Capturing photosequences of fast events is a challenge in the photography milieu. High speed capture is costly to implement since it requires specialized electronics capable of handling the high bandwidth of data as well as highly sensitive image sensors that can make low noise measurements at short exposures. As a consequence, it is still a major obstacle in commodity cameras, especially without sacrificing the full spatial resolution of the sensor. This paper provides a pathway for the implementation of such a capability with no additional hardware.
|(a) Short exp.||(b) Long exp.||(c) Short exp.||(d) Photoseq.|
|Click the images in (d) to play animation in Adobe Reader©.|
One approach is to recover photosequences from motion blur. A single motion-blurred photograph embeds motion events inherently, but recovering them can be hard due to ill-posed temporal ordering, as well as the erasure of spatial textures. While prior single-blur sequencing approaches [11, 18]
handle both these issues using data-driven priors encoded using deep neural networks, they are incapable of correctly sequencing multiple local motion events happening across the sensor space. A recent multi-blur sequencing technique handles the overall sequencing problem by processing multiple blurred photographs captured in succession. As much as texture recovery from blur is conditioned using deep neural networks, fine textures can still be lost due to fast motion since all of the captured photographs are blurred. An orthogonal approach to motion blur is to first capture a short-exposure photosequence at higher frame-rates followed by frame-wise denoising . Even though this looks promising, texture loss could still be an issue due to denoising. Further, static regions, which would have benefited from long exposures, suffer due to postprocessing which would otherwise be clean.
This paper proposes to capture a short-long-short exposure triplet to handle both motion ordering and texture recovery in photosequencing. The two additional short-exposure photographs are designed to have an exposure that is much smaller than the original long exposure photograph. Hence, while these additional images might be noisy, they are practically free of motion-blur. Further, the short exposure photographs resolve temporal ordering by acting as peripheral keypoints of the long exposure. Such a capture mechanism is easily implemented in modern cameras since they are endowed with a burst mode. Once we capture the short-long-short exposure images, we computationally recover the photosequence equivalent to a high-speed capture of the underlying scene. The blurred image is first decomposed into two half-blurred images with reduced blur corresponding to the two halves of the exposure period and a single sharp image corresponding to the mid-point. We learn this decomposition by training a deep neural network using images synthesized from high frame-rate video datasets. A recursive decomposition leads to the sharp photosequence without any enforced temporal order. The recovered images gain from the complementary goodness of the short and long exposures for static and moving scene regions.
Figs. 1(a,b,c) show the short-long-short exposure images captured in succession of a scene with a moving jellyfish. The short exposures are noisy while the long exposure embeds motion blur. The intricate tentacles are captured in the noisy image but are blurred in the long exposure. Our recovered 15x photosequence corresponding to the long exposure duration is shown in (d). Both texture and motion are recovered correctly in our reconstruction.
The main contributions of this work are as follows:
We propose the novel idea of capturing short-long-short exposure images for the problem of photosequencing of motion blur.
We propose a recursive blur decomposition strategy in which increase in temporal super-resolution can be achieved through multiple levels of decomposition till the removal of blur.
We present a new short-long-short exposure dataset for a variety of dynamic events captured using a machine vision camera. We provide qualitative evaluation and comparisons to prior art on this data.
2 Related Works
Traditional deblurring approaches [3, 12, 17, 30, 28, 2, 25] aim to get a single sharp image along with local motion kernels and camera trajectories. Reconstructing the whole photosequence for combined object and camera motions has been dealt only recently [11, 18]. Single-blur techniques produce photosequence from a single image by imposing ordering constraints through explicit temporal image costs as in  or through an implicit cost using a video encoder-decoder framework as in . These methods suffer from ambiguities in temporal ordering of multiple objects. The recent multi-blur approach  does photosequencing using multiple motion-blurred images to impart more information for reconstruction and ordering. All these photosequencing approaches use neural network priors to reconstruct sharp textures from blur.
One can also increase framerate through temporal interpolation of video frames. An interpolation approach based on gradients and phase is employed in and , respectively, while  fuses recurring video patches to perform spatio-temporal super-resolution. Recently,  employed neural networks to linearly interpolate optical flows. However, frame interpolation methods are inherently limited from the assumption of video frames being non-blurred.
Pre-regularizing the ill-posedness of image recovery during capture time is a central tenet of computational photography. A hybrid high resolution, lower frame rate and a low resolution, higher frame rate camera setup is used in [1, 27] to remove motion blur from the high resolution capture, but a further photosequencing step is not performed. The coded exposure work  suggests changing exposure design to improve the conditioning of the deblurring problem. The idea of capturing a noisy-blurry pair in  leads to the extraction of complementary information that regularizes the deblurring problem better. While this work employs an additional short exposure image to produce a single sharp image, our goal is to recover the whole photosequence.
Let be the clean ground-truth image of a scene at . Let be an observed image for the time interval defined as where represents noise. The goal of motion-blur photosequencing is capture a blurred image
and to estimate the imagessuch that where s are equi-spaced timepoints and represents the sequence-rate. In essence, the recovered sequence represents the series of images of the scene if it had been captured with a hypothetical higher frame-rate camera operating at the same spatial resolution and without the noise level associated with that frame rate.
We propose to capture two short exposure images and , one before and one after the long exposure image . Though the short exposure images will be noisy owing to the very short exposure interval , they provide the much-needed information of scene texture. They also act as temporal endpoints for the blurred image to disambiguate motion directions. Our problem statement is to estimate the image sequence happened during long exposure, given the three input images, as inputs.
3.2 Recursive Blur Decomposition
We adopt a multi-step sequencing strategy wherein we progressively increase the number of reconstructed sharp images. We first decompose the long exposure into two half-blurred images and and the sharp image . Estimating just would correspond to deblurring. In addition, we also estimate and that contain lesser motion blur corresponding to each half of the original exposure interval. Our core blur decomposition step, hence, is the following:
Our idea then is to perform blur decomposition on both the half-blurred images to further split the blur interval and get a sharp image corresponding to their respective middle timepoints as shown in Fig. 2(a). The second-level will result in the sharp sequence corresponding to 3x frame-rate. We could perform blur decomposition recursively to achieve a desired sequence-rate. For instance, a third level of blur decomposition would provide us with 7x sequence-rate, a fourth level 15x, and so on. In practice, one could stop the decomposition at a desired level when the blur present in half-blurred images is negligible.
We learn the blur decomposition mapping in (1) by training a neural network.
4.1 Network Architecture
We adopt an encoder-decoder architecture similar to U-net [20, 8] as shown in Fig. 3. We use dense residual blocks  which have rich local connections, instead of serialized convolutional layers. We use carry-on convolutional layers through the skip connections from encoder to decoder. For our network, the inputs are the short-long-short exposure observations and the outputs are the estimates of half-blurred images and the deblurred image,
. The input images pass through different initial convolutional layers; similarly the output layers are different for half-blurred and the deblurred images. The input layer of the short exposures share the same weights; the output layer of the half-blurred images share the same weights. The image intensities are in the range [0,1]. All the convolutional layers are followed by Leaky ReLU nonlinearity except for the last layer which is followed by rescaled-tanh to enforce the output range to [0,1]. All convolutional layers use 3x3 filters except for the first layers of both noisy and blurred images which use a filter size of 7x7. More details of the architecture are provided in the supplementary material.
4.2 Training Data
Our goal is to have the neural network learn to decompose different amounts of blur in the long exposure image with the help of sharp and noisy short exposure images. Training a neural network requires a large number of blurred, half-blurred, and sharp images according to (1). Hence, we use existing high-speed 240fps video datasets to create our training set. We employ multiple video datasets, Adobe240fps , GoProTrain240fps , and Sony240fps , to avoid camera bias. Our single training sample is defined by random 128x128 crops created from full-sized video frames. We follow the procedure in Fig. 2(b) to create a training sample from a series of high-speed video frames. For instance, as shown for images, we have , where , , , , and . We vary
based on the variance of pixel-wise intensities of the chosen video frames along the temporal dimension to aggregate different amounts of blur. The higher the variance, the larger is the motion. We ignore static examples in the training set. Typically the value ofranged from 11 to 39 frames. We demonstrate our blur decomposition idea further in a discrete time representation in Fig. 2(b). We also augment data by randomly employing the following operations: (i) horizontal spatial flipping, (ii) or spatial rotations, and (iii) temporal flipping by swapping and , and and , during training.
To emulate proper short exposure images and , we add scene-dependent noise according the calibrated noise parameters on-the-fly during training based on the noise model described in . For the gain level used in our experiments, we calibrate the noise parameters of the camera based on an affine model for the noise variance given by , where is the observed mean intensity, and and are the calibrated noise parameters. We use the machine vision Blackfly BFS-U3-16S2C camera to capture our short and long exposure images.
Since our technique uses recursive decomposition, the inputs to the network beyond the first level would have denoised short exposure images. However, we observed no significant difference in our test results between employing three separate trained networks with two, one, and zero noisy images for the short-exposure input images appropriately at different decomposition levels, and a single trained network with two noisy images. Hence, we report our results for the single trained model approach, that takes in as input noisy short exposure images, and provide comparisons to the three model approach in the supplemental material.
We train the neural network by employing the following costs during optimization: (a) supervised cost and sum cost for , , and , and (b) gradient, perceptual, and adversarial costs on the sharp image .
The supervised cost is defined as the mean square error between the estimated and ground-truth outputs corresponding to , , and . The sum cost is defined by the mean square error according to the blur decomposition process. The gradient cost is based on the isotropic total-variation norm  on the sharp image that encourages sharp edges with homogeneous regions. The perceptual cost is defined as the mean squared error between the VGG [23, 13] features at the conv54 layer of the estimated and ground truth sharp images. We also train a two-class discriminator alongside our network following a generative adversarial training procedure , which contributes the generator adversarial cost to encourage the sharp image to lie in the natural image distribution.
The cost function is given as follows:
where , , , and are weights of the individual costs, is the total variation norm. We use , , , and in our experiments for the image intensity range . We train for iterations using Adam as our optimizer with initial learning rate as scaling it by every iterations.
We first demonstrate our blur decomposition through a visualization of blur kernels. We then provide quantitative comparisons with existing methods followed by an analysis on blur amount. Finally, we show qualitative results on real data captured by our cameras.
|Blurred||Level 1||Level 2|
5.1 Successive Reduction of Blur
We demonstrate our blur decomposition through blur kernels estimated using the state-of-the-art blind deblurring method of . A blur kernel describes the motion experienced by a point light source located at the image center, and thus acts as an indicator of residual blur/motion present in the image. Fig. 4(a) shows a patch from a motion blurred image and its long blur kernel. The network takes this image and the short exposure images as inputs (not shown). At first level of decomposition, the half-blurred images have blur kernels of reduced length indicating shorter blur. One can neatly trace down the long kernel trajectory of by conjoining the split trajectories of level-1. (The kernel estimation is blind, and therefore, it is always centered.) Also, the blur kernel of the middle image has a close-to-delta kernel indicating a negligible blur. Similarly, in the second level, we get four half-blurred images with further reduction of blur and the corresponding two deblurred images. Thus, our recursive decomposition provides an elegant way to remove blur and achieve our goal.
|Short/Noisy||Long/Blurry||Single-blur||Multi-blur||Ours (L-only)||Ours (S-L-S)||Ground-truth|
|(a) Short and Long exposure images for different exposure intervals.|
|(b) Single-blur sequencing outputs  (takes a single blurred image as input)|
|(c) Multi-blur sequencing outputs  (takes four blurred images as inputs)|
|(d) Proposed short-long-short sequencing outputs|
|Single-blur ||Multi-blur ||Proposed sequencing|
|Ours (long only)||27.13||27.81||27.32|
|Blur frame length||9||11||15||19|
5.2 Quantitative Analysis
We analyze the performance of 3x sequence-rate level, i.e. the PSNR of the middle deblurred image and that of the second-level decomposition images, and against the single-blur sequencing of  and multi-blur sequencing of . In addition, we also consider an ablation case of our method by considering only the long exposure blurred image as input without any short exposure images, indicated by long-only.
Since each of these methods need different types of inputs, we prepare the testing set as follows. We created a set of eleven examples from the eleven test videos of the GoPro 240fps data . Each example is a sequence of alternating short and long exposure images. The short exposure is created by taking a single video frame, while the long exposure is synthesized as an average of 11 frames. Our method takes a single consecutive short-long-short triplet as input with added noise to the short exposures. The single-blur sequencing method takes only a single long exposure image, while multi-blur sequencing takes four long exposure images as inputs.
The results of our analysis are provided in Table 1. First, our network trained with short-long-short exposure inputs performs better than training with only the long exposure image indicating the benefit of capturing additional short exposure images in photosequencing. The multi-blur sequencing performs better than the single-blur sequencing owing to more available information as expected. In turn, we are able to perform better than the multi-blur sequencing. Our method recovers textures missed in heavy blur from the short exposure images. Fig. 5(top) depicts this behavior where the prior works are able to reconstruct the leg on the ground which has lesser blur, while the other leg is not recovered even by the multi-blur technique. Our output shows better textures with minimal residual blur and is practically noise-free.
5.3 Blur Amount Analysis
The amount of blur observed in the long exposure image is a synergy of exposure time and motion. We repeated our experiments on the test data for different frame lengths shown in Table 2. The multi-blur sequencing method performed better for shorter frame lengths almost on par with our method and worse for the longer ones.
Fig. 6(a) shows our real captures of a spinner for multiple exposure configurations. At the lowest long exposure, the blur is minimal, while at the longest setting, the spinner texture is almost lost. Three frames from sequencing results of different methods are shown in (b,c) and (d). Single-blur technique (b) shows residual blur artifacts even at medium blur shown in the third column-set. While the multi-blur technique (c) could recover some texture at the highest setting, our method outperforms it. Further, single-blur technique could not disambiguate temporal ordering leading to wrong local spinner motion as shown in Fig. 7, while our short-long-short sequencing correctly recovers the ordering.
|(a) Short||(b) Long||(c) Multi-blur sequencing ||(d) Deblur+Interp [28, 9]||(e) Denoise+Interp [4, 9]||(f) Ours|
|(a) Input capture||(b) Recovered photosequence|
|(a) Blurred||(b) Short-long-short crops|
|(b) Multi-blur sequencing ||(c) Proposed sequencing|
5.4 Results on Real Data
We capture sequences of short and long exposures of a wide variety of scenes using our Blackfly camera to show the efficacy of our photosequencing, some of which are shown in Fig. 8. Our captures comprise both indoor and outdoor scenes with different types of motions including linear blur in Race, rotations in Foosball, human nonlinear motions in Gym and Skate, fine textured motion of Jellyfish, and closeup finger movement in Keyboard. Note that we cannot use any of the existing real blurred videos since our technique requires short exposure images as well.
Comparison with multi-blur sequencing. Fig. 9 shows the Foosball scene with noisy short exposures, and blurry player and ball in long exposures. (Please zoom-in to see noise and blur clearly in first two rows.) The third row and fourth row show the cropped results of  and our method.  recovers the direction of motion correctly but the blur is not completely removed. Our method correctly recovers the sharpness of the player and the ball as well as the motion ordering.
Comparison with frame interpolation. Fig. 10 shows input images and crops of the Skate scene in (a,b). in which heavy noise and blur can be observed. The multi-blur sequencing fails to recover intricate textures of the skateboard and fist as seen in (c). We follow two pipelines to compare with frame interpolation . First, we deblur two long exposures using the state-of-the-art deblurring method of  and interpolate frames. Second, we denoise two short exposures using BM3D  followed by frame interpolation. In the first case result shown in (d), the heavy residual blur due to poor deblurring of heavy motion is passed on to interpolation which can only recover blurred frames. In the second case (e), we do note that the texture in the fist is devoid of blur since it uses only the short exposure frames, however the denoised image has a washed-out appearance. Further, the static wall undergoes noise-denoise process for no reason only to have its texture erased. Our method correctly exploits textures of static regions (wall) from the blurred image and textures of moving objects (hand, fist) from the short exposure image as shown in (f).
The proposed technique recovers a sharp frame sequence for a short-long-short triplet. By combining the outputs from a longer sequence of alternating short and long exposures, we can produce high frame-rate videos of long time durations. We showcase some examples of this in the supplemental video. We do note that such sequences have temporal tiling artifacts since each triplet leads to sequences in isolation. We show XT and YT slices for the result of Skate data over multiple triplets in Fig. 11.
Failure Example. A challenging scenario is that of heavy motion of thin structures. Fig. 12(a) portrays the JumpingToy scene wherein the thin legs of the jumping metal toy move very fast. The motion is so ragged that the line of blur marked in yellow is disconnected from the two short exposure points (white to red) as shown in the image crops of Fig. 12(a). Our method shows artifacts in the photosequence with partial leg reconstructions as shown in (c-top). In comparison, the multi-blur sequencing method performs worse as shown in (b), and suffers residual blur artifacts in other regions as well where we perform better as shown in the last row.
We proposed a new technique to record fast motion events by capturing short-long-short exposure images. We utilize their complementary information of texture and motion in these images to estimate the sharp high frame-rate photosequence associated with the long exposure. Our technique provides an approach that can be easily implemented on mobile devices, thereby providing the capability of high-speed capture with little change to existing hardware. Hence, we believe this would be a fascinating new application of mobile computational photography.
The work of VR, SZ, and ACS was supported in part by the ARO Grant W911NF-15-1-0126, a gift from Samsung, and the Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior/Interior Business Center (DOI/IBC) contract number D17PC00345. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied of IARPA, DOI/IBC or the U.S. Government.
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S7 Comparison of Single and Three Model Approaches
As mentioned in Sec. 4.2 of the main paper, since our technique uses recursive decomposition, the inputs to the network beyond the first level would have at least one noise-free estimated image. However, our training involves noise for both the short exposure images. We showed results using this single-model approach in the main paper. As a variation to our single trained model, we also trained three different models (with the same architecture) for the three cases with two, one, and zero noisy images for the short-exposure inputs. This is explained in Fig. S13.
We observed no significant difference in our test results for these two approaches. This can be seen in Fig. S15. For four levels of decomposition as depicted in Fig. S13, we show the estimated images , inferred using Model-1 and using Model-2 in Fig. S15(b) for Skate and Jellyfish scenes. The corresponding estimated images using the single trained model approach inferred using Model-0 is shown in Fig. S15(a). We can see no observable difference. The relative PSNRs between the estimated images of the two approaches are on the high end showing that both the approaches performs very similarly, and hence, we used the single trained model approach for all our results in the main paper.
S8 Network Architecture
The architecture of our neural network with layer numbering is shown in Fig. S14S3.
|Rel. PSNR 43.83dB||40.38 dB||42.14 dB|
|Rel. PSNR 43.62dB||40.96 dB||43.70 dB|
|(a) Single trained model||(b) Three trained models|
|Layer||Type||chan-in chan-out||filt, pad, stride|
|ip1||Conv||3 16||7x7, 3, 1|
|ip2||Conv||3 32||7x7, 3, 1|
|1||ResB||64 64||3x3, 1, 1|
|2||ResB||64 64||3x3, 1, 1|
|3||Conv||64 128||3x3, 1, 2|
|4||ResB||128 256||3x3, 1, 1|
|5||ResB||128 256||3x3, 1, 1|
|6||Conv||128 256||3x3, 1, 2|
|7||ResB||256 512||3x3, 1, 1|
|8||ResB||256 512||3x3, 1, 1|
|9||Conv||256 512||3x3, 1, 2|
|10||ResB||512 512||3x3, 1, 1|
|11||ResB||512 512||3x3, 1, 1|
|12||Conv||512 1024||3x3, 1, 2|
|13||ResB||1024 1024||3x3, 1, 1|
|Layer||Type||chan-in chan-out||filt, pad, stride|
|14||ConvT||1024 256||4x4, 1, 2|
|15||ResB||512 512||3x3, 1, 1|
|16||ResB||512 512||3x3, 1, 1|
|17||ConvT||512 128||4x4, 1, 2|
|18||ResB||256 256||3x3, 1, 1|
|19||ResB||256 256||3x3, 1, 1|
|20||ConvT||256 64||4x4, 1, 2|
|21||ResB||128 128||3x3, 1, 1|
|22||ResB||128 128||3x3, 1, 1|
|23||ConvT||128 32||4x4, 1, 2|
|24||ResB||64 64||3x3, 1, 1|
|25||ResB||64 64||3x3, 1, 1|
|op1||Conv||64 3||3x3, 1, 1|
|op2||Conv||64 3||3x3, 1, 1|
|26||Conv||512 256||3x3, 1, 1|
|27||Conv||256 128||3x3, 1, 1|
|28||Conv||128 64||3x3, 1, 1|
|29||Conv||64 32||3x3, 1, 1|
Conv - convolutional layer, ConvT - transpose convolutional layer .
All convolutional layers are followed by Leaky ReLU. Only op1 and op2 are followed by (tanh()+1)/2.
Structure of Dense Residual Block (ResB)
|Layer||Type||chan-in chan-out||filt, pad, stride|
|d1||Conv||nchan nchan||3x3, 1, 1|
|d2||Conv||nchan nchan||3x3, 1, 1|
|d3||Conv||nchan nchan||3x3, 1, 1|
|d4||Conv||nchan nchan||3x3, 1, 1|