Single-pixel three-dimensional imaging with time-based depth resolution

Abstract

Time-of-flight three-dimensional imaging is an important tool for applications such as object recognition and remote sensing. Conventional time-of-flight three-dimensional imaging systems frequently use a raster scanned laser to measure the range of each pixel in the scene sequentially. Here we show a modified time-of-flight three-dimensional imaging system, which can use compressed sensing techniques to reduce acquisition times, whilst distributing the optical illumination over the full field of view. Our system is based on a single-pixel camera using short-pulsed structured illumination and a high-speed photodiode, and is capable of reconstructing 128 × 128-pixel resolution three-dimensional scenes to an accuracy of ∼3 mm at a range of ∼5 m. Furthermore, by using a compressive sampling strategy, we demonstrate continuous real-time three-dimensional video with a frame-rate up to 12 Hz. The simplicity of the system hardware could enable low-cost three-dimensional imaging devices for precision ranging at wavelengths beyond the visible spectrum.

ARTICLE

Received 30 Sep 2015 | Accepted 20 May 2016 | Published 5 Jul 2016

Ming-Jie Sun1,2, Matthew P. Edgar2, Graham M. Gibson2, Baoqing Sun2, Neal Radwell2, Robert Lamb3

& Miles J. Padgett2

Time-of-ight three-dimensional imaging is an important tool for applications such as object recognition and remote sensing. Conventional time-of-ight three-dimensional imaging systems frequently use a raster scanned laser to measure the range of each pixel in the scene sequentially. Here we show a modied time-of-ight three-dimensional imaging system, which can use compressed sensing techniques to reduce acquisition times, whilst distributing the optical illumination over the full eld of view. Our system is based on a single-pixel camera using short-pulsed structured illumination and a high-speed photodiode, and is capable of reconstructing 128 128-pixel resolution three-dimensional scenes to an accuracy

of B3 mm at a range of B5 m. Furthermore, by using a compressive sampling strategy, we demonstrate continuous real-time three-dimensional video with a frame-rate up to 12 Hz.

The simplicity of the system hardware could enable low-cost three-dimensional imaging devices for precision ranging at wavelengths beyond the visible spectrum.

DOI: 10.1038/ncomms12010 OPEN

Single-pixel three-dimensional imaging with time-based depth resolution

1 Department of Opto-electronic Engineering, Beihang University, Beijing 100191, China. 2 SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, UK. 3 Selex ES, Edinburgh EH5 2XS UK. Correspondence and requests for materials should be addressed to M.-J.S. (email: mailto:[email protected]

Web End [email protected] ) or M.J.P. (email: mailto:[email protected]

Web End [email protected] ).

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Whilst a variety of three-dimensional (3D) imaging technologies are suited for different applications, time-of-ight (TOF) systems have set the benchmark

for performance with regards to a combination of accuracy and operating range. TOF imaging is performed by illuminating a scene with a pulsed light source and observing the back-scattered light. Correlating the detection time of the back-scattered light with the time of the illumination pulse allows the distance d to objects within the scene to be estimated by d tc/2, where t is the

TOF and c is the propagation speed of light.

The transverse spatial resolution of the image obtained is retrieved either by using a pixelated array or by using a single-pixel detector with a scanning approach18. In both cases, the inherent speed of light demands the use of detectors with a fast response time and high-speed electronic read-out to obtain high precision depth resolution. Advances in sensor development have enabled the rst TOF single-photon avalanche detector array cameras to enter the commercial market, having a resolution of 32 32 pixels. However, such devices are still in

their infancy911. On the contrary, there are mature single-pixel detectors on the market, which provide stable time-resolved measurements, and by using compressed sensing principles for image reconstruction, which takes advantage of the sparsity in natural scenes, the acquisition times of the scanning approach is largely reduced1216.

Recently there have been some interesting developments in 3D imaging utilizing single-pixel detectors. One technique utilizes structured illumination and spatially separated photodiodes to obtain multiple images with different shading properties from which 3D images can be reconstructed via photometric stereo17. Another scheme scans a scene, pixel by pixel, using a pulsed illumination source and measures the reected light using an avalanche photodiode, whereon the rst detected photon is used to recover depth and reectivity via TOF18. An alternative method for scanning a scene and recovering depth and reectivity via TOF has also been demonstrated utilizing structured pulsed illumination1922.

Among the mentioned demonstrations, many5,18,2022 used photon-counting detection (that is, Geiger mode), which is well suited for low-light-level imaging. However, one limitation of photon-counting detectors is the inherent electronic dead time between successive measurements, often 10s of nanoseconds, which prohibits the retrieval of short-range timing information from a single illumination pulse. Instead, an accurate temporal

response from a 3D scene requires summing the data over many back-scattered photons and hence many illumination pulses (usually several hundreds or thousands21,22). In contrast, as rst demonstrated by Kirmani et al.19, a high-speed photodiode can retrieve the temporal response from a single illumination pulse, which can be advantageous in certain circumstances, for instance when the reected light intensity is comparatively large. Incidentally, photon counting cannot operate under such conditions since the detection will always be triggered by backscattered photons from the nearest, or most reective, object, rendering more distant objects invisible (Supplementary Note 1).

In this paper, we present a single-pixel 3D imaging system using pulsed structured illumination and a high-speed (short response time) photodiode for sampling the time-varying intensity of the back-scattered light from a scene. We show that by using an analogue photodiode to record the full temporal form of the backscattered light, along with our original 3D reconstruction algorithm, it is possible to recover surface proles of objects with an accuracy much better than that implied by the nite temporal bandwidth of the detector and digitization electronics. At distances of B5 m we demonstrate a range prole accuracy of B3 mm with image resolutions of 128 128 pixels, whilst simultaneously

recovering reectivity information of the object. This accuracy is achieved despite a detection bandwidth and a digitization interval corresponding to distances of 150 and 60 mm, respectively. We further demonstrate that by using a compressive sampling scheme, the system is capable of performing continuous real-time 3D video with a frame-rate up to 12 Hz.

ResultsExperimental set-up. The single-pixel 3D imaging system, illustrated in Fig. 1, consists of a pulsed laser and a digital micromirror device (DMD) to provide time-varying structured illumination. A high-speed photodiode is used in conjunction with a fresnel lens condenser system to measure the backscattered intensity resulting from each pattern. The analogue photodiode output is passed through a low-noise amplier and sampled using a high-speed digitizer. In our work we chose to use the Hadamard matrices23 for providing structured illumination. To remove sources of noise, such as uctuations in ambient light levels, we obtain differential signals by displaying each Hadamard pattern, followed by its inverse pattern, and taking the difference in the measured intensities24,25. Detailed information about experimental set-up is provided in the Methods section.

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Figure 1 | Single-pixel 3D imaging system. A pulsed laser uniformly illuminates a DMD, used to provide structured illumination onto a scene, and the back-scattered light is collected onto a photodiode. The measured light intensities are used in a 3D reconstruction algorithm to reconstruct both depth and reectivity images.

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A 3D image of the scene is reconstructed utilizing the time-varying back-scattered intensities (measured for each output pulse of the laser) and the associated set of N patterns used to provide the structured illumination. An overview of the reconstruction algorithm is shown in Fig. 2 (the result in this diagram represents a scene of three objects B0.5 m apart in depth). An incident laser pulse (Fig. 2a) is back-scattered from a scene. The high-speed digitizer converts the amplied analogue signals (Fig. 2b) into discrete data points (Fig. 2c), which are subsequently processed by the computer algorithm. Whereas typical single-pixel imaging schemes use the integrated signal for each illumination pattern to reconstruct a two-dimensional image, our algorithm utilizes M discretely sampled intensity points from the time-varying signal to reconstruct M two-dimensional images, resulting in an x, y, z image cube (Fig. 2d). In the image cube, each transverse pixel (x, y) has an intensity distribution (Fig. 2e) along the longitudinal axis (z), which is related to the temporal shape of the pulse, the detector response, the read-out digitization and the pixel depth and reectivity information.

To enhance the range precision beyond the limits imposed by the sampling rate of the system, methods such as parametric deconvolution19,21 and curve tting can be used. However, often these methods can be computationally intensive, which makes them unsuitable for real-time applications. Instead we choose to apply cubic spline interpolation to the reconstructed temporal signal at each pixel location, which introduces minimal computational overhead. The depth map of the scene (Fig. 2f) is subsequently determined by nding the maximum in these interpolated signals. In addition, the scene reectivity (Fig. 2g)

can be calculated by averaging the image cube along the longitudinal axis. Utilizing both the depth and reectivity information, a 3D image of the scene is then reconstructed.

It is worth mentioning that, with the assumption that there is only one surface at each transverse pixel location, our depth estimation (see detail in Methods) works well for scenes that have smooth features, such as the mannequin head and ball, since the reconstructed temporal signals should be slowly varying between sample points. We note that the depth accuracy is limited by the amplitude noise of the data points, over-interpolation only increases the depth precision, but not necessarily the accuracy. In addition, more interpolation adds more processing time, therefore, in our experiments we chose to interpolate by a factor of ve times when investigating the static scenes with 20 pulses per pattern (Figs 35), and four times when investigating scenes with motion (Fig. 6), balancing the computational overhead and 3D image quality.

High-resolution imaging. In one experiment, a scene containing a 140-mm diameter polystyrene soccer ball, a life-size skin-tone mannequin head and a screen was located at a distance of B5.5 m from the imaging system (Fig. 3a). The objects were closely separated in distance such that the total depth of the scene was B360 mm. A complete Hadamard set of 16,384 patterns, and their inverse, was used as the structured illumination, and the back-scattered intensities (Fig. 3b) measured for reconstructing 128 128-pixel resolution depth map, reectivity and 3D image

(Fig. 3c-3e). The illumination time of each pattern was 2.66 ms, corresponding to 20 laser pulses. The total time for acquisition,

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Figure 2 | Overview of the reconstruction algorithm. The incident laser pulses (a) back-scattered from a 3D scene are temporally broadened (b) and discretely sampled using a high-speed digitizer (c). An image cube (d) is obtained using a reconstruction algorithm, having an intensity distribution along the longitudinal axis (e), from which the depth map (f) and the reectivity (g) of the scene can be estimated.

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Figure 3 | 3D image of a scene. (a) Illustration of the scene containing multiple objects in close proximity. (b) Reected intensity measured for uniform illumination, indicating temporally indistinguishable objects. (c) The estimated depth map of the scene. (d) The reconstructed scene reectivity. (e) A textured 3D image of the scene.

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Figure 4 | Quantitative analysis of 3D reconstruction. The depth estimation (a) reectivity (b) and 3D reconstruction (c) of a white polystyrene mannequin head at a range of B5.5 m. Superposed depth reconstruction and photograph of the mannequin head, viewed from the front (d) and side (e). For a chosen region of interest an error map (f) showing the absolute differences between our depth result and that obtained using a stereophotogrammetric camera system.

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Figure 5 | 3D imaging through obscuring material. (a) Illustration of scene containing a mannequin head with black netting material obscuring the line-of-sight. (b) A photograph of the scene taken from the perspective of the 3D imaging system. The scene depth (c) and reectivity (d) reconstructed by time-gating the measured intensity data. (e) 3D reconstruction of the mannequin head.

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Figure 6 | Real-time 3D video. (a) Illustration of the scene containing a static mannequin head and a swinging ball. (bh) Sample of consecutive depth and reectivity frames reconstructed at B5 Hz frame-rate in real-time for a transverse resolution of 64 64 pixels. The experiments of Figs 36 were

replicated more than 10 times.

data transfer from the digitizer buffer to the computer and image processing was B130 s. The 3D reconstruction shown in Fig. 3e exhibits distinguishable features, such as the prole of the head and the ball.

To quantitatively determine the accuracy of our 3D imaging system, the scene was modied to contain only a polystyrene mannequin head (180 270 250 mm), for which we had

reference 3D data obtained via a high-accuracy stereophotogram-metric camera system17,26. The mannequin head was located at a distance of 5.5 m from the imaging system. To further demonstrate the system capability for retrieving reectivity in addition to the depth, two grey stripes were placed on the head. Performing the same acquisition and imaging processing used in Fig. 3, we obtained the results shown in Fig. 4ac. Figure 4d,e show the front and side view comparisons between our 3D reconstruction (green) and photographs of the head (white), respectively. After lateral and angular registration and subsequent depth scaling, an error map representing the absolute differences for a chosen region of interest was obtained (shown in Fig. 4f). From this comparison we nd our single-pixel 3D imaging system has a root mean squared error of 2.62 mm. More detailed analysis is provided in Supplementary Fig. 1 and Supplementary Note 2.

Time-gated imaging. One advantage of time-resolved imaging is the ability to distinguish objects at different depths, by articially time-gating the measured intensity. In certain cases this enables obscuring objects to be isolated from objects of interest. Similar to previous demonstrations20, we constructed a 3D scene containing a polystyrene mannequin head (located at a distance of B3.5 m)

and black-coloured netting used to obstruct the line of sight (located at a distance of B3 m), as illustrated in Fig. 5a. An image of the scene taken using a conventional camera is shown in Fig. 5b, where the head is obscured by the black netting. Performing the same acquisition and imaging processing used in

Figs 3 and 4, along with an articial gating on the photodiode data to ensure no reected signals from the black netting are included in the 3D reconstruction, we obtained the results shown in Fig. 5ce. As before, we note the characteristic features of the mannequin head can be resolved.

Real-time compressed video. In addition to obtaining high-quality 3D images of static scenes, many applications demand video frame-rates for motion tracking in dynamic scenes. A key merit of single-pixel imaging is the ability to take advantage of the sparsity of the scene and use compressive sensing to reduce the acquisition time. Most compressive-sensing schemes are performed by minimizing a certain measure of the sparsity, such as L1-norm, to nd the sparsest image as the optimal reconstruction of the scene. However, for resolutions greater than 32 32 pixels, the time taken by the construction algorithm often

prohibits real-time application22,27.

In this work we use an alternative scheme, known as evolutionary compressive sensing6,7, which aims to reconstruct the image with signicant less time than conventional compressive sensing by performing a linear iteration (Supplementary Figs 2 and 3 and Supplementary Note 3). In short, the evolutionary compressive sensing scheme chooses a subset of the Hadamard basis to display, by selecting the patterns with the most signicant intensities measured in the previous frame, in addition to a fraction of randomly selected patterns that were not displayed. In this experiment, a scene consisting of a static polystyrene mannequin head and a polystyrene white ball (140 mm diameter) swinging along the line of sight with a period of B3 s (Fig. 6a). The scene was located at a distance of B4 m from the imaging system. Two laser pulses were used per illumination pattern. With the approach described above we obtained continuous real-time 3D video with a frame-rate of 5 Hz using 600 patterns (including their inverse) from the available 64 64 Hadamard set, equivalent to a

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compression ratio of C7% (Supplementary Movie 1). The experimental parameters for this result were chosen to balance the inherent trade-off between frame-rate and image quality (Supplementary Note 3). Figure 6bh show a sample of consecutive frames from the 3D video. The result shows an identiable 3D image of the mannequin head and ball, in addition to the real-time motion of the ball. Importantly, however, 3D reconstruction can be performed using fewer patterns to achieve higher frame-rates if required, for instance using 256 patterns provides 12 Hz video (Supplementary Movie 2).

DiscussionWe have demonstrated that our single-pixel 3D imaging system is capable of reconstructing a scene with millimetric ranging accuracy using modest hardware. In addition, we obtained real-time video rates by taking advantage of a modied compressive sensing scheme that does not rely on lengthy post-processing.

The performance of the system in this work was mainly limited by the repetition rate of the laser used, 7.4 kHz. Using a laser with a repetition rate greater than or equal to the DMD modulation rate, could enable faster 3D video rates by a factor of three and/or increase reconstruction accuracy by increased averaging.

Furthermore, the broad operational spectrum (4002,500 nm) of the DMD could enable the system to be extended to the non-visible wavelength, such as the infrared, using modied source and detection optics. The use of DMDs in the infrared has already been demonstrated in microscopy6 and real-time video cameras7. The potential application of 3D imaging in the infrared could provide enhanced visibility at long-range, due to reduced atmospheric scattering28.

Methods

Hardware specications. The following components were used in the experimental set-up (Fig. 1): a pulsed laser (Teem Photonics SNG-03E-100, 532 nm); a DMD (Texas Instruments Discovery 4100 DMD); a projection lens (Nikon ED, f 180 mm); a collection lens (customized fresnel condenser lens,

f 20 mm); a Si biased photodiode (Thorlabs DET10A); and a high-speed USB

digitizer (PicoScope 6407, 2.5 GS s 1 for two-channel acquisition).

Operating congurations. There are several important points worth mentioning.(a) The modulation rate of the DMD can reach up to 22.7 kHz, however, in this experiment the DMD is operated in slave-mode, meaning the modulation rate is determined by the repetition rate of the laser at 7.4 kHz. (b) The active area of the photodiode is 0.8 mm2, used in conjuction with a 20-mm focal length fresnel lens system, giving a 2.6 eld of view, which matches that of the projection system. The depth estimation includes Gaussian smoothing, intensity calibration, cubic spline interpolation and depth determination. More experiment methods and details are provided in Supplementary Methods.

Data availability. The data used to generate all of the gures in this study can be found at http://dx.doi.org/10.5525/gla.researchdata.317

Web End =http://dx.doi.org/10.5525/gla.researchdata.317 .

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Acknowledgements

We thank Prof. Adrian Bowman and Dr Liberty Vittert for providing the stereophotogrammetric 3D data of the polystyrene mannequin head. M.S. acknowledges the support from National Natural Foundation of China (Grant No. 61307021) and China Scholarship Council (Grant No. 201306025016). M.J.P. acknowledges nancial support from UK Quantum Technology Hub in Quantum Enhanced Imaging (Grant No. EP/M01326X/1), the Wolfson foundation and the Royal Society.

Author contributions

M.-J.S., R.L. and M.J.P. conceived the concept of the experiment; M.-J.S., M.P.E. and G.M.G. designed and performed the experiments; M.-J.S., M.P.E. and M.J.P. designed the reconstruction algorithm; N.R. developed the evolutionary compressed sensing algorithm; M.-J.S., M.P.E., B.S. and M.J.P. analysed the results; M.-J.S., M.P.E. and M.J.P. wrote the manuscript and other authors provided editorial input.

Additional Information

Supplementary Information accompanies this paper at http://www.nature.com/naturecommunications

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How to cite this article: Sun, M.-J. et al. Single-pixel three-dimensional imaging with time-based depth resolution. Nat. Commun. 7:12010 doi: 10.1038/ncomms12010 (2016).

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