Gesture-Based Interaction with Time-of-Flight Cameras

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CHAPTER 2. TIME-OF-FLIGHT CAMERAS light to the measurements of A0, . . . , A3, In the second case, the generation of the signal e(t), the noise sources can only be partially compensated. One deviation of a technical implementation from the measurement principle introduced in Section 2.4 is that the signal e(t) will not be ideally sinusoidal. This has the effect that the range measurement deviates depending on the distance of the object from the camera. Since this error is systematic, it can be corrected (Lange, 2000; Rapp, 2007). Another noise source related to the illumination unit is the so-called photon shot noise, which is a principal physical limitation of sensors based on active illumination. It refers to the fact that light sources do not emit a steady stream of photons at well defined time intervals, but that the generation of photons happens according to a Poisson distribution, i.e. the time interval between the emission of photons represents a Poisson-distributed random variable. Given that the standard deviation of such a Poisson-distributed random variable is the square root of the mean, the same is true for the standard deviations of the samples A0, . . . , A3, i.e. σAi = sqrt(Ai) ∀i = 0, . . . , 3. According to Lange (2000) this yields a standard deviation of the phase measurement √ B ∆φ = A √ 2 and, hence, a standard deviation of the range measurement ∆R = c 4πfmod √ B · √ . cdemodAsig 2 ✞ ☎ ✝2.7 ✆ ✞ ☎ ✝2.8 ✆ Equation (2.8) shows that the measurement accuracy is governed by three factors. As already mentioned above, a high amount of background illumination increases the measurement error. At the same time, the measurement error is reduced if we in- creased the optical power of the active illumination, i.e. if we increase the amplitude of the signal e(t). Here, care has to be taken in situations where the TOF system has to comply with standards of eye safety. Finally, increasing the modulation frequency also reduces the measurement error. Note however, that a higher demodulation frequency reduces also the disambiguity range and that there is a physical limitation in terms of the circuitry on the sensor that toggles between the samples A0, . . . , A3. Generally speaking, Equation (2.8) reflects a principal physical limitation of the measurement accuracy and TOF cameras currently on the market are already close to reaching this limit (Büttgen et al., 2005). 22
2.7 Limitations 2.7. LIMITATIONS As the previous sections have shown, TOF cameras constitute very appealing image sensors. Throughout this work we will see that they can ease numerous computer vision applications because they provide both range and intensity data. However, there also exist a number of limitations of the TOF sensor technology that need to be taken into account when designing applications for such cameras. Apart from the above mentioned non-ambiguity range, these limitations entail measurement errors which can be put into the categories of systematic errors, errors due to multiple re- flections in the scene, wrong range estimates at jump edges (so-called flying pixels), motion artefacts, and problems that arise when multiple cameras are used together. In this section, we will review these sources of measurement errors and discuss so- lutions that avoid or overcome these limitations. 2.7.1 Non-Ambiguity Range As mentioned earlier in this chapter, TOF cameras based on the modulation principle can only yield non-ambiguous range measurements within a certain distance from the camera. This effect depends on the modulation frequency of the active illumination unit. To further investigate this effect, let us recall Equation (2.5) as it was introduced in Section 2.4: R = φ c 2 ω . ✞ ☎ ✝2.9 ✆ As before, φ denotes the phase shift between the periodic signal that was emitted by the camera and the delayed version that is reflected back into the camera from the scene. The modulation frequency fmod contributes to the denominator via the relation ω = 2πfmod. A TOF camera can only disambiguate distances of objects when the signal does not pass through more than one period of the modulation signal while the light trav- els to the object and back to the camera. Thus, the non-ambiguity range Rmax is defined as: Rmax = φ c 2 ω . ✞ ☎ ✝2.10 ✆ Given a typical modulation frequency of fmod = 30MHz the non-ambiguity range limits well-defined range measurements to up to 5 meters distance from the 23
Page 1 and 2: Aus dem Institut für Neuro- und Bi
Page 3 and 4: Contents Acknowledgements vi I Intr
Page 5 and 6: CONTENTS 7.3.2 Sparse Features . .
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The first type of feature is relate
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7.1 Geometric Invariants 7.1.1 Intr
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7.1. GEOMETRIC INVARIANTS The featu
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7.1. GEOMETRIC INVARIANTS We were a
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an algorithm for the fast evaluatio
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7.2. SCALE INVARIANT FEATURES the o
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detection rate detection rate 1 0.8
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7.2. MULTIMODAL SPARSE FEATURES 7.3
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false positive rate 0.4 0.35 0.3 0.
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Part III Applications 119
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CHAPTER 8. INTRODUCTION an alternat
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CHAPTER 9. FACIAL FEATURE TRACKING
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10.1 Introduction 10 Gesture-Based
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10.2. METHOD scenarios: One, where
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10.2. METHOD Figure 10.3: Segmented
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Table 10.1: Interpretation of point
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corner along the ray. 10.2. METHOD
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600 500 400 300 200 100 0 0 10 20 3
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10.4. DISCUSSION tention here was t
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CHAPTER 11. DEPTH OF FIELD BASED ON
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CHAPTER 12. CONCLUSION alization of
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Bibliography ARTTS 3D TOF Database.
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BIBLIOGRAPHY James R. Diebel and Se
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BIBLIOGRAPHY ence on Computer Visio
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BIBLIOGRAPHY Stefan Kunis and Danie
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BIBLIOGRAPHY Thierry Oggier, Michae
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BIBLIOGRAPHY Rudolf Schwarte, Horst
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BIBLIOGRAPHY ’06: Proceedings of
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modulation frequency, 8, 23, 26 Mon
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