Colorful Image Colorization

Introduction

Consider the grayscale photographs in Figure 1. At first glance, hallucinating their colors seems daunting, since so much of the information (two out of the three dimensions) has been lost. Looking more closely, however, one notices that in many cases, the semantics of the scene and its surface texture provide ample cues for many regions in each image: the grass is typically green, the sky is typically blue, and the ladybug is most definitely red. Of course, these kinds of semantic priors do not work for everything, e.g., the croquet balls on the grass might not, in reality, be red, yellow, and purple (though it’s a pretty good guess). However, for this paper, our goal is not necessarily to recover the actual ground truth color, but rather to produce a plausible colorization that could potentially fool a human observer. Therefore, our task becomes much more achievable: to model enough of the statistical dependencies between the semantics and the textures of grayscale images and their color versions in order to produce visually compelling results.

Given the lightness channel $L$, our system predicts the corresponding $a$ and $b$ color channels of the image in the CIE $Lab$ colorspace. To solve this problem, we leverage large-scale data. Predicting color has the nice property that training data is practically free: any color photo can be used as a training example, simply by taking the image’s $L$ channel as input and its $ab$ channels as the supervisory signal. Others have noted the easy availability of training data, and previous works have trained convolutional neural networks (CNNs) to predict color on large datasets . However, the results from these previous attempts tend to look desaturated. One explanation is that use loss functions that encourage conservative predictions. These losses are inherited from standard regression problems, where the goal is to minimize Euclidean error between an estimate and the ground truth.

We instead utilize a loss tailored to the colorization problem. As pointed out by , color prediction is inherently multimodal – many objects can take on several plausible colorizations. For example, an apple is typically red, green, or yellow, but unlikely to be blue or orange. To appropriately model the multimodal nature of the problem, we predict a distribution of possible colors for each pixel. Furthermore, we re-weight the loss at training time to emphasize rare colors. This encourages our model to exploit the full diversity of the large-scale data on which it is trained. Lastly, we produce a final colorization by taking the annealed-mean of the distribution. The end result is colorizations that are more vibrant and perceptually realistic than those of previous approaches.

Evaluating synthesized images is notoriously difficult . Since our ultimate goal is to make results that are compelling to a human observer, we introduce a novel way of evaluating colorization results, directly testing their perceptual realism. We set up a “colorization Turing test,” in which we show participants real and synthesized colors for an image, and ask them to identify the fake. In this quite difficult paradigm, we are able to fool participants on $32\%$ of the instances (ground truth colorizations would achieve 50% on this metric), significantly higher than prior work . This test demonstrates that in many cases, our algorithm is producing nearly photorealistic results (see Figure 1 for selected successful examples from our algorithm). We also show that our system’s colorizations are realistic enough to be useful for downstream tasks, in particular object classification, using an off-the-shelf VGG network .

We additionally explore colorization as a form of self-supervised representation learning, where raw data is used as its own source of supervision. The idea of learning feature representations in this way goes back at least to autoencoders . More recent works have explored feature learning via data imputation, where a held-out subset of the complete data is predicted (e.g., ). Our method follows in this line, and can be termed a cross-channel encoder. We test how well our model performs in generalization tasks, compared to previous and concurrent self-supervision algorithms, and find that our method performs surprisingly well, achieving state-of-the-art performance on several metrics.

Our contributions in this paper are in two areas. First, we make progress on the graphics problem of automatic image colorization by (a) designing an appropriate objective function that handles the multimodal uncertainty of the colorization problem and captures a wide diversity of colors, (b) introducing a novel framework for testing colorization algorithms, potentially applicable to other image synthesis tasks, and (c) setting a new high-water mark on the task by training on a million color photos. Secondly, we introduce the colorization task as a competitive and straightforward method for self-supervised representation learning, achieving state-of-the-art results on several benchmarks.

Prior work on colorization Colorization algorithms mostly differ in the ways they obtain and treat the data for modeling the correspondence between grayscale and color. Non-parametric methods, given an input grayscale image, first define one or more color reference images (provided by a user or retrieved automatically) to be used as source data. Then, following the Image Analogies framework , color is transferred onto the input image from analogous regions of the reference image(s) . Parametric methods, on the other hand, learn prediction functions from large datasets of color images at training time, posing the problem as either regression onto continuous color space or classification of quantized color values . Our method also learns to classify colors, but does so with a larger model, trained on more data, and with several innovations in the loss function and mapping to a final continuous output.

Concurrent work on colorization Concurrently with our paper, Larsson et al. and Iizuka et al. have developed similar systems, which leverage large-scale data and CNNs. The methods differ in their CNN architectures and loss functions. While we use a classification loss, with rebalanced rare classes, Larsson et al. use an un-rebalanced classification loss, and Iizuka et al. use a regression loss. In Section 3.1, we compare the effect of each of these types of loss function in conjunction with our architecture. The CNN architectures are also somewhat different: Larsson et al. use hypercolumns on a VGG network , Iizuka et al. use a two-stream architecture in which they fuse global and local features, and we use a single-stream, VGG-styled network with added depth and dilated convolutions . In addition, while we and Larsson et al. train our models on ImageNet , Iizuka et al. train their model on Places . In Section 3.1, we provide quantitative comparisons to Larsson et al., and encourage interested readers to investigate both concurrent papers.

Approach

We train a CNN to map from a grayscale input to a distribution over quantized color value outputs using the architecture shown in Figure 2. Architectural details are described in the supplementary materials on our project webpagehttp://richzhang.github.io/colorization/, and the model is publicly available. In the following, we focus on the design of the objective function, and our technique for inferring point estimates of color from the predicted color distribution.

Given an input lightness channel $\mathbf{X}\in\mathds{R}^{H\times W\times 1}$, our objective is to learn a mapping $\mathbf{\widehat{Y}}=\mathcal{F}(\mathbf{X})$ to the two associated color channels $\mathbf{Y}\in\mathds{R}^{H\times W\times 2}$, where $H,W$ are image dimensions.

(We denote predictions with a $\widehat{\cdot}$ symbol and ground truth without.) We perform this task in CIE Lab color space. Because distances in this space model perceptual distance, a natural objective function, as used in , is the Euclidean loss $\text{L}_{2}(\cdot,\cdot)$ between predicted and ground truth colors:

However, this loss is not robust to the inherent ambiguity and multimodal nature of the colorization problem. If an object can take on a set of distinct ab values, the optimal solution to the Euclidean loss will be the mean of the set. In color prediction, this averaging effect favors grayish, desaturated results. Additionally, if the set of plausible colorizations is non-convex, the solution will in fact be out of the set, giving implausible results.

Instead, we treat the problem as multinomial classification. We quantize the ab output space into bins with grid size 10 and keep the $Q=313$ values which are in-gamut, as shown in Figure 3(a). For a given input $\mathbf{X}$, we learn a mapping $\mathbf{\widehat{Z}}=\mathcal{G}(\mathbf{X})$ to a probability distribution over possible colors $\mathbf{\widehat{Z}}\in^{H\times W\times Q}$, where $Q$ is the number of quantized ab values.

To compare predicted $\mathbf{\widehat{Z}}$ against ground truth, we define function $\mathbf{Z}=\mathcal{H}_{gt}^{-1}(\mathbf{Y})$, which converts ground truth color $\mathbf{Y}$ to vector $\mathbf{Z}$, using a soft-encoding schemeEach ground truth value $\mathbf{Y}_{h,w}$ can be encoded as a 1-hot vector $\mathbf{Z}_{h,w}$ by searching for the nearest quantized $ab$ bin. However, we found that soft-encoding worked well for training, and allowed the network to quickly learn the relationship between elements in the output space . We find the 5-nearest neighbors to $\mathbf{Y}_{h,w}$ in the output space and weight them proportionally to their distance from the ground truth using a Gaussian kernel with $\sigma=5$.. We then use multinomial cross entropy loss $\text{L}_{cl}(\cdot,\cdot)$, defined as:

where $v(\cdot)$ is a weighting term that can be used to rebalance the loss based on color-class rarity, as defined in Section 2.2 below. Finally, we map probability distribution $\mathbf{\widehat{Z}}$ to color values $\mathbf{\widehat{Y}}$ with function $\mathbf{\widehat{Y}}=\mathcal{H}(\mathbf{\widehat{Z}})$, which will be further discussed in Section 2.3.

2 Class rebalancing

The distribution of ab values in natural images is strongly biased towards values with low $ab$ values, due to the appearance of backgrounds such as clouds, pavement, dirt, and walls. Figure 3(b) shows the empirical distribution of pixels in ab space, gathered from 1.3M training images in ImageNet . Observe that the number of pixels in natural images at desaturated values are orders of magnitude higher than for saturated values. Without accounting for this, the loss function is dominated by desaturated ab values. We account for the class-imbalance problem by reweighting the loss of each pixel at train time based on the pixel color rarity. This is asymptotically equivalent to the typical approach of resampling the training space . Each pixel is weighed by factor $\mathbf{w}\in\mathds{R}^{Q}$, based on its closest $ab$ bin.

To obtain smoothed empirical distribution $\mathbf{\widetilde{p}}\in\Delta^{Q}$, we estimate the empirical probability of colors in the quantized $ab$ space $\mathbf{p}\in\Delta^{Q}$ from the full ImageNet training set and smooth the distribution with a Gaussian kernel $\mathbf{G}_{\sigma}$. We then mix the distribution with a uniform distribution with weight $\lambda\in$, take the reciprocal, and normalize so the weighting factor is 1 on expectation. We found that values of $\lambda=\tfrac{1}{2}$ and $\sigma=5$ worked well. We compare results with and without class rebalancing in Section 1.

3 Class Probabilities to Point Estimates

Finally, we define $\mathcal{H}$, which maps the predicted distribution $\mathbf{\widehat{Z}}$ to point estimate $\mathbf{\widehat{Y}}$ in ab space. One choice is to take the mode of the predicted distribution for each pixel, as shown in the right-most column of Figure 4 for two example images. This provides a vibrant but sometimes spatially inconsistent result, e.g., the red splotches on the bus. On the other hand, taking the mean of the predicted distribution produces spatially consistent but desaturated results (left-most column of Figure 4), exhibiting an unnatural sepia tone. This is unsurprising, as taking the mean after performing classification suffers from some of the same issues as optimizing for a Euclidean loss in a regression framework. To try to get the best of both worlds, we interpolate by re-adjusting the temperature $T$ of the softmax distribution, and taking the mean of the result. We draw inspiration from the simulated annealing technique , and thus refer to the operation as taking the annealed-mean of the distribution:

Setting $T=1$ leaves the distribution unchanged, lowering the temperature $T$ produces a more strongly peaked distribution, and setting $T\rightarrow 0$ results in a 1-hot encoding at the distribution mode. We found that temperature $T=0.38$, shown in the middle column of Figure 4, captures the vibrancy of the mode while maintaining the spatial coherence of the mean.

Our final system $\mathcal{F}$ is the composition of CNN $\mathcal{G}$, which produces a predicted distribution over all pixels, and the annealed-mean operation $\mathcal{H}$, which produces a final prediction. The system is not quite end-to-end trainable, but note that the mapping $\mathcal{H}$ operates on each pixel independently, with a single parameter, and can be implemented as part of a feed-forward pass of the CNN.

Experiments

In Section 3.1, we assess the graphics aspect of our algorithm, evaluating the perceptual realism of our colorizations, along with other measures of accuracy. We compare our full algorithm to several variants, along with recent and concurrent work . In Section 3.2, we test colorization as a method for self-supervised representation learning. Finally, in Section 10.1, we show qualitative examples on legacy black and white images.

We train our network on the 1.3M images from the ImageNet training set , validate on the first 10k images in the ImageNet validation set, and test on a separate 10k images in the validation set, same as in . We show quantitative results in Table 1 on three metrics. A qualitative comparison for selected success and failure cases is shown in Figure 5. For a comparison on a full selection of random images, please see our project webpage.

To specifically test the effect of different loss functions, we train our CNN with various losses. We also compare to previous and concurrent methods , which both use CNNs trained on ImageNet, along with naive baselines:

Ours (full) Our full method, with classification loss, defined in Equation 2, and class rebalancing, as described in Section 2.2. The network was trained from scratch with k-means initialization , using the ADAM solver for approximately 450k iterations$\beta_{1}=.9$, $\beta_{2}=.99$, and weight decay = $10^{-3}$. Initial learning rate was $3\times 10^{-5}$ and dropped to $10^{-5}$ and $3\times 10^{-6}$ when loss plateaued, at 200k and 375k iterations, respectively. Other models trained from scratch followed similar training protocol..

Ours (class) Our network on classification loss but no class rebalancing ($\lambda=1$ in Equation 4).

Ours (L2) Our network trained from scratch, with L2 regression loss, described in Equation 1, following the same training protocol.

Ours (L2, ft) Our network trained with L2 regression loss, fine-tuned from our full classification with rebalancing network.

Larsson et al. A CNN method that also appears in these proceedings.

Dahl A previous model using a Laplacian pyramid on VGG features, trained with L2 regression loss.

Gray Colors every pixel gray, with $(a,b)=0$.

Random Copies the colors from a random image from the training set.

Evaluating the quality of synthesized images is well-known to be a difficult task, as simple quantitative metrics, like RMS error on pixel values, often fail to capture visual realism. To address the shortcomings of any individual evaluation, we test three that measure different senses of quality, shown in Table 1.

1. Perceptual realism (AMT): For many applications, such as those in graphics, the ultimate test of colorization is how compelling the colors look to a human observer. To test this, we ran a real vs. fake two-alternative forced choice experiment on Amazon Mechanical Turk (AMT). Participants in the experiment were shown a series of pairs of images. Each pair consisted of a color photo next to a re-colorized version, produced by either our algorithm or a baseline. Participants were asked to click on the photo they believed contained fake colors generated by a computer program. Individual images of resolution $256\times 256$ were shown for one second each, and after each pair, participants were given unlimited time to respond. Each experimental session consisted of 10 practice trials (excluded from subsequent analysis), followed by 40 test pairs. On the practice trials, participants were given feedback as to whether or not their answer was correct. No feedback was given during the 40 test pairs. Each session tested only a single algorithm at a time, and participants were only allowed to complete at most one session. A total of 40 participants evaluated each algorithm. To ensure that all algorithms were tested in equivalent conditions (i.e. time of day, demographics, etc.), all experiment sessions were posted simultaneously and distributed to Turkers in an i.i.d. fashion.

To check that participants were competent at this task, $10\%$ of the trials pitted the ground truth image against the Random baseline described above. Participants successfully identified these random colorizations as fake $87\%$ of the time, indicating that they understood the task and were paying attention.

Figure 6 gives a better sense of the participants’ competency at detecting subtle errors made by our algorithm. The far right column shows example pairs where participants identified the fake image successfully in $100\%$ of the trials. Each of these pairs was scored by at least 10 participants. Close inspection reveals that on these images, our colorizations tend to have giveaway artifacts, such as the yellow blotches on the two trucks, which ruin otherwise decent results.

Nonetheless, our full algorithm fooled participants on $32\%$ of trials, as shown in Table 1. This number is significantly higher than all compared algorithms ($p<0.05$ in each case) except for Larsson et al., against which the difference was not significant ($p=0.10$; all statistics estimated by bootstrap ). These results validate the effectiveness of using both a classification loss and class-rebalancing.

Note that if our algorithm exactly reproduced the ground truth colors, the forced choice would be between two identical images, and participants would be fooled $50\%$ of the time on expectation. Interestingly, we can identify cases where participants were fooled more often than $50\%$ of the time, indicating our results were deemed more realistic than the ground truth. Some examples are shown in the first three columns of Figure 6. In many case, the ground truth image is poorly white balanced or has unusual colors, whereas our system produces a more prototypical appearance.

2. Semantic interpretability (VGG classification): Does our method produce realistic enough colorizations to be interpretable to an off-the-shelf object classifier? We tested this by feeding our fake colorized images to a VGG network that was trained to predict ImageNet classes from real color photos. If the classifier performs well, that means the colorizations are accurate enough to be informative about object class. Using an off-the-shelf classifier to assess the realism of synthesized data has been previously suggested by .

The results are shown in the second column from the right of Table 1. Classifier performance drops from 68.3% to 52.7% after ablating colors from the input. After re-colorizing using our full method, the performance is improved to 56.0% (other variants of our method achieve slightly higher results). The Larsson et al. method achieves the highest performance on this metric, reaching 59.4%. For reference, a VGG classification network fine-tuned on grayscale inputs reaches a performance of 63.5%.

In addition to serving as a perceptual metric, this analysis demonstrates a practical use for our algorithm: without any additional training or fine-tuning, we can improve performance on grayscale image classification, simply by colorizing images with our algorithm and passing them to an off-the-shelf classifier.

3. Raw accuracy (AuC): As a low-level test, we compute the percentage of predicted pixel colors within a thresholded L2 distance of the ground truth in ab color space. We then sweep across thresholds from 0 to 150 to produce a cumulative mass function, as introduced in , integrate the area under the curve (AuC), and normalize. Note that this AuC metric measures raw prediction accuracy, whereas our method aims for plausibility.

Our network, trained on classification without rebalancing, outperforms our L2 variant (when trained from scratch). When the L2 net is instead fine-tuned from a color classification network, it matches the performance of the classification network. This indicates that the L2 metric can achieve accurate colorizations, but has difficulty in optimization from scratch. The Larsson et al. method achieves slightly higher accuracy. Note that this metric is dominated by desaturated pixels, due to the distribution of ab values in natural images (Figure 3(b)). As a result, even predicting gray for every pixel does quite well, and our full method with class rebalancing achieves approximately the same score.

Perceptually interesting regions of images, on the other hand, tend to have a distribution of ab values with higher values of saturation. As such, we compute a class-balanced variant of the AuC metric by re-weighting the pixels inversely by color class probability (Equation 4, setting $\lambda=0$). Under this metric, our full method outperforms all variants and compared algorithms, indicating that class-rebalancing in the training objective achieved its desired effect.

2 Cross-Channel Encoding as Self-Supervised Feature Learning

In addition to making progress on the graphics task of colorization, we evaluate how colorization can serve as a pretext task for representation learning. Our model is akin to an autoencoder, except that the input and output are different image channels, suggesting the term cross-channel encoder.

To evaluate the feature representation learned through this kind of cross-channel encoding, we run two sets of tests on our network. First, we test the task generalization capability of the features by fixing the learned representation and training linear classifiers to perform object classification on already seen data (Figure 7). Second, we fine-tune the network on the PASCAL dataset for the tasks of classification, detection, and segmentation. Here, in addition to testing on held-out tasks, this group of experiments tests the learned representation on dataset generalization. To fairly compare to previous feature learning algorithms, we retrain an AlexNet network on the colorization task, using our full method, for 450k iterations. We find that the resulting learned representation achieves higher performance on object classification and segmentation tasks relative to previous methods tested (Table 2).

ImageNet classification The network was pre-trained to colorize images from the ImageNet dataset, without semantic label information. We test how well the learned features represent the object-level semantics. To do this, we freeze the weights of the network, provide semantic labels, and train linear classifiers on each convolutional layer. The results are shown in Figure 7.

AlexNet directly trained on ImageNet classification achieves the highest performance, and serves as the ceiling for this test. Random initialization, with Gaussian weights or the k-means scheme implemented in , peak in the middle layers. Because our representation is learned on grayscale images, the network is handicapped at the input. To quantify the effect of this loss of information, we fine-tune AlexNet on grayscale image classification, and also run the random initialization schemes on grayscale images. Interestingly, for all three methods, there is a 6% performance gap between color and grayscale inputs, which remains approximately constant throughout the network.

We compare our model to other recent self-supervised methods pre-trained on ImageNet . To begin, our conv1 representation results in worse linear classification performance than competiting methods , but is comparable to other methods which have a grayscale input. However, this performance gap is immediately bridged at conv2, and our network achieves competitive performance to throughout the remainder of the network. This indicates that despite the input handicap, solving the colorization task encourages representations that linearly separate semantic classes in the trained data distribution.

PASCAL classification, detection, and segmentation We test our model on the commonly used self-supervision benchmarks on PASCAL classification, detection, and segmentation, introduced in . Results are shown in Table 2. Our network achieves strong performance across all three tasks, and state-of-the-art numbers in classification and segmentation. We use the method from , which rescales the layers so they “learn” at the same rate. We test our model in two modes: (1) keeping the input grayscale by disregarding color information (Ours (gray)) and (2) modifying conv1 to receive a full 3-channel $Lab$ input, initializing the weights on the $ab$ channels to be zero (Ours (color)).

We first test the network on PASCAL VOC 2007 classification, following the protocol in . The network is trained by freezing the representation up to certain points, and fine-tuning the remainder. Note that when conv1 is frozen, the network is effectively only able to interpret grayscale images. Across all three classification tests, we achieve state-of-the-art accuracy.

We also test detection on PASCAL VOC 2007, using Fast R-CNN , following the procedure in . Doersch et al. achieves 51.1%, while we reach 46.9% and 47.9% with grayscale and color inputs, respectively. Our method is well above the strong k-means baseline of 45.6%, but all self-supervised methods still fall short of pre-training with ImageNet semantic supervision, which reaches 56.8%.

Finally, we test semantic segmentation on PASCAL VOC 2012 , using the FCN architecture of , following the protocol in . Our colorization task shares similarities to the semantic segmentation task, as both are per-pixel classification problems. Our grayscale fine-tuned network achieves performance of 35.0%, approximately equal to Donahue et al. , and adding in color information increases performance to 35.6%, above other tested algorithms.

3 Legacy Black and White Photos

Since our model was trained using “fake” grayscale images generated by stripping $ab$ channels from color photos, we also ran our method on real legacy black and white photographs, as shown in Figure 9 (additional results can be viewed on our project webpage). One can see that our model is still able to produce good colorizations, even though the low-level image statistics of the legacy photographs are quite different from those of the modern-day photos on which it was trained.

Conclusion

While image colorization is a boutique computer graphics task, it is also an instance of a difficult pixel prediction problem in computer vision. Here we have shown that colorization with a deep CNN and a well-chosen objective function can come closer to producing results indistinguishable from real color photos. Our method not only provides a useful graphics output, but can also be viewed as a pretext task for representation learning. Although only trained to color, our network learns a representation that is surprisingly useful for object classification, detection, and segmentation, performing strongly compared to other self-supervised pre-training methods.

Acknowledgements

This research was supported, in part, by ONR MURI N000141010934, NSF SMA-1514512, an Intel research grant, and a hardware donation by NVIDIA Corp. We thank members of the Berkeley Vision Lab and Aditya Deshpande for helpful discussions, Philipp Krähenbühl and Jeff Donahue for help with self-supervision experiments, and Gustav Larsson for providing images for comparison to .

References

Appendix

The main paper is our ECCV 2016 camera ready submission. All networks were re-trained from scratch, and are referred to as the v2 model. Due to space constraints, we were unable to include many of the analyses presented in our original arXiv v1 paper. We include these analyses in this Appendix, which were generated from a previous v1 version of the model. All models are publicly available on our website.

Section 5 contains additional representation learning experiments. Section 6 investigates additional analysis on the VGG semantic interpretability test. In Section 7, we explore how low-level queues affect the output. Section 8 examines the multi-modality learned in the network. Section 9 defines the network architecture used. In Section 10, we compare our algorithm to previous approaches and , and show additional examples on legacy grayscale images.

Cross-Channel Encoding as Self-Supervised Feature Learning (continued)

In Section 3.2, we discussed using colorization as a pretext task for representation learning. In addition to learning linear classifiers on internal layers for ImageNet classifiers, we run the additional experiment of learning non-linear classifiers, as proposed in . Each internal layer is frozen, along with all preceding layers, and the layers on top are randomly reinitialized and trained for classification. Performance is summarized in Table 2. Of the unsupervised models, Noroozi et al. have the highest performance across all layers. The architectural modifications result in $5.6\times$ feature map size and $7.35\times$ model run-time, up to the pool5 layer, relative to an unmodified Alexnet. Of the remaining methods, Donahue et al. performs best at conv2 and Doersch et al. performs best at conv3 and conv4. Our method performs strongly throughout, and best across methods at the conv5 layer.

Semantic Interpretability of Colorizations

In Section 3.1, we investigated using the VGG classifier to evaluate the semantic interpretability of our colorization results. In Section 6.1, we show the categories which perform well, and the ones which perform poorly, using this metric. In Section 6.2, we show commonly confused categories after recolorization.

In Figure 10, we show a selection of classes that have the most improvement in VGG classification with respect to grayscale, along with the classes for which our colorizations hurt the most. Interestingly, many of the top classes actually have a color in their name, such as the green snake, orange, and goldfinch. The bottom classes show some common errors of our system, such as coloring clothing incorrectly and inconsistently and coloring an animal with a plausible but incorrect color. This analysis was performed using 48k images from the ImageNet validation set, and images in the top and bottom 10 classes are provided on the website.

Our process for sorting categories and images is described below. For each category, we compute the top-5 classification performance on grayscale and recolorized images, $\mathbf{a}_{gray},\mathbf{a}_{recolor}\in^{C}$, where $C=1000$ categories. We sort the categories by $\mathbf{a}_{recolor}-\mathbf{a}_{gray}$. The re-colored vs grayscale performance per category is shown in Figure 12(a), with top and bottom 50 categories highlighted. For the top example categories, the individual images are sorted by ascending rank of the correct classification of the recolorizeed image, with tiebreakers on descending rank of the correct classification of the grayscale image. For the bottom example categories, the images are sorted in reverse, in order to highlight the instances when recolorization results in an errant classification relative to the grayscale image.

2 Common Confusions

To further investigate the biases in our system, we look at the common classification confusions that often occur after image recolorization, but not with the original ground truth image. Examples for some top confusions are shown in Figure 11. An image of a “minibus” is often colored yellow, leading to a misclassification as “school bus”. Animal classes are sometimes colored differently than ground truth, leading to misclassification to related species. Note that the colorizations are often visually realistic, even though they lead to a misclassification.

To find common confusions, we compute the rate of top-5 confusion $\mathbf{C}_{orig},\mathbf{C}_{recolor}\in^{C\times C}$, with ground truth colors and after recolorization. A value of $\mathbf{C}_{c,d}=1$ means that every image in category $c$ was classified as category $d$ in the top-5. We find the class-confusion added after recolorization by computing $\mathbf{A}=\mathbf{C}_{recolor}-\mathbf{C}_{orig}$, and sort the off-diagonal entries. Figure 12(b) shows all $C\times(C-1)$ off-diagonal entries of $\mathbf{C}_{recolor}$ vs $\mathbf{C}_{orig}$, with the top 100 entries from $\mathbf{A}$ highlighted. For each category pair $(c,d)$, we extract the images that contained the confusion after recolorization, but not with the original colorization. We then sort the images in descending order of the classification score of the confused category.

Is the network exploiting low-level cues?

Unlike many computer vision tasks that can be roughly categorized as low, mid or high-level vision, color prediction requires understanding an image at both the pixel and the semantic-level. We have investigated how colorization generalizes to high-level semantic tasks in Section 3.2. Studies of natural image statistics have shown that the lightness value of a single pixel can highly constrain the likely color of that pixel: darker lightness values tend to be correlated with more saturated colors .

Could our network be exploiting a simple, low-level relationship like this, in order to predict color?E.g., previous work showed that CNNs can learn to use chromatic aberration cues to predict, given an image patch, its (x,y) location within an image . We tested this hypothesis with the simple demonstration in Figure 13. Given a grayscale Macbeth color chart as input, our network was unable to recover its colors. This is true, despite the fact that the lightness values vary considerably for the different color patches in this image. On the other hand, given two recognizable vegetables that are roughly isoluminant, the system is able to recover their color.

In Figure 13, we also demonstrate that the prediction is somewhat stable with respect to low-level lightness and contrast changes. Blurring, on the other hand, has a bigger effect on the predictions in this example, possibly because the operation removes the diagnostic texture pattern of the zucchini.

Does our model learn multimodal color distributions?

As discussed in Section 2.1, formulating color prediction as a multinomial classification problem allows the system to predict multimodal distributions, and can capture the inherent ambiguity in the color of natural objects. In Figure 14, we illustrate the probability outputs $\mathbf{\widehat{Z}}$ and demonstrate that the network does indeed learn multimodal distributions. The system output $\mathbf{\widehat{Y}}$ is shown in the top-left of Figure 14. Each block illustrates the probability map $\mathbf{\widehat{Z}}_{q}\in^{H,W}$ given $ab$ bin $q$ in the output space. For clarity, we show a subsampling of the $Q$ total output bins and coarsely quantize the probability values. In Figure 14(a), the system clearly predicts a different distribution for the background vegetation and the foreground bird. The background is predicted to be green, yellow, or brown, while the foreground bird is predicted to be red or blue. Figure 14(b) shows that oranges can be predicted to be different colors. Lastly, in Figure 14(c), the man’s sarong is predicted to be either red, pink, or purple, while his shirt is classified as turquoise, cyan or light orange. Note that despite the multi-modality of the prediction, taking the annealed-mean of the distribution produces a spatially consistent prediction.

Network architecture

Figure 2 showed a diagram of our network architecture. Table 3 in this document thoroughly lists the layers used in our architecture during training time. During testing, the temperature adjustment, softmax, mean, and bilinear upsampling are all implemented as subsequent layers in a feed-forward network. Note the column showing the effective dilation. The effective dilation is the spacing at which consecutive elements of the convolutional kernel are evaluated, relative to the input pixels, and is computed by the product of the accumulated stride and the layer dilation. Through each convolutional block from conv1 to conv5, the effective dilation of the convolutional kernel is increased. From conv6 to conv8, the effective dilation is decreased.

Colorization comparisons on held-out datasets

Though our model was trained on object-centric ImageNet dataset, we demonstrate that it nonetheless remains effective for photos from the scene-centric SUN dataset selected by Deshpande et al. . Deshpande et al. recently established a benchmark for colorization using a subset of the SUN dataset and reported top results using an algorithm based on LEARCH . Table 4 provides a quantitative comparison of our method to Deshpande et al.. For fair comparison, we use the same grayscale input as , which is $\frac{R+G+B}{3}$. Note that this input space is non-linearly related to the $L$ channel on which we trained. Despite differences in grayscale space and training dataset, our method outperforms Deshpande et al. in both the raw accuracy AuC CMF and perceptual realism AMT metrics. Figure 15 shows qualitative comparisons between our method and Deshpande et al., one from each of the six scene categories. A complete comparison on all 240 images are included in the supplementary material. Our results are able to fool participants in the real vs. fake task $17.2\%$ of the time, significantly higher than Deshpande et al. at $9.8\%$.

2 Comparison to Deep Colorization [1]

We provide qualitative comparisons to the 23 test images in on the website, which we obtained by manually cropping from the paper. Our results are about the same qualitative level as . Note that Deep Colorization has several advantages in this setting: (1) the test images are from the SUN dataset , which we did not train on and (2) the 23 images were hand-selected from 1344 by the authors, and is not necessarily representative of algorithm performance. We were unable to obtain the 1344 test set results through correspondence with the authors.

Additionally, we compare the methods on several important dimensions in Table 5: algorithm pipeline, learning, dataset, and run-time. Our method is faster, straightforward to train and understand, has fewer hand-tuned parameters and components, and has been demonstrated on a broader and more diverse set of test images than Deep Colorization .

3 Additional Examples on Legacy Grayscale Images

Here, we show additional qualitative examples of applying our model to legacy black and white photographs. Figures 17, 18, and 19 show examples including work of renowned photographers, such as Ansel Adams and Henri Cartier-Bresson, photographs of politicians and celebrities, and old family photos. One can see that our model is often able to produce good colorizations, even though the low-level image statistics of old legacy photographs are quite different from those of modern-day photos.