- Research Article
- Open Access
Generating the Depth Map from the Motion Information of H.264-Encoded 2D Video Sequence
© Mahsa T. Pourazad et al. 2010
- Received: 1 May 2009
- Accepted: 10 March 2010
- Published: 19 April 2010
An efficient method that estimates the depth map of a 3D-scene using the motion information of the H.264-encoded 2D-video is presented. The motion information of the video-frames captured via a single camera is either directly used or modified to approximate the displacement (disparity) that exists between the right and left images when the scene is captured by stereoscopic cameras. Then, depth is estimated based on its inverse relation with disparity. The low-complexity of this method and its compatibility with future broadcasting networks allow its real-time implementation at the receiver; thus 3D-signal is constructed at no additional burden to the network. Performance evaluations show that this method outperforms the other existing H.264-based technique by up to 1.98 dB PSNR, providing more realistic depth information of the scene. Moreover subjective comparisons of the results, obtained by viewers watching the generated stereo video sequences on a 3D-display system, confirm the superiority of our method.
- Motion Vector
- Motion Information
- Luma Intensity
- Segmented Object
- Optimize Rate Distortion
Three-dimensional television (3D TV) generates a compelling sense of physical real space for the viewers by allowing on-screen scenes to emerge and penetrate into the viewers' space. Viewers thus feel that they are part of the scene they are watching. It is predicted that by commercialization of 3D TV applications, another revolution will take place in TV's history (the last one being the introduction of digital video broadcasting).
The history of 3D TV can be traced back to 1920s, when the first experimental 3D TV set-up was built . Since then, several attempts have been made to introduce this technology into the market. Despite the immense keenness towards 3D, the great expectations of viewers, content providers, and distributors have not yet been fulfilled. The main drawbacks were the discomfort of the viewers (headaches, eyestrain) due to the poor quality content, the low-tech display systems, and the high costs involved in the production and distribution of 3D content.
The successful introduction of 3D TV to the consumer market relies not only on technological advances but also on the availability of a wide variety of 3D content. Thus the production of 3D-format videos is important. Equally important is the ability to convert existing 2D material to 3D format. This allows the existing popular movies and documentaries to be watched on 3D screens. Converting 2D content to 3D video streams is possible if the depth information is estimated from the original 2D video sequence. Using the depth information, 3D video content in the stereoscopic format (two temporally synchronized video streams, one for the right and another for the left eye) can be rendered from the 2D video stream, via a process known as depth image based rendering (DIBR) .
Depth map estimation techniques generally fall into one of the following categories: manual, semiautomatic, and automatic. For the manual methods, an operator would manually draw the outlines of objects that are associated with an artistically chosen depth value. As expected, these methods are extremely time consuming and expensive. For this reason, semiautomatic and automatic techniques are preferred for the depth map estimation. These techniques are designed based on the human visual depth perception mechanism. There are several factors (referred as monocular depth cues) such as light and shade, relative size, motion parallax, interposition (partial occlusion), textural gradient, and geometric perspective, which help the human visual system perceive the relative distance of objects within a real scene. In fact, depth map estimation techniques try to use these monocular depth cues and imitate the human visual system when estimating the distance between objects to generate binocular parallax (disparity) for the viewer.
A machine learning approach for estimating the depth map for 2D video sequences is proposed in . Although the results of this approach are promising, it requires an operator to input the local depth information of some selected frames. Extraction of depth from blur has also been explored by researchers . The problem in this case is that depth is not the only cause of the blur in a picture. Other reasons include motion, climate conditions, and fuzziness of objects within a scene. The estimation of depth based on the edge information has also been studied [5, 6]. Another group of researchers has utilized the motion/edge-corrected color-segmentation via a K-means algorithm to estimate the depth map . This algorithm does not provide solutions when the camera is moving or when the objects have complicated motion. Also, since supervised image segmentation is implemented, when the number of objects within the scene is higher than a prespecified number, the algorithm cannot recognize the silhouette of all objects and estimate their relative distance from the camera. The study in  applies an unsupervised image segmentation algorithm to separate the objects. Then to decide on the depth value of each object, the proposed algorithm uses the assumption that the objects on the top part of the image are further from the viewer and the ones at the bottom part of image are closer. This assumption, however, is not valid for all video sequences.
There is a relationship between the distance of moving objects from the camera and their registered motion, which has been utilized in previous studies for motion estimation  and also for depth map approximation [10–12]. For objects traveling with the same speed, but different distance from a still camera, this relationship implies that the camera registers larger displacements (in pixel) for the closer objects to the camera. This approach is based on the principle known as the Pulfrich effect [13, 14]. The Pulfrich effect is a psychophysical phenomenon wherein lateral motion of an object in the field of view is interpreted by the visual cortex as having a depth component, due to a relative difference in the signal timings between two eyes. To utilize this principle, the study in  uses a modified time difference method (MTD) to detect the horizontal motion of objects and determine the image-presentation time-delay for synthesizing a stereo pair. The MTD method does not work for images containing objects with complicated motion.
The study in  uses color segmentation and the KLT (Kanade-Lucas-Tomasi) feature tracker to estimate motion information. Then, the depth map is approximated based on the estimated motion information. In this approach, factors such as camera movement, scene complexity, and the magnitude of the estimated motion are used for converting the motion information of each frame into depth map. The facts that this method is not based on existing video coding standards and it involves a relatively complex motion estimation extraction process do not allow its cost-effective real-time implementation at the decoder side. In , motion estimation is based on the H.264 standard but uses fixed (rather than variable) block-size matching technique. This study assumes that the motion of every object is directly proportional to its distance from the camera; thus the depth map is approximated as a constant factor of the estimated motion. Unfortunately, this is only true for a relatively small part of real life footage (when the camera is panning across a stationary scene, or a still camera captures a scene with moving objects). Otherwise, when the objects and the camera are both moving, there would be ambiguity in the depth estimation based on the motion information. The other issue in  is related to the accuracy of H.264-estimated motion vectors when they are used to derive the objects' motion. The principle idea behind the motion estimation process in H.264/AVC and other standards relies on maximizing the compression performance and optimizing rate distortion and not on obtaining accurate estimates of the objects' displacement in the scene. Thus, not all motion vectors can be used to accurately estimate the depth unless they reflect the objects' displacement.
In this paper, we present an effective scheme that finds an approximate depth map of the scene using the motion information of the H.264 encoded video which is derived (at quarter pixel accuracy) via matching blocks with different sizes, where the sizes dynamically adjust to the video content. This proposal is an improved version of algorithm in  from two aspects: (i) generalizing previous assumption that any motion is directly proportional to distance from camera, and (ii) improving accuracy from motion vectors in H.264.
To resolve the issue regarding the accuracy of motion vectors, we propose an algorithm that examines the motion vectors and (whenever necessary) properly modifies their values, to ensure that the values of the motion vectors reflect the displacement of objects. When a moving camera captures a scene with moving objects, our proposed scheme provides a solution to estimate the motion of moving objects and uses this information to find the scene's depth map 1. Since the motion estimation procedure is based on the block-matching technique, there will be depth ambiguity between the foreground and the background at the object boundaries. To solve this problem, our algorithm first adopts a color-texture segmentation algorithm known as JSEG to properly distinguish between the different object-regions . Then it reevaluates and modifies the estimated values of the motion vectors of the object-boundary pixels. To ensure that the final estimated depth map is smooth and free of artifacts, our algorithm assumes that each segmented object has a unique depth value and accordingly corrects the estimated motion of the object-body pixels using the object-boundary pixels. This enhances the visual quality of 3D video that is rendered based on the estimated depth map.
After refining the motion vectors in different stages, the absolute horizontal values of the refined motion vectors are used to approximate initial depth values. To enhance the visual depth perception, we propose to increase the contrast among the initial approximated depth values by using a nonlinear scaling model.
Finally, a DIBR technique is used to render the 3D videos based on the approximated depth map and 2D video. The 3D videos created using this scheme are of the stereoscopic format and are supposed to be watched on 3D TVs in the sense of stereoscopic TV. Note in this paper that by "3D TV," we mean 3D TV in the sense of stereoscopic TV.
The rest of this paper is organized as follows. Section 2 provides background information on the principal idea behind this study. Section 3 elaborates on our 2D-to-3D conversion scheme. Section 4 presents the performance evaluation of our scheme and discusses the results in detail. Section 5 presents the conclusions.
In 3D video capturing using stereo camera set-up, the displacement between the left and right camera images is directly related to the distance of objects from the camera. This displacement, which is known as disparity , creates an intrinsic feeling of depth for viewers watching stereo videos. Basically when two slightly different images are projected on the left and right eye retinas (each from a slightly different viewpoint), the brain fuses these images such that the perceived image represents everything included in two images, but in a three-dimensional format.
where and are the coordinates of and , respectively. is the distance of point from the cameras (depth), is the distance between the two cameras (baseline), and is the focal length of the cameras. In a practical stereoscopic camera set-up, is usually equal to the average distance between the human eyes and is chosen based on the region of the interest within the scene.
For our case where the 2D scene is captured by only one camera, we shall obtain the depth of a moving point using the registered displacement that is resulted from its motion. In other words, if the left and right side frames shown in Figure 1 are aligned in the time domain to form two consecutive frames, then and would be two consecutive images of moving point , and would be the displacement between them. Since the time delay between two consecutive frames is small (as in the studies [10–12]), we assume that the displacement due to motion in the 2D case is equivalent to the disparity in a stereoscopic set-up. Then , the depth of point , can be calculated using (1), if is measured. The displacement ( ) between two consecutive frames could be obtained using information embedded in the motion vectors of the encoded video, assuming that is constant. The following section provides detailed information on this process.
To find the displacement of objects within a scene captured by single camera, we use the motion vector estimation procedure of the H.264 standard. Since H.264 motion vector estimation is block-based (i.e., it measures the displacement of a block and not a point or object), we propose correction steps that reevaluate and refine the estimated motion vectors in order to calculate the motion vectors for the objects within the scene. Then the resulting object motion vectors are transformed to depth information. The following subsections elaborate on different steps of our proposed scheme.
3.1. Motion Vector Estimation
H.264/AVC-based motion vectors (MVs) are estimated using variable block sizes of , , , , , , and pixels, at quarter-pixel matching accuracy . These two H.264 features (variable block size and quarter-pixel matching accuracy) have been shown to yield motion vector precision that is far superior to those of any previous standards . An additional advantage of using the H.264/AVC standard is the fact that H.264 has been chosen as the platform for 3D TV applications . This means that the proposed scheme will be compatible with future 3D networks and players and also could be implemented at the receiver-end where the motion vectors are readily available at no additional computational cost. The existing approach in  forces the encoder to use only block sizes and this will significantly decrease the compression performance and will increase the computational complexity of the overall system.
In H.264, depending on the application and content, some frames are selected to be compressed as I-frames. For compressing I-frames only intraprediction is utilized and no motion estimation is involved. Thus, to retrieve the motion information, we utilize the estimated motion vectors of the P-frame just after each I-frame. Since the MVs for the P-frame are estimated in relation to the I-frame (as reference), a simple solution for finding MVs of the I-frame is to invert the MVs of the P-frame. This will give us the displacement of some overlapped blocks of the I-frame. To estimate the approximated MVs of each separate block of the I-frame, the MVs of overlapped blocks are weighted and averaged . Since the use of I-frames in compression is not as common as P-frames and B-frames, an alternative solution is to estimate the MVs of an I-frame at the decoder side by implementing block matching process between the decoded I-frame and the previously decoded frame.
There also exist blocks within a P-frame or B-frame which are compressed based on intraprediction. In this case we estimate the block's motion as the median of its neighbouring-block motion vectors. There is no provision for the intraprediction case in .
Multiple reference frames may be used in H.264 motion estimation for enhancing the compression performance. In this case, the estimated motion vectors do not represent the displacement of objects over two consecutive frames any more. To resolve this problem, we assume that the motion vector length is related to the reference image distance . Therefore, to find the motion information between two consecutive frames, the H.264 estimated motion vectors should be rescaled proportionally, according to the distance between the used reference image and the last encoded image in the video sequence as suggested in .
For B-frames, forward or backward reference frames are used for predicting the blocks. To ensure that the estimated motion vectors represent the displacement of objects over consecutive frames, the motion vectors of each block should refer to the same region2 in forward or backward reference frames. If that is not the case, the block's motion is estimated as the median of its neighbouring-block motion vectors.
3.2. Camera Motion Correction
A potential problem that arises in motion-based depth estimation algorithms is when both the objects and the camera are in motion, that is, neither of them is stationary. In this case, an object that is estimated to have captured larger motion than others may not be closer to the camera, since the camera may have moved in the opposite direction from the object. To resolve this issue, the camera motion needs to be approximated and the motion information registered by the camera should be corrected accordingly.
In the camera panning case, the registered motion information for the stationary areas of the scene would be equivalent to the camera motion. These areas are often flagged as "Skip Mode" by the H.264/AVC motion estimation process. The "Skip Mode" is used for blocks, where the motion characteristics of the block can be effectively predicted from the motion of its neighboring blocks, and the quantized transform coefficients of the block are all zeros. When a block is skipped, the transformed coefficients and the motion data are not transmitted, since the motion of the block is equivalent to the median of the motion vectors of the surrounding blocks. This median is known as the predicted motion vector ( ) .
As long as there is no camera motion, the predicted motion vector of a skipped block is zero. However, when camera panning is present, all the predicted motion vectors of the skipped blocks become equal to a unique nonzero value (which represents the camera motion). Since most of the skipped blocks over the entire frame are blocks that contain background areas, our proposed scheme uses the predicted motion vector ( ) with the maximum occurrence to estimate the value of the camera motion. In order to find this vector for each frame, we compute the histogram of the s of all the skipped blocks. The that corresponds to the maximum of the histogram is recognized as the camera (panning) motion . The net motion of each object is extracted by subtracting the camera motion from the MVs of all blocks within the frame. This procedure cannot be accommodated in  since only blocks are used and the size of the skip-mode blocks is . The following code summarizes the above-mentioned procedure:
for each frame:
(2) calculate the histogram of the MV p s of blocks found in 1.
(3) assign the MV p with maximum occurrence to camera panning motion.
(4) subtract camera panning motion from all the MVs within the frame.
Besides panning, camera zoom-in/out can also cause depth ambiguity. To address this issue, we check the tendency of MVs in the four corners of the frame to detect zoom in/out . Then the estimated MVs are scaled accordingly. Note that zoom-in/out may cause reverse depth or eye fatigue if not corrected in the depth estimation process.
3.3. Correction of False Displacement Estimates
The criterion used in video compression standards is to optimize the rate distortion and maximize the compression performance, that is, to transmit the least number of bits. The motion vectors obtained by H.264/AVC coding are thus derived so as to minimize the compression rate and optimize rate distortion and not maximize the accuracy of the estimated motion of the objects within a scene. Thus, the matching blocks determined by a motion vector do not necessarily relate to the same part of an object in the scene. In such a case the estimated motion vectors do not accurately convey the displacement of an object; that is, they do not point to the corresponding left and right areas as defined by the disparity in a stereoscopic scenario (Figure 1).
We have found through performance evaluations that if the variance (i.e., ) is less than 1000, then there is a very high probability that there is no moving edge within the block and therefore the MV needs to be replaced by the median MV the instant neighboring blocks. Otherwise (i.e., there is a moving edge within the block), the H.264-estimated MV is correct.
Assume that the MV of a certain block is presently being estimated. To find the adjacent blocks that belong to the same object as this block, we use an unsupervised segmentation algorithm called JSEG . This algorithm consists of color quantization and spatial segmentation as two separate steps. As a result, each frame is segmented into different regions based on the color and texture of the region, without any presumption about the number of objects (see Figure 4(b)). For detailed information on this algorithm see .
The following code summarizes the above procedure for displacement correction:
for each frame:
(1) calculate MVdiff = abs(MV − MV p ) for each block.
(2) compute residue frame as:
resFrame = abs(luma current frame − luma previous frame )
(3) calculate the variance of each block within residue frame (resVAR).
(4) implement JSEG algorithm to segment the frame based on color and texture and distinguish different object regions.
(5) for the blocks which MVdiff > Th 1 & resVar < Th 2 , new MVs are calculated as of median MV of their instant neighboring blocks belong to the same segmented object.
3.4. Displacement Correction of Object-Border Pixels
In this study, we use the absolute value of the horizontal component of the motion vectors (i.e., ) for estimating the depth map. This is because, as explained earlier, the disparity, ( ), which is the horizontal displacement between the two camera images, is related to the depth Z (as shown in Figure 1).
Since all the pixels within each matching block are assumed to have the same amount of motion, the is assigned to each pixel within the block. This assumption, however, is not valid for blocks that include both stationary background pixels and moving object pixels. For such blocks, a different procedure should be used; otherwise the resulting object borders in the constructed 3D video may appear blurred, and the small details or even entire objects may be removed.
A computationally expensive solution is to perform pixel-based motion vector estimation for the object-border pixels. We propose an alternative solution which detects the border blocks with nonzero motion vectors and, then, classifies each pixel within each of these blocks as a background pixel or an object pixel. This process is based on the results of the JSEG algorithm (Section 3.3). The estimated is assigned to the object pixels, while the median of the of the surrounding nonobject pixels is assigned to the background pixels. The background pixels inside the block who have been assigned with updated might be utilized in the motion correction process. Note that if the block includes multiple segmented regions, the MV of the pixels within each segmented region is calculated as the median of MVs of pixels within the neighboring blocks which belong to the similar segmented region.
JSEG algorithm is robust, but as it can be observed from Figure 4(b), oversegmentation may occur because of the varying illumination shades . For this reason, pixel classification of border blocks is further verified by calculating the average luma intensity of the corresponding block in the "residue frame" and then comparing it with the luma intensity of each pixel within the block. The luma intensity of the background pixels in the "residue frame" should be less than the calculated average. This is because the intensity of the still-background pixels in the "residue frame" is close to zero, while the intensity level of moving region edges is high.
The following code summarizes object-border correction process:
for each object:
(2) label pixels within the blocks found in 1 as background-pixel or object-pixel based on the object-segmentation results by JSEG.
(3) find corresponding blocks of the ones found in 1 in the resFrame.
(4) compute average luma intensity of blocks found in 3 (resAVR)
(5) compare the luma intensity background pixels within each block found in 3 (in the resFrame) with resAVR; if it was higher than that, change the pixel's label to object-pixel.
(6) label the corresponding pixels within the blocks found in 1 (in the current frame) according to the ones in 5.
(7) for background pixels within the blocks found in 1 recalculate motion as of median of abs(MV x ) of instant-neighboring background-pixels by iteration.
(8) for the object pixels assign the estimated abs(MV x ) of the block.
3.5. Displacement Correction of Object-Body Pixels
3.6. Perceptual Depth Enhancement
The visual depth perception on 3D display systems is limited to the objects within a certain range from the camera. This means that only the objects within a certain distance from camera can be seen on a 3D display system, while distant objects have no depth perception. Considering this limitation, to enhance visual depth perception of videos to be watched on 3D display, we apply a nonlinear scaling model to the values, which increases the disparity of closer objects and decreases that of distant objects. Since there is a nonlinear relation between the visual depth perception (disparity) and the distance of an object as shown in Figure 2, the proposed scaling factors are defined such that the further the object is, the smaller the scaling factor. This will increase the contrast among depth values and enhance the visual depth perception.
Using the approximated depth map and the 2D video sequence, the stereoscopic pair images are rendered via the depth-image-based rendering algorithm proposed in . This algorithm includes a depth map smoothing process (using asymmetric Gaussian filter) to resolve the occlusion problem of depth image-based rendering. In our implementation, only the right-eye stream is rendered (based on the estimated depth map and the 2D video sequence), and the original 2D video is used as the left-eye stream [5, 6].
The performance of our proposed depth map estimation method is tested using the 2D video sequences "Interview," "Orbi," "Breakdancers," and "Ballet." "Interview" and "Orbi" have been captured by a 3D-depth range camera (Zcam) , which measures the depth map of the scene while recording the 2D video. Thus, the true depth-measures of the scene are available in the form of sequences which consist of luma information only. The 2D streams of "Interview" and "Orbi" are 10-seconds and 5-seconds long, respectively, with pixels resolution and 4 : 2 : 2 YUV format . "Breakdancers" and "Ballet" are two multiview video test sequences (8 views), with pixels resolution, provided by Microsoft Research (MSR) group for research on multiview video coding (MVC) standard . MSR also has provided the approximated depth map of the scene using stereo matching. For our experiment, the forth view video sequence of each test set and its corresponding depth map was used.
In our experiments, the motion between two consecutive frames is estimated using the H.264 encoder (JM 12.2 version). We assume that the broadcasted video is of acceptable visual quality. For this reason, in our experiments the quantization parameter was set to , which yields PSNR values above 37 dB for the tested sequences. The GOP size was set to 25 frames, and the frame structure was IBBP with 5 reference frames. We compare our method with the one presented in . Since the recorded depth per each pixel is an integer number between 0 and 255, (where 255 represent the shortest distance from the camera), we assume that there are 256 depth layers for the perceptual depth enhancement step. For the same reason, the estimated depth maps of both methods are normalized as integer numbers between 0 and 255.
Comparing the results in Figure 8 shows that both techniques like other motion-based depth estimation approaches fail to estimate the depth maps of static objects (e.g., the table in Figure 8(b)). According to the human visual system, which integrates different depth cues to perceive the depth, one can expect the integration of depth cues to provide more sufficient means for depth map estimation techniques [5, 6]. Improvement on retrieving depth information of static objects may require integration of our approach with other depth cues, such as sharpness, and it is recommended path for future research.
The visual quality of the resulting 3D video streams using our method and the one presented in  are subjectively tested against the original depth map (for Orbi & Interview) and the one acquired via stereo matching by MSR (for Breakdancers & Ballet), based on the ITU-R Recommendation BT.500-11 . Eighteen people graded the videos from 1 to 100 in terms of 3D visual perception and visual picture quality in two separate experiment sets (with a short rest period between sessions). The evaluation is performed using the SeeReal, 3D display. For the 3D visual perception part of the experiment, the viewers were asked to score the videos based on the depth or volume that objects appeared to have. For the visual picture quality part, the viewers were asked to rank the videos based on picture quality, which could be affected by visual noise, blur, or various other distortions and picture instabilities (which may cause visual discomfort for viewers). Higher picture quality corresponded to higher scores.
Since our technique and the one suggested by  are both capable of approximating the depth information only for areas with moving objects, watching the resultant stereoscopic video streams may create visual discomfort for viewers. However the use of the object-body displacement correction procedure in our method has been successful in reducing this effect. This procedure reduces the artifacts and results in a smooth depth map. Without it, the rendered stereoscopic image would have the binocular parallax effect only for parts of moving objects (for which the H.264-based motion information is nonzero). In this case, some part of an object is perceived in 3D format and the rest in 2D, something that would increase the viewer's visual discomfort.
For the quantitative analysis, we chose to compare the quality of the stereoscopic videos synthesized using our technique with those of the technique proposed in  and the stereoscopic videos rendered from the actual (recorded) depth map. Note that since the ground truth depth maps of Breakdancers and Ballet are not available, the results for these two streams did not go under quantitative analysis.
Average PSNR (dB)
Right view rendered based on the actual depth map versus actual 2D view
Right view rendered based on our estimated depth map versus actual 2D view
Right view rendered based on the estimated depth map the by existing method versus actual 2D view
where is the number of all pixels within the depth map, is the estimated depth map, is the recorded depth map, and is the error tolerance. In our experiment we use . The results show that for our method the percentage of the correctly matched pixels is 53% (Interview) and 48% (Orbi). For , the percentage of correctly matched pixels is 34% (Interview) and 27% (Orbi). The comparison confirms that our method outperforms the existing method by 19% to 21%.
We present a new and efficient method that approximates the depth map of a 2D video sequence using H.264/AVC estimated motion information. This method exploits the existing relationship between the motion of objects and their distance from the camera to estimate the depth map of the scene. Our proposed method revises the motion information based on the characteristics of the 3D visual perception. In this study, the 2D horizontal motion is approximated as the displacement existing between the right and left images when the scene is captured by a stereoscopic camera. For cases involving a moving camera and for possible problems regarding the displacement of object borders and false displacement estimates, our proposed method provides appropriate solutions. To improve the quality and smoothness of the estimated depth, our algorithm utilizes color-texture segmentation. Our proposed approach can be implemented in real-time at the receiver-end, offering 3D experience without increasing transmission bandwidth requirements. Performance evaluations have shown that our approach outperforms the other existing H.264 motion-based depth map estimation technique by up to 1.98 dB PSNR, that is, providing more realistic depth information of the scene.
The visual quality of our constructed 3D stream was also tested subjectively, with viewers watching the generated 3D streams on a stereoscopic display. The subjective tests showed that the 3D streams created based on our approach provided viewers with superior 3D experience. Moreover, in terms of visual quality, our approach outperforms the other existing H.264-based depth estimation method.
This work is supported by the British Columbia Innovation Council, Canada.
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