Structured Prediction using cGANs with Fusion Discriminator

We propose a novel method for incorporating conditional information into a generative adversarial network ( GAN ) for structured prediction tasks . This method is based on fusing features from the generated and conditional information in feature space and allows the discriminator to better capture higher-order statistics from the data . This method also increases the strength of the signals passed through the network where the real or generated data and the conditional data agree . The proposed method is conceptually simpler than joint convolutional neural network - conditional Markov random field ( CNN-CRF ) models and enforces higher-order consistency without being limited to a very specific class of high-order potentials . Experimental results demonstrate that this method leads to improvement on a variety of different structured prediction tasks including image synthesis , semantic segmentation , and depth estimation . 1 INTRODUCTION . Convolutional neural networks ( CNNs ) have demonstrated groundbreaking results on a variety of different learning tasks . However , on tasks where high dimensional structure in the data needs to be preserved , per-pixel regression losses typically result in unstructured outputs since they do not take into consideration non-local dependencies in the data . Structured prediction frameworks such as graphical models and joint CNN-graphical model-based architectures e.g . CNN-CRFs have been used for imposing spatial contiguity using non-local information ( Lin et al. , 2016 ; Chen et al. , 2018a ; Schwing & Urtasun , 2015 ; Mahmood & Durr , 2018 ) . The motivation to use CNN-CRF models stems from their ability to capture some structured information from second order statistics using the pairwise part . However , statistical interactions beyond the second-order are tedious to incorporate and render the models complicated ( Arnab et al. , 2016 ; Kohli et al. , 2009 ) . Other approaches have used task-specific perceptual losses to solve this problem ( Johnson et al. , 2016 ) . Generative models provide another way to represent the structure and spacial contiguity in large high-dimensional datasets with complex dependencies . Implicit generative models specify a stochastic procedure to produce outputs from a probability distribution . Such models are appealing because they do not demand parametrization of the probability distribution they are trying to model . Recently , there has been great interest in CNN-based implicit generative models using autoregressive ( Chen et al. , 2018b ) and adversarial training frameworks ( Luc et al. , 2016 ) . Generative adversarial networks ( GANs ) ( Goodfellow et al. , 2014 ) can be seen as a two player minimax game where the first player , the generator , is tasked with transforming a random input to a specific distribution such that the second player , the discriminator , can not distinguish between the true and synthesized distributions . The most distinct feature of adversarial networks is the discriminator that assesses the discrepancy between the current and target distributions . The discriminator acts as a progressively precise critic of an increasingly accurate generator . Despite their structured prediction capabilities , such a training paradigm is often unstable and can suffer from mode collapse . However , recent work on spectral normalization ( SN ) and gradient penalty has significantly increased training stability ( Miyato et al. , 2018 ; Gulrajani et al. , 2017 ) . Conditional GANs ( cGANs ) ( Mirza & Osindero , 2014 ) incorporate conditional image information in the discriminator and have been widely used for class conditioned image generation ( Miyato et al. , 2018 ; Miyato & Koyama , 2018 ) . To that effect , unlike in standard GANs , a discriminator for cGANs discriminates between the generated distribution and the target distribution on pairs of samples y and conditional information x . For class conditioning , several unique strategies have been presented to incorporate class information in the discriminator ( Reed et al. , 2016 ; Miyato & Koyama , 2018 ; Odena et al. , 2016 ) . However , a cGAN can also be conditioned by structured data such as an image . Such conditioning is much more useful for structured prediction problems . Since the discriminator in image conditioned-GANs has access to large portions of the image the adversarial loss can be interpreted as a learned loss that incorporates higher order statistics , essentially eliminating the need to manually design higher order loss functions . Consequently , this variation of cGANs has extensively been used for image-to-image translation tasks ( Isola et al. , 2017 ; Zhu et al. , 2017 ) . However , the best way of incorporating image conditional information into a GAN is not always clear and methods of feeding generated and conditional images to the discriminator tend to use a naive concatenation approach . In this work we address this gap by proposing a discriminator architecture specifically designed for image conditioning . Such a discriminator can contribute to the promise of generalization GANs bring to structured prediction problems whereby a singular and simplistic setup can be used for capturing higher order non-local structural information from higher dimensional data without complicated modeling of energy functions . Contributions . We propose an approach to incorporating conditional information into a cGAN using a fusion architecture ( Fig . 1b ) . In particular , we make the following key contributions : 1 . We propose a novel discriminator architecture optimized for incorporating conditional information in cGANs for structured prediction tasks . The method is designed to incorporate conditional information in feature space and thereby allows the discriminator to enforce higher-order consistency in the model . At the same time , this method is conceptually simpler than alternative structured prediction methods such as CNN-CRFs where higher-order potentials have to be manually incorporated in the loss function . 2 . We demonstrate the effectiveness of this method on a variety of structured prediction tasks including semantic segmentation , depth estimation , and generating real images from semantic masks . Our empirical study demonstrates that using a fusion discriminator is more effective in preserving high-order statistics and structural information in the data . 2 RELATED WORK . 2.1 CNN-CRF MODELS . Models for structured prediction have been extensively studied in computer vision . In the past these models often entailed the construction of hand-engineered features . In 2015 , Long et al . ( 2015 ) demonstrated that a fully convolutional approach to semantic segmentation could yield state-ofthe-art results at that time with no need for hand-engineering features . Chen et al . ( 2014 ) showed that post-processing the results of a CNN with a conditional Markov random field led to significant improvements . Subsequent work by many authors have refined this approach by incorporating the CRF as a layer within a deep network and thereby enabling the parameters of both models to be learnt simultaneously ( Knöbelreiter et al. , 2017 ) . Many researchers have used this approach for other structured prediction problems , including image-to-image translation and depth estimation ( Liu et al. , 2015 ; Mahmood & Durr , 2018 ; Mahmood et al. , 2018 ) . In most cases CNN-CRF models only incorporate unary and pairwise potentials . Recent work by Arnab et al . ( 2016 ) has investigated incorporating higher-order potentials into CNN-based models for semantic segmentation , and has found that while it is possible to learn the parameters of these potentials , they can be tedious to incorporate and render the model quite complex . There is a need for developing methods that can incorporate higher-order statistical information with out manual modeling of higher order potentials . 2.2 GENERATIVE ADVERSARIAL NETWORKS . Adversarial Training . Generative adversarial networks were introduced in Goodfellow et al . ( 2014 ) . A GAN consists of a pair of models ( G , D ) , where G attempts to model the distribution of the source domain and D attempts to evaluate the divergence between the generative distribution q and the true distribution p. GANs are trained by training the discriminator and the generator in turn , iteratively refining both the quality of the generated data and the discriminator ’ s ability to distinguish between p and q . The result is that D and G compete to reach a Nash equilibrium that can be expressed by the training procedure . While GAN training is often unstable and prone to issues such as mode collapse , recent developments such as spectral normalization and gradient penalty have increased GAN training stability ( Miyato et al. , 2018 ; Gulrajani et al. , 2017 ) . Furthermore , GANs have the advantage of being able to access the joint configuration of many variables , thus enabling a GAN to enforce higher-order consistency that is difficult to enforce via other methods ( Luc et al. , 2016 ; Isola et al. , 2017 ) . Conditional GANs . A conditional GAN ( cGAN ) is a GAN designed to incorporate conditional information ( Mirza & Osindero , 2014 ) . cGANs have shown promise for several tasks such as class conditional image synthesis and image-to-image translation ( Mirza & Osindero , 2014 ; Isola et al. , 2017 ) . There are several advantages to using the cGAN model for structured prediction , including the simplicity of the framework . Image conditioned cGANs can be seen as a structured prediction problem tasked with learning a new representation given an input image while making use of non-local dependencies . However , the method by which the conditional information should be incorporated into the model is often unmotivated . Usually , the conditional data is concatenated to some layers in the discriminator ( often the input layers ) . A notable exception to this methodology is the projection cGAN , where for data is either known or assumed to follow certain simple distributions and a hard mathematical rule for incorporating conditional data can be derived from the underlying probabilistic graphical model ( Miyato & Koyama , 2018 ) . As mentioned in Miyato & Koyama ( 2018 ) , the method is more likely to produce good results if the data follows one of the prescribed distributions . For structured prediction tasks where the GAN framework has to be conditioned by an image , this is often not the case . In the following section we introduce the fusion discriminator and explain the motivation behind it . 3 PROPOSED METHOD : CGANS WITH FUSION DISCRIMINATOR . As mentioned , the most significant part of cGANs for structured prediction is the discriminator . The discriminator has continuous access to pairs of the generated data or real data y and the conditional information ( i.e . the image ) x . The cGAN discriminator can then be defined as , DcGAN ( x , y , θ ) : = A ( f ( x , y , θ ) ) , whereA is the activation function , and f is a function of x and y and θ represents the parameters of f . Let p and q designate the true and the generated distributions . The adversarial loss for the discriminator can then be defined as L ( D ) = −Eq ( y ) [ Eq ( x|y ) log ( D ( x , y , θ ) ] − Ep ( y ) [ Ep ( x|y ) [ log ( 1−D ( x , G ( x ) , θ ) ] . ( 1 ) Here , A represents the sigmoid function , D represents the conditional discriminator , and G represents the generator . By design , this frameworks allows the discriminator to significantly effect the generator ( Goodfellow et al. , 2014 ) . The most common approach currently in use to incorporate conditional image information into a GAN is to concatenate the conditional image information to the input of the discriminator at some layer , often the first ( Isola et al. , 2017 ) . Other approaches for conditional information fusion are limited to class conditional fusion where conditional information is often a one-hot vector rather than higher dimensional structured data . Since the discriminator classifies pairs of input and output images , concatenating high-dimensional data may not exploit some inherent dependencies in the structure of the data . Fusing the input and output information in an intuitive way such as to preserve the dependencies is instrumental in designing an adversarial framework with high structural capacity . We propose the use of a fusion discriminator architecture with two branches . The branches of this discriminator are convolutional neural networks , say φ ( x ) and ψ ( y ) , that extract features from both the conditional data and the generated or real data respectively . The features extracted from the conditional data are then fused with the features from the real or generated data at various stages ( Fig . 2 ) . The proposed discriminator architecture is similar to the encoder-part of the FuseNet architecture , which has been used to incorporate depth information from RGB-D images for semantic segmentation ( Hazirbas et al. , 2017 ) . In Figure 2 , we illustrate a four layer and a VGG16-style fusion discriminator , in which both branches are similar in depth and structure to the VGG16 model ( Simonyan & Zisserman , 2014 ) . The key ingredient of the fusion discriminator architecture is the fusion block , which combines the feature maps of x and y . The fusion layer ( red , Fig . 2 ) is implemented as element-wise summation and is always inserted after a convolution → spectral normalization→ ReLU instance . By making use of this fusion layer the discontinuities in the features maps of x and y are added into the y branch in order to enhance the overall feature maps . This preserves representation from both x and y . For structured prediction tasks x and y often have features that complement each other ; for instance , in tasks like depth estimation , semantic segmentation , and image synthesis x and y all have complimentary features .

Summary: This paper proposes a new method to input data to a conditional discriminator network. The standard setup would simply concatenate the "condition" image with the "output" image (i.e., the real image, or the generator's output corresponding to the condition). The setup here is to feed these two images to two separate encoders, and gradually fuse the features produced by the two. The experiments show that this delivers superior performance to concatenation, on three image-to-image translation tasks.