions of recorded faces and quantitatively with the aid of simulated data sets. Since standard simulation methods do not work in holography due to the non-constance of the holographic point spread function, an adapted simulation strategy is developed, which shows remarkable accordance with the real data. The simulation holds the additional advantage of making a systematic investigation of influencing factors possible. In principle, the process of surface extraction is done by axially maximizing the contrast values. Four advanced methods are presented, which can be applied separately or in a combined way. By fitting a Gaussian curve to the points to be maximized, the influence of noise is reduced, artifacts are eliminated and in particular continuous surface values not restricted to the digitization positions are produced. It is the first time that such an approach is reported. With this the resolution of the models is higher than the digitization step size, which makes the whole procedure most effective. A typical resolution for facial models is 0.25 mm gained with a digitization step size of 0.5 mm. A different method extracts the surface with a special symmetry criterion and diminishes artifacts like the Gaussian fit does, but produces discrete values only. It is valuable if a quick, first estimate of the surface is required. The two following methods work with such a first estimate and refine the surface in a second step using different approaches. All four methods highly improve the quality of the extracted surface. Combined they achieve results almost independent from the noise content of the images, which makes holographic facial measurement applicable for a wider range of applications. The presented advancements improve the quality of the resulting computer models tremendously. Single hairs and wrinkles, earlier only visible in the texture, are for the first time pronounced in the extracted surface itself. It is demonstrated that the improved robustness against noise makes high quality models possible even if the signal-to-noise ratio is low, as it is the case for people with a dark skin color.
Exemplary applications of holographic facial models are discussed. In the medical field, their high resolu- tion enables a quantitative documentation and analysis of face-lifting surgery. Further on the holographic recording of the skull cap of the neanderthal man for scientific and exhibition purposes is presented. Finally the concepts and first steps of forensic facial reconstruction using holographic facial models are explained. They have the tremendous advantage of making soft tissue measurement for the whole facial area possible and not restricting it to anatomical landmarks. Even the soft tissue measurement at anatomical landmarks can be improved through high resolved, holographic facial models.
x CONTENTS
My face is my passport. Vladimir Horowitz
Vladimir Horowitz (1904-1989), an American classical pianist born in Kiev, did most definitely not refer to biometrical data in passports, as he stated this sentence in 1986 to a Soviet official on visit to the USSR. Twenty years later, three-dimensional computer models of the face, which is unique and has an unrepeatable combination of features, are of great interest not only as biometrical characteristics for identification but for a wide range of applications.
He more likely meant that the face is a symbol for the individuality and is a key for judgement by other people in many aspects of life. Considering this it becomes clear, that surgical correction of congenital deformations and reconstructive surgery of tumor or accident patients are very important. Not only an optimal medical result but also an optimal aesthetical outcome is highly desired. This is why precise surgery planning and documentation are indispensable in this field. A necessity for this is highly resolved, three-dimensional information about the face [PCA+02].
Various contact-free, optical measurement systems, for an overview see [CBS00], can in principle be used for this task. But as Bongartz [Bon02], [BGF+03] pointed out, none of them is adequate for facial measurement since either their resolution does not meet the medical requirements or the measuring time is too long, so that the result is affected by motion artifacts caused by changes of the face due to mimic, breathing or heartbeat.
To fulfill the special requirements of three-dimensional measurement of living human faces, a topometry system based on pulsed holography was first implemented successfully by the
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[ELS+04] or acoustic waves [YFB02].
One important application of holography is interferometric metrology, where two or more wave fields are compared interferometrically, at least one of them must be recorded holo- graphically. This technique makes it possible to measure changes of the phase of the wave field and thus the change of any physical quantity that affects the phase. They range from measurement of vibration modes, over deformation measurement to contour measurement [Kre05, p. 4], [May01].
Apart from these techniques, also the three-dimensional information stored in a single- pulse hologram was utilized for various applications. At Fermilab, a holographic system was used for the measurement of position and thickness of particle traces in a bubble chamber [Ade99], [Har99], since it enables a short recording time combined with a large recording volume. The same principles find nowadays application in systems for cloud particle measurement for example, where holograms are taken out of an airplane with typical speed [FSSS04] or for spray diagnostics [BHK03]. Three-dimensional topometry in holographic particle imaging is done by locating intensity maxima in the reconstructed real image of the hologram. That can be done since the light scattering particles are separated from the non-scattering and thus dark background. Total new problems arise if the three-dimensional information of a continuous object is to be extracted out of the hologram, where an intensity maximization is not necessarily capable of locating the scattering surface. The intensity maximization has to be replaced by a contrast maximization, as was demonstrated for example by [Ste68] and [GMS73].
The procedure of surface extraction stays the same equally if analogue or digital recording material is used. For analogue recording, the hologram is optically reconstructed and then digitized. If a digital recording takes place, the real image is reconstructed numerically. Both procedures lead to a set of two-dimensional projections of the real image as basis for further image processing. For a digital recording, this was recently demonstrated for small objects by Ma et. al. [MWLJ04].
The major advantage of holography, namely the possibility of capturing a large image volume three-dimensionally in an extremely short amount of time, can be used for the three-dimensional measurement of moving objects, where measurement systems work- ing on point by point basis fail. Especially for living human faces, where involuntary movements cannot be avoided, pulsed holography is an ideal tool for three-dimensional measurement [Bon02].
1.2 Shape from focus
The emphasis of this thesis is the digital image processing steps to extract the geometry of the recorded surface from the digitized three-dimensional holographic reconstruction. It can in principle be reduced to the problem of focus detection in a set of images, where each image contains focused as well as unfocused points, a so-called focus series. Recently no work was reported realizing such a procedure in holography. This is why adjacent fields of research, where similar principles are established, were consulted. One of these relevant methods is called shape-from-focus.
The acquisition of three-dimensional information out of two-dimensional images has been one of the most important issues in computer vision. These techniques are often referred to as shape-from-x, where x is one of visual cues such as shading, texture, contour, focus, stereo, and motion [YSK99]. Blurring phenomena due to defocusing are among the important cues for depth recovery. Shape-from-focus, originally called depth-from-focus, is a method where a sequence of images is taken while changing the focus setting in small steps. The focus setting, that locally optimizes image focus, is determined and with it the three-dimensional information about the imaged object.
A lot of work was invested to improve the focus criterion [Jar76], [Kro87], [LG82], [DW88]. Three-dimensional topometry of microscopic objects using this method was demonstrated for firearm bullets and cartridge cases but also for machine tools for inspection purposes [FB97], for material structure analysis in mineralogical research [NNS03] or for micro structures such as a micro-cogwheel [RW96].
Especially in white light microscopy, such an approach, which is based on contrast mea- surement, is able to compensate for the small depth of focus due to the large magni- fication by creating both a completely focused image and a depth map containing the three-dimensional information [NN94]. Shape recovery methods not basing on measur- ing contrast but on intensity variations [AJM98] or wavelet-based methods [LMM95], [KFZS02], [FVdVB+04] are not considered in this thesis.
Many algorithms can be adapted or advanced for the use in holographic facial mea- surement, as will be demonstrated in the course of this thesis. A crucial advantage of holographic imaging in comparison to the described method of subsequently capturing two-dimensional images with different focus settings is its capability of storing all the three-dimensional information at the same time. This is why also in microscopy holo- graphic recordings are used and the focusing to different layers is done through numerical
1.4 Outline of this thesis
Chapter 2 describes briefly the holographic principle, the experimental realization of holo- gram recording, optical reconstruction and digitization as well as the state of the art sur- face extractions procedure proposed in the preceding theses, that proved to be applicable and usable in the every day practice of holographic surface measurement.
The following chapter 3 discusses the possibilities of evaluating new surface extraction algorithms and in this context a new method for the simulation of the holographic to- mography process is introduced.
Chapter 4 deals with the basics of contrast measurement. Twelve different focus criteria are tested and evaluated, including two newly developed ones. Additionally, chapter 4 demonstrates, how the selection of the neighborhood size for contrast determination is automated through an adaptive algorithm, choosing the smallest possible neighborhood size automatically while maintaining the robustness against noise.
How the actual process of surface extraction is improved is shown in chapter 5. Four newly invented or adapted methods are introduced here, which are applicable separately, or, as is demonstrated in the last section of chapter 5, can be combined to cumulate the improvement.
Chapter 6 presents a method for surface refinement, which is able to eliminate noise while preserving object features. The holographic recording of a test object combined with a quantitative comparison is also included in this chapter.
Various applications from medicine, archaeology and forensic sciences are presented in chapter 7, followed by a conclusion in chapter 8 and appendices on focus criteria and binomial filters.
The algorithms presented in this thesis are implemented as plug-ins to the open source image processing software ImageJ created by Wayne Rasband [Ras06]. Despite the usage of basic functionality of ImageJ, all plug-ins were written by myself except if indicated otherwise.
This chapter deals with the basics of holographic imaging in general (section 2.1) and its experimental realization (section 2.2) with regard to the established setup for facial measurement described in the preceding works [Bon02], [Gie03], [Fre05]. It covers all aspects from the holographic recording setup, the modified recording with structured illumination, the chemical processing, optical reconstruction to the digitization of the real image. These aspects are only covered briefly, since they are described in detail in the theses of Bongartz, Giel and Frey. The concepts of the image processing of the digitized holographic reconstruction and the surface extraction principle are also outlined in this section in a general way. They build the basis for the more sophisticated methods for surface extraction presented in this thesis. The section concludes with the visualization of the gained three-dimensional computer models and a discussion of the spatial resolution of the real image.
In all conventional imaging techniques, such as photography, a picture of a three-dimensional scene is recorded on a light-sensitive surface by a lens. What is recorded is merely the intensity distribution in the original scene. As a result, all information on the relative phases of the light waves from different points or, in other words, information about the relative optical paths to different points of the scene is lost.
The unique characteristic of holography is the idea of recording the complete wave field, that is to say, both the phase and the amplitude of the light waves scattered by an object. Since all recording media respond only to the intensity, it is necessary to convert the phase
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The photographic material responds to the total energy per area received during the exposure time and converts it into an optical density. This on the other hand leads to a complex amplitude transmittance τ given by:
τ (x, y) = (^) EEt(x, y) e(x, y)
where Et describes the outgoing light wave immediately behind the holographic plate and Ee is the incident light wave. The complex amplitude transmittance can be expressed in general terms as:
τ (x, y) = T (x, y) exp(iφ(x, y)). (2.5)
Two cases are distinguished in the recording of a hologram: the amplitude hologram where the phase is constant (φ=const.) and the phase hologram, where the amplitude is constant (T =const.) In both cases, the complete information of the wave field is recorded. For the rest of this section, only amplitude holograms are considered.
The real amplitude transmittance T depends on the exposure B (see figure 2.2), which can be expressed, if the intensity does not vary with the time, by the product of the intensity I and the exposure time tB : B = ItB.
Figure 2.2: Amplitude transmittance of the holographic plate versus exposure B.
The holographic recording is carried out in the linear part of the curve shown in figure 2.2, near the working point BA. The real transmittance can then be expressed as:
T = a − bB = a − bItB , (2.6)
where the constants a and b depend on the photographic material and on the details of the chemical processing.
After the recording, the holographic plate stores a transmittance distribution [LK03, p. 102ff]
T (x, y) = a − btB (RR∗^ + OO∗^ + R∗O + RO∗) (x, y). (2.7)
If illuminating the recorded hologram with a reconstruction wave C = C(x, y) exp(−iωt), the latter is modulated with the complex transmittance τ (x, y). One gets the complex amplitude of the resulting wave
A(x, y) = T (x, y)C(x, y) = aC − btB C (RR∗^ + OO∗^ + R∗O + RO∗) =
( a − btB |R|^2
) C ︸ ︷︷ ︸ A 0
− bt ︸ B |︷︷O |^2 C︸ A^ ˜ 0
− bt ︸ B R︷︷∗ OC︸ AV
− bt ︸ B RO︷︷ ∗C︸ AR
Four terms are obtained, which have the following meaning:
A 0 Zeroth order diffraction. The reconstruction wave is multiplied with a constant factor. A˜ 0 Broadened zeroth diffraction order, modulated by |O|^2.
AV Virtual image. This part contains the original object wave O prop- agating in its initial direction. It only is proportional to the orig- inal wave if the multiplied factor is real-valued, otherwise it is a distorted version of O. AR Real image. The summand contains the complex conjugate object wave O∗, which can be visualized as the original object wave O travelling back in time. It also is only undistorted in the case of a real-valued factor.
Choosing the reconstruction wave to be a replica of the reference wave (C = R), one gets a virtual image term of AV = btB |R|^2 O, (2.9)
which is proportional to the undistorted object wave, while the real image AR is multiplied with a complex factor and is therefore distorted (see figure 2.3(a)).
Using on the other hand the complex conjugate reference wave as reconstruction wave (C = R∗), the real image term has the form
AR = btB |R|^2 O∗, (2.10)
which is proportional to the undistorted complex conjugate object wave O∗^ and a distorted virtual image (see figure 2.3(b)). The real image is a three-dimensional light field, which is
