. The progress in saliency detection has been beneficial to a wide range of vision applications, including image retrieval, visual tracking 45], content-aware video compression 
, and weakly supervised learning[58, 59]. Although numerous models have been presented [31, 5, 70, 37, 21, 17] and significant improvement has been made, it still remains an open problem to accurately detect complete salient objects in static images, especially in complicated scenarios.
usually design hand-crafted low-level features and heuristic priors, which are difficult to represent semantic objects and scenes. Recent advances on saliency detection mainly benefit fromconvolutional neural networks (CNNs) [41, 34, 70, 57, 67, 27, 28, 72]
. On the one hand, CNNs naturally learn multi-scale and multi-level feature representations in each layer due to the increasingly larger receptive fields and downsampled (strided) scales. On the other hand, salient object detection requires multi-scale learning because of the various object/scene scales in intra- and inter-images. Therefore, current state-of-the-art saliency detectors[5, 64, 57, 67, 37, 56, 68, 55, 18] mainly aim at designing complex network architectures to leverage multi-scale CNN features, e.g., the semantic meaningful information in the top sides and the complementary spatial details in the bottom sides.
Owing to the superiority of U-Net  (or FCN ) and HED  in multi-scale learning, many state-of-the-art saliency detectors add deep supervision onto U-Net networks [70, 57, 37, 21, 68, 34, 17, 33, 22] (Figure 1(d)). We notice that these networks first predict multi-scale saliency maps using side-outputs. The generated multi-scale side-output predictions are then linearly aggregated, e.g., via a pixel-wise convolution (i.e., convolution), to obtain the final saliency prediction which thus can combine the advantages of all side-output predictions. However, we theoretically and experimentally demonstrate that the linear aggregation of side-output predictions is suboptimal, and it makes limited use of the complementary multi-scale information implicated in side-output features. We provide detailed proofs in Section 3.
Based on this observation, we propose a new solution to this problem, namely Deeply-supervised Nonlinear Aggregation (DNA). Specifically, instead of linearly aggregating side-output predictions, we concatenate the side-output features and apply nonlinear transformations to predict salient objects, as illustrated in Figure 1(e). In this way, the concatenated features can make the most of the multi-scale side-output features. The experiments demonstrate that DNA can successfully break through the bottleneck of current linear aggregation. Specifically, we apply DNA into a simply redesigned U-Net without bells and whistles. The proposed network performs favorably against all previous state-of-the-art salient object detectors with less parameters and faster speed. Our contributions are twofold:
We theoretically and experimentally analyze the natural limitation of traditional linear side-output aggregation which can only make limited use of multi-scale side-output information.
We propose Deeply-supervised Nonlinear Aggregation (DNA) for side-output features, whose effectiveness has been proved by introducing it into a simple network with less parameters and faster speed.
2 Related Work
Salient object detection is a very active research field due to its wide range of applications and challenging scenarios. Early heuristic saliency detection13, 51, 60]. Some heuristic saliency priors are utilized to ensure the accuracy, such as color contrast [1, 9], center prior [25, 24] and background prior [63, 73]
. With vast successes achieved by deep CNNs in computer vision, CNN-based methods have been introduced to improve saliency detection[65, 66, 49, 26, 32]. Region-based saliency detection [71, 52, 29, 27, 6] appeared in the early era of deep learning based saliency. These approaches view each image patch as a basic processing unit to perform saliency detection. More recently, CNN-based image-to-image saliency detection has dominated this field. We continue our discussion by briefly categorizing multi-scale deep learning into four classes: hyper feature learning, U-Net style, HED style, and U-Net + HED style.
Hyper feature learning: Hyper feature learning [15, 20] is the most intuitive way to learn multi-scale information, as illustrated in Figure 1(a). Examples of this structure for saliency include [30, 64, 7, 55, 35, 48, 36]
. These models concatenate/sum multi-scale deep features from multiple layers of backbone nets[30, 64] or branches of the multi-stream nets [7, 55, 35]. The fused hyper features, called hypercolumn, are then used for final saliency predictions.
U-Net style: It is widely accepted that the top layers of deep neural networks contain high-level semantic information, while the bottom layers learn low-level fine details. Therefore, a reasonable revision of hyper feature learning is to progressively fuse deep features from upper layers to lower layers [40, 46], as shown in Figure 1(b). Many saliency detectors are of this type [54, 69, 41, 19, 56, 67, 31, 3]. Note that hyper feature learning and U-Net do not apply deep supervision, so they do not have side-outputs.
HED style: HED-like networks [61, 39, 38] were first presented for edge detection. Afterwards, similar ideas have been also introduced for saliency detection [5, 18]. HED-like networks add deep supervision at the intermediate sides to obtain side-output predictions, and the final result is a linear combination of all side-output predictions (shown in Figure 1(c)). Unlike multi-scale feature fusion, HED performs multi-scale prediction fusion.
U-Net + HED style: These methods combine the advantages of both U-Net and HED. We outline this architectures in Figure 1(d). Specifically, deep supervision is imposed at each of the convolution stage of U-Net decoder. Many recent saliency models fall into this category [70, 57, 37, 21, 68, 34, 17, 33, 22]. They differ from each other by applying different fusion strategies. One notable similarity of these models is that the final prediction is produced by a linear aggregation of side-output predictions. Hence the multi-scale learning is achieved in two aspects: i) the U-Net aggregates multi-level convolutional features from top layers to bottom layers in an encoder-decoder form; ii) the multi-scale side-output predictions are further linearly aggregated for final prediction. Current research in this field mainly focuses on the first aspect, and state-of-the-art models have designed very complex feature fusion strategies for this [37, 68].
A full literature review of salient object detection is beyond the scope of this paper. Please refer to [2, 4, 10, 14] for more comprehensive surveys. We find that the upper bound of traditional linear side-output prediction aggregation is limited to the side-output predictions. Hence we propose DNA to aggregate side-output features in the nonlinear way, so that the aggregated hybrid features can make good use of the complementary multi-scale deep features.
3 Revisiting Linear Side-output Aggregation
Deep supervision and corresponding linear side-output prediction aggregation have been demonstrated to be effective in many vision tasks [61, 38, 37, 68]. This section analyzes the natural limitation of the linear side-output aggregation from both theoretical and experimental perspectives. To the best of our knowledge, this is a novel contribution.
Suppose a deeply-supervised network has side-output prediction maps , all of which are supervised by ground-truth maps (Figure 1(c)(d)). Without loss of generality, we assume the linear side-output aggregation is a pixel-wise convolution, i.e., convolution. Hence, current linear side-output aggregation can be written as
where weights of pixel-wise convolution can be learned. Note that we have here. Otherwise, would have negative effect toshould be applied to . The aggregated probability map becomes
Similarly, we can compute side-output probability maps .
If , the mean absolute error (MAE) of fused output is limited by side-output predictions.
If , it is natural to show
because as discussed above. Since the sigmoid function is monotonically increasing, we have that
If a pixel is positive, and , so that . If the pixel is negative, and , so that . Note that usually only has ( in VGG16  and ResNet ) dimensions, so it is also difficult to make aforementioned left equality hold. Hence traditional linear aggregation is limited in terms of MAE metric. However, what we expect is to break through the limitation by making full use of multi-scale information. ∎
If , we set , so we have . The computation of becomes
in which is a monotonically increasing function in terms of . ∎
The monotonically increasing mapping of cannot change the ROC curve and AUC metric111AUC is the area under the ROC Curve..
Suppose the predicted scores of positive samples obey the distribution of , while the predicted scores of negative samples obey the distribution of . We may assume and are continuous functions. is a variant of sigmoid function, so we have and is a monotonically increasing function. Let and be two transformed distributions. It is easy to show
and thus we can obtain and .
Let be a threshold, true positive rate (TPR) and false positive rate (FPR) can be computed as
as shown in Figure 2. Hence we can denote the ROC curve as . It is easy to show that as goes from to continuously, will change from to continuously and monotonically. It is also obvious to see that and are symmetric about the point . Suppose the area under the curve is , and the area under the curve is . By symmetry, we have .
With the above conclusions, we can compute as
Therefore, is independent of the specific form of the function , and is independent of , too. Moreover, as ranges in , thus ranges in , we have
which is also independent of the form of . When and are discrete, the set is discrete but still independent of . Therefore, we can conclude that cannot change the ROC curve and AUC metric. ∎
Similar to the proof for Theorem 1, we can easily demonstrate that the first step in Lemma 1, i.e., linear aggregation with , has limited MAE results. From Theorem 2, we know the second step in Lemma 1, i.e., a monotonically increasing mapping, cannot change the ROC curve and AUC value. Therefore, we can conclude that traditional linear aggregation with has limited improvement. Combined with Theorem 1, we can conclude that linear aggregation of side-outputs only has limited improvement.
|Datasets||Metrics||HED ||DSS ||DNA|
Besides the theoretical proofs, we also perform experiments to compare linear aggregation versus nonlinear aggregation for salient object detection. To this end, we use the proposed nonlinear side-output feature aggregation (in Section 4.2) for nonlinear regression to evaluate two well-known models: HED  and DSS , and the proposed DNA model. The results are summarized in Table 1
. We can see significant improvement from linear regression to nonlinear regression. Based on this observation, this paper aims at designinga simple network with nonlinear side-output aggregation for effective salient object detection.
In this section, we will elaborate our proposed framework for salient object detection. We first introduce our base network in Section 4.1. Then, we present the deeply-supervised nonlinear aggregation in Section 4.2. An overall network architecture is illustrated in Figure 3.
4.1 Base Network
as our backbone net, whose final fully connected layers are removed to serve for image-to-image translation. Salient object detection usually requires global information to judge which objects are salient, so enlarging the receptive field of the network would be helpful. To this end, we keep the final pooling layer as in  and replace the last two fully connected layers with convolution layers, one of which has the kernel size of with channels and another of which has the kernel size of with channels. Here, we use the convolution layer to reduce the feature channels, because large kernel sizes (e.g., ) lead to much more parameters.
There are five pooling layers in the backbone net. They divide the convolution layers into six convolution blocks, which are denoted as from bottom to top, respectively. We consider as the top valve that controls the overall contextual information that flows in the network. The resolution of the feature maps in each convolution block is half of the preceding one. Following [18, 61], the side-output of each convolution block is connected from the last layer of this block.
Encoder-Decoder Network. Based on the backbone net, we build an encoder-decoder network that can be seen in Figure 3. Concretely, we connect a convolution layer to each of the convolution blocks and to prepare for a proper number of channels. Then, we upsample the obtained feature maps from by two. The upsampled feature maps and resulting feature maps from are concatenated. To fuse the concatenated feature maps, two sequential convolution layers are used to generate the decoder side . The decoder sides can be obtained in the similar manner. In this way, the proposed encoder-decoder lets top contextual information flow into the lower layers. Here, both two sequential convolution layers () at the decoder side are with kernel size of and output channels of . When , equals to ; When , equals to . The values for are 64, 128, 128, 128 and 128, respectively. We will discuss the parameter settings in detail in the experiment part.
4.2 Deeply-Supervised Nonlinear Aggregation
Instead of linearly aggregating side-output predictions at multiple sides as in previous literature [70, 57, 37, 21, 68, 34, 17], we propose to aggregate the side-output features in a nonlinear way. The proposed DNA module is displayed in the dotted box of Figure 3. Specifically, we adopt a convolution for each to prepare for proper channels. Then, the feature maps are upsampled into the same size of the original image to generate side-output features. The side-output features can predict saliency maps using a simple convolution. In the training phase, deep supervision is added for these predicted maps.
We concatenate all side-output features to construct hybrid features that contain rich multi-scale and multi-level information. One of the key ideas in our nonlinear aggregation is that we use asymmetric convolution that decomposes a standard two-dimensional convolution into two one-dimensional convolutions. That is to say, a convolution is decomposed into two sequential convolutions with kernel sizes of and . Here, the reasons why we use asymmetric convolution are twofold. On one hand, in the experiments, we find large kernel size in the DNA module can improve performance, and we believe it is because hybrid feature maps have large resolution, i.e., the same resolution as the original image. On the other hand, convolutions with large kernel sizes are very time-consuming for large feature maps. We use two groups of asymmetric convolutions, each of which consists of a and a convolution. The asymmetric convolutions have FLOPs (multiply-adds) of standard two-dimensional convolutions. At last, we connect a convolution after the asymmetric convolutions to predict the final output saliency maps.
In the training, we adopt class-balanced cross-entropy loss function to supervise side-output predictions and the final fused prediction. Since each one-dimensional convolution is followed by nonlinear activation (e.g.
, ReLU), the aggregation of concatenated hybrid features is nonlinear. The traditional linear side-output prediction aggregation can only linearly combine multi-scale predictions, while the proposed nonlinear side-output feature aggregation can make use of the complementary multi-scale features for final prediction and thus is more effective. With the simple encoder-decoder described in Section4.1, DNA performs favorably against previous methods. Note that previous methods [70, 57, 37, 21] usually present various network architectures, modules and operations to improve performance, but in this paper, the proposed DNA only applies a simply-modified U-Net as base network.
5.1 Experimental Setup
We implement the proposed network using the well-known Caffe framework. The convolution layers contained in the original VGG16 
are initialized using the publicly available pretrained ImageNet model
. The weights of other layers are initialized from the zero-mean Gaussian distribution with standard deviation 0.01. Biases are initialized to 0. The upsampling operations are implemented by deconvolution layers with bilinear interpolation kernels which are frozen in the training process. Since the deconvolution layers do not need training, we exclude them when computing the number of parameters. The network is optimized using SGD with learning rate policy ofpoly, in which the current learning rate equals the base one multiplying . The hyper parameters and are set to 0.9 and 20000, respectively, so that the training takes 20000 iterations in total. The initial learning rate is set to 1e-7. The momentum and weight decay are set to 0.9 and 0.0005, respectively. All the experiments in this paper are performed on a TITAN Xp GPU.
Datasets. We extensively evaluate our method on six popular datasets, including DUTS , ECSSD , SOD , HKU-IS , THUR15K  and DUT-O (or DUT-OMRON) . These six datasets consist of 15572, 1000, 300, 4447, 6232 and 5168 natural complex images with corresponding pixel-wise ground truth labeling. Among them, the DUTS dataset  is a very recent dataset consisting of 10553 training images and 5019 test images in very complex scenarios. For fair comparison, we follow recent studies [56, 37, 55, 64] to use DUTS training set for training and test on the DUTS test set and other datasets.
Evaluation Criteria. We utilize three evaluation metrics to evaluate our method as well as other state-of-the-art salient object detectors, including max F-measure score, mean absolute error (MAE), and weighted -measure score . We follow [41, 18, 68, 69, 37, 31, 5, 37] to use the default settings for these metrics.
|VGG16  backbone|
|ResNet-50  backbone|
|VGG16  backbone|
|ResNet-50  backbone|
|Datasets||Metrics||U-Net||ED w/ K3||ED||ED w/ lin||DNA|
|No.||Side 1||Side 2||Side 3||Side 4||Side 5||Side 6|
|#1||, 64)||, 128)||, 128)||, 128)||, 128)||(192, 128)|
|#2||, 64)||, 128)||, 128)||, 128)||, 128)||(192, 128)|
|#3||, 64)||, 128)||, 128)||, 256)||, 256)||(256, 256)|
|#4||, 64)||, 128)||, 256)||, 256)||, 512)||(256, 256)|
5.2 Performance Comparison
We compare our proposed salient object detector with 16 recent state-of-the-art saliency models, including DRFI , MDF , LEGS , DCL , DHS , ELD , RFCN , NLDF , DSS , SRM , Amulet , UCF , BRN , PiCA , C2S  and RAS . Among them, DRFI  is the state-of-the-art non-deep-learning based method, and the other 15 models are all based on deep learning. We do not report MDF  results on the HKU-IS  dataset because MDF uses a part of HKU-IS for training. Due to the same reason, we do not report DHS  results on the DUT-O  dataset. For fair comparison, all these models are tested using their publicly available code and pretrained models released by the authors with default settings. We also report the results of the ResNet-50  version of our proposed DNA.
Table 3 summarizes the numeric comparison in terms of and MAE on six datasets. DNA can significantly outperform other competitors in most cases, which demonstrates its effectiveness. With VGG16  backbone, the values of DNA are 2.8%, 1.2%, 1.4%, 1.4%, 0.6% and 1.0% higher than the second best method on the DUTS, ECSSD, HKU-IS, DUT-O, SOD and THUR15K datasets, respectively. On the SOD dataset in terms of MAE metric, DNA performs slightly worse than the best result. PiCA  seems to achieves the second place overall. With the ResNet-50 backbone, DNA also performs better than previous competitors. DNA has less parameters, i.e., about 20M parameters for VGG16 backbone and 29M parameter for ResNet-50 backbone. DNA also runs faster than other methods, achieving 25fps for VGG16 backbone and 12.8fps for ResNet-50 backbone.
In Table 2, we evaluate DNA using the -measure. The VGG16 version of DNA achieves 4.5%, 3.3%, 2.7%, 3.4%, 3.4% and 2.1% higher -measure than other methods on DUTS-TE, ECSSD, HKU-IS, DUT-O, SOD and THUR15K datasets, respectively. For ResNet-50 version, DNA achieves 5.6%, 1.4%, 2.2%, 2.6%, 1.7% and 1.8% better -measure than other competitors. We provide a qualitative comparison in Figure 4. For objects with various shapes and scales, DNA segments the entire objects with fine details (1-2 rows). DNA is also robust with complicated background (3-5 rows), multiple objects (6-7 rows) and confusing stuff (8 row).
5.3 Ablation Studies
Nonlinear aggregation linear aggregation. To demonstrate the effectiveness of nonlinear aggregation, we replace the DNA module in our network with the traditional linear side-output prediction aggregation  to obtain a deeply-supervised encoder-decoder, i.e., ED w/ lin. The results are shown in Table 5. We can clearly see that nonlinear aggregation performs significantly better than linear aggregation, in terms of both and MAE.
The proposed encoder-decoder standard U-Net. If removing the DNA module and deep supervision, the proposed encoder-decoder is a simply modified version of U-Net . First, we change the kernel size of all convolutions at top sides, i.e., , and , into . As displayed in Table 5, the resulting model, ED w/ K3, perform worse than the standard U-Net . This could be because the proposed encoder-decoder has less feature channels and thus less parameters (U-Net has 31.06M parameters). Nest, we use the default kernel size of for top sides. The resulting model, ED, performs better than U-Net. This demonstrates large kernel size at the top sides is important for better performance.
Encoder-decoder with or without deep supervision. In Table 5, we can also find deep supervision can consistently improve the encoder-decoder networks.
Parameter settings. To evaluate the effect of different parameter settings, we try various parameter settings in Table 6. The results are summarized in Table 4. From the first and second experiment, we can see that large kernel sizes at top sides lead to better results, but the improvement is not as significant as in Table 5 where deep supervision is not used. From the third and fourth experiments, we find that introducing more parameters by increasing the convolution channels can generate slightly better results. Considering the trade-off between performance, number of parameters and speed, we choose the second setting as our default parameters.
The asymmetric convolutions in DNA module. In Table 7, we evaluate various convolution kernel sizes for the DNA model. Large convolution kernel sizes, e.g., , can achieve better performance. However, convolution is very time-consuming as shown in Table 7, because the feature maps in DNA is with the same resolution as original images. Hence, we use asymmetric convolutions to achieve both large kernel size and fast speed.
Previous deeply-supervised saliency detection networks use linear side-output prediction aggregation. We theoretically and experimentally demonstrate that linear side-output aggregation is suboptimal and worse than nonlinear aggregation. Based on this observation, we propose the DNA module that aggregates multi-level side-output features in a nonlinear way. With a simply modified U-Net, DNA can reach new state-of-the-art under various metrics when compared with 16 recent saliency models. The proposed network also has less parameters and faster running speed, which demonstrate the effectiveness of DNA. In the future, we plan to apply DNA to further improve salient object detection and exploit it in other computer vision tasks that need multi-scale and multi-level information.
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