Gesture-Based Interaction with Time-of-Flight Cameras

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CHAPTER 2. TIME-OF-FLIGHT CAMERAS .s(t) .s(t) .s(t) . .δ(t) . . .t .t .t .−fmod .−fmod .−fmod .S(f) .S(f) .S(f) .fmod .fmod .fmod Figure 2.4: Influence of the physical realization of an ideal sampling by integrating over a certain time interval ∆t. The left column shows the integration in the time domain with intervals ∆t = 0 (top), ∆t < Tmod (middle), and ∆t = Tmod (bottom). The right column shows the effect in the Fourier domain. The signal is either not affected (top), attenuated (middle), or lost (bottom). 18 .f .f .f
2.5. TECHNICAL REALIZATION form H(fmod) = sinc(π ∆t ). Thus, the frequency components of s(t) are atten- Tmod uated as depicted in Figure 2.4. This results in an attenuation of the amplitude of the received signal, which has a negative effect on the reconstruction of the signal parameters ϕ, A, and B in the presence of noise. In case we further elongate the integration interval to an entire period of the modulation frequency (∆t = Tmod), the zero-crossings of the transfer function H(f) fall in place with the frequency components of s(t), i.e. H(fmod) = 0, and we lose all information on the signal. This effect is leads us to the concept of the demodulation contrast. In the case that ∆t < Tmod, the transfer function H(f) does not affect the phase of the signal s(t) and the phase shift φ can be estimated as defined in Equation (2.2). The illustration above indicates however that an increase of the integration interval ∆t leads to an attenuation of the received signal’s amplitude A relative to the amplitude Asig of the emitted signal. The ratio between the received amplitude and the emitted amplitude is referred to as the demodulation contrast, which is defined as cdemod = A Asig . ✞ ☎ ✝2.6 ✆ Thus, integrating over a time window of length ∆t yields a demodulation contrast of cdemod = sinc(π ∆t ). Again, we can observe that the demodulation contrast and Tmod thus the robustness of the reconstruction increases for small ∆t. We now consider the case where the length of the integration interval is one fourth of the modulation period (∆t = Tmod 4 ). In this case, we obtain a demodula- √ 8 tion contrast of cdemod = π ≈ 0.90 and the samples A0, . . . , A3 can be estimated consecutively during one period, as illustrated in Figure 2.5. In practice, this is done by collecting and storing the photoelectrons generated on the sensor during one of these time intervals in corresponding potential wells - one for each sample Ak. This is achieved by applying an electric field over the light sensitive area of the pixel to guide the photoelectrons into one of the potential wells. This electric field is actu- ated in synchrony with the illumination unit so that the photoelectrons are driven cyclically into one of the four potential wells corresponding to A0, . . . , A3 during one cycle of the modulation period. This approach is known as the 4-tap pixel. In order to obtain reliable estimates Ak, the total exposure time for one image is extended over several periods of the modulation signal and the above procedure of sampling s(t) is repeated for each period during the entire duration of the exposure time. Apparently, an increased exposure time reduces the frame rate of the camera 19
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 . .
Page 7: Acknowledgements There are a number
Page 11 and 12: 1 Introduction Nowadays, computers
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6.4. DISCUSSION learning. As a resu
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7 Features In image processing, the
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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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4 3 ǫ2 2 5 ×10−3 1 7.1. GEOMETR
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7.1. GEOMETRIC INVARIANTS Figure 7.
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7.1. GEOMETRIC INVARIANTS We were a
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7.2. SCALE INVARIANT FEATURES measu
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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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7.2. SCALE INVARIANT FEATURES exhib
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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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7.3. MULTIMODAL SPARSE FEATURES Fig
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7.3. MULTIMODAL SPARSE FEATURES Fig
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7.3. MULTIMODAL SPARSE FEATURES eac
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7.3. MULTIMODAL SPARSE FEATURES tem
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false positive rate 0.4 0.35 0.3 0.
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7.3. MULTIMODAL SPARSE FEATURES thi
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7.4. LOCAL RANGE FLOW FOR HUMAN GES
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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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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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Gesture-Based Interaction with Time-of-Flight Cameras

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