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Posit AI Weblog: Picture-to-image translation with pix2pix


What do we have to practice a neural community? A standard reply is: a mannequin, a price operate, and an optimization algorithm.
(I do know: I’m leaving out a very powerful factor right here – the information.)

As laptop applications work with numbers, the price operate needs to be fairly particular: We are able to’t simply say predict subsequent month’s demand for garden mowers please, and do your greatest, now we have to say one thing like this: Decrease the squared deviation of the estimate from the goal worth.

In some circumstances it could be simple to map a activity to a measure of error, in others, it could not. Take into account the duty of producing non-existing objects of a sure sort (like a face, a scene, or a video clip). How can we quantify success?
The trick with generative adversarial networks (GANs) is to let the community study the price operate.

As proven in Producing photos with Keras and TensorFlow keen execution, in a easy GAN the setup is that this: One agent, the generator, retains on producing pretend objects. The opposite, the discriminator, is tasked to inform aside the actual objects from the pretend ones. For the generator, loss is augmented when its fraud will get found, which means that the generator’s value operate is dependent upon what the discriminator does. For the discriminator, loss grows when it fails to appropriately inform aside generated objects from genuine ones.

In a GAN of the sort simply described, creation begins from white noise. Nonetheless in the actual world, what’s required could also be a type of transformation, not creation. Take, for instance, colorization of black-and-white photos, or conversion of aerials to maps. For functions like these, we situation on further enter: Therefore the title, conditional adversarial networks.

Put concretely, this implies the generator is handed not (or not solely) white noise, however information of a sure enter construction, similar to edges or shapes. It then has to generate realistic-looking photos of actual objects having these shapes.
The discriminator, too, could obtain the shapes or edges as enter, along with the pretend and actual objects it’s tasked to inform aside.

Listed here are a number of examples of conditioning, taken from the paper we’ll be implementing (see under):

Figure from Image-to-Image Translation with Conditional Adversarial Networks Isola et al. (2016)

On this publish, we port to R a Google Colaboratory Pocket book utilizing Keras with keen execution. We’re implementing the essential structure from pix2pix, as described by Isola et al. of their 2016 paper(Isola et al. 2016). It’s an attention-grabbing paper to learn because it validates the method on a bunch of various datasets, and shares outcomes of utilizing completely different loss households, too:

Figure from Image-to-Image Translation with Conditional Adversarial Networks Isola et al. (2016)

Stipulations

The code proven right here will work with the present CRAN variations of tensorflow, keras, and tfdatasets. Additionally, you’ll want to test that you just’re utilizing at the least model 1.9 of TensorFlow. If that isn’t the case, as of this writing, this

will get you model 1.10.

When loading libraries, please be sure to’re executing the primary 4 strains within the precise order proven. We want to verify we’re utilizing the TensorFlow implementation of Keras (tf.keras in Python land), and now we have to allow keen execution earlier than utilizing TensorFlow in any method.

No must copy-paste any code snippets – you’ll discover the entire code (so as obligatory for execution) right here: eager-pix2pix.R.

Dataset

For this publish, we’re working with one of many datasets used within the paper, a preprocessed model of the CMP Facade Dataset.

Photographs comprise the bottom fact – that we’d want for the generator to generate, and for the discriminator to appropriately detect as genuine – and the enter we’re conditioning on (a rough segmention into object lessons) subsequent to one another in the identical file.

Figure from https://people.eecs.berkeley.edu/~tinghuiz/projects/pix2pix/datasets/

Preprocessing

Clearly, our preprocessing should break up the enter photos into elements. That’s the very first thing that occurs within the operate under.

After that, motion is dependent upon whether or not we’re within the coaching or testing phases. If we’re coaching, we carry out random jittering, by way of upsizing the picture to 286x286 after which cropping to the unique dimension of 256x256. In about 50% of the circumstances, we additionally flipping the picture left-to-right.

In each circumstances, coaching and testing, we normalize the picture to the vary between -1 and 1.

Word using the tf$picture module for picture -related operations. That is required as the photographs shall be streamed by way of tfdatasets, which works on TensorFlow graphs.

img_width <- 256L
img_height <- 256L

load_image <- operate(image_file, is_train) {

  picture <- tf$read_file(image_file)
  picture <- tf$picture$decode_jpeg(picture)
  
  w <- as.integer(k_shape(picture)[2])
  w2 <- as.integer(w / 2L)
  real_image <- picture[ , 1L:w2, ]
  input_image <- picture[ , (w2 + 1L):w, ]
  
  input_image <- k_cast(input_image, tf$float32)
  real_image <- k_cast(real_image, tf$float32)

  if (is_train) {
    input_image <-
      tf$picture$resize_images(input_image,
                             c(286L, 286L),
                             align_corners = TRUE,
                             technique = 2)
    real_image <- tf$picture$resize_images(real_image,
                                         c(286L, 286L),
                                         align_corners = TRUE,
                                         technique = 2)
    
    stacked_image <-
      k_stack(record(input_image, real_image), axis = 1)
    cropped_image <-
      tf$random_crop(stacked_image, dimension = c(2L, img_height, img_width, 3L))
    c(input_image, real_image) %<-% 
      record(cropped_image[1, , , ], cropped_image[2, , , ])
    
    if (runif(1) > 0.5) {
      input_image <- tf$picture$flip_left_right(input_image)
      real_image <- tf$picture$flip_left_right(real_image)
    }
    
  } else {
    input_image <-
      tf$picture$resize_images(
        input_image,
        dimension = c(img_height, img_width),
        align_corners = TRUE,
        technique = 2
      )
    real_image <-
      tf$picture$resize_images(
        real_image,
        dimension = c(img_height, img_width),
        align_corners = TRUE,
        technique = 2
      )
  }
  
  input_image <- (input_image / 127.5) - 1
  real_image <- (real_image / 127.5) - 1
  
  record(input_image, real_image)
}

Streaming the information

The photographs shall be streamed by way of tfdatasets, utilizing a batch dimension of 1.
Word how the load_image operate we outlined above is wrapped in tf$py_func to allow accessing tensor values within the ordinary keen method (which by default, as of this writing, shouldn’t be doable with the TensorFlow datasets API).

# change to the place you unpacked the information
# there shall be practice, val and take a look at subdirectories under
data_dir <- "facades"

buffer_size <- 400
batch_size <- 1
batches_per_epoch <- buffer_size / batch_size

train_dataset <-
  tf$information$Dataset$list_files(file.path(data_dir, "practice/*.jpg")) %>%
  dataset_shuffle(buffer_size) %>%
  dataset_map(operate(picture) {
    tf$py_func(load_image, record(picture, TRUE), record(tf$float32, tf$float32))
  }) %>%
  dataset_batch(batch_size)

test_dataset <-
  tf$information$Dataset$list_files(file.path(data_dir, "take a look at/*.jpg")) %>%
  dataset_map(operate(picture) {
    tf$py_func(load_image, record(picture, TRUE), record(tf$float32, tf$float32))
  }) %>%
  dataset_batch(batch_size)

Defining the actors

Generator

First, right here’s the generator. Let’s begin with a birds-eye view.

The generator receives as enter a rough segmentation, of dimension 256×256, and will produce a pleasant colour picture of a facade.
It first successively downsamples the enter, as much as a minimal dimension of 1×1. Then after maximal condensation, it begins upsampling once more, till it has reached the required output decision of 256×256.

Throughout downsampling, as spatial decision decreases, the variety of filters will increase. Throughout upsampling, it goes the other method.

generator <- operate(title = "generator") {
  
  keras_model_custom(title = title, operate(self) {
    
    self$down1 <- downsample(64, 4, apply_batchnorm = FALSE)
    self$down2 <- downsample(128, 4)
    self$down3 <- downsample(256, 4)
    self$down4 <- downsample(512, 4)
    self$down5 <- downsample(512, 4)
    self$down6 <- downsample(512, 4)
    self$down7 <- downsample(512, 4)
    self$down8 <- downsample(512, 4)
    
    self$up1 <- upsample(512, 4, apply_dropout = TRUE)
    self$up2 <- upsample(512, 4, apply_dropout = TRUE)
    self$up3 <- upsample(512, 4, apply_dropout = TRUE)
    self$up4 <- upsample(512, 4)
    self$up5 <- upsample(256, 4)
    self$up6 <- upsample(128, 4)
    self$up7 <- upsample(64, 4)
    
    self$final <- layer_conv_2d_transpose(
      filters = 3,
      kernel_size = 4,
      strides = 2,
      padding = "similar",
      kernel_initializer = initializer_random_normal(0, 0.2),
      activation = "tanh"
    )
    
    operate(x, masks = NULL, coaching = TRUE) {           # x form == (bs, 256, 256, 3)
     
      x1 <- x %>% self$down1(coaching = coaching)         # (bs, 128, 128, 64)
      x2 <- self$down2(x1, coaching = coaching)           # (bs, 64, 64, 128)
      x3 <- self$down3(x2, coaching = coaching)           # (bs, 32, 32, 256)
      x4 <- self$down4(x3, coaching = coaching)           # (bs, 16, 16, 512)
      x5 <- self$down5(x4, coaching = coaching)           # (bs, 8, 8, 512)
      x6 <- self$down6(x5, coaching = coaching)           # (bs, 4, 4, 512)
      x7 <- self$down7(x6, coaching = coaching)           # (bs, 2, 2, 512)
      x8 <- self$down8(x7, coaching = coaching)           # (bs, 1, 1, 512)

      x9 <- self$up1(record(x8, x7), coaching = coaching)   # (bs, 2, 2, 1024)
      x10 <- self$up2(record(x9, x6), coaching = coaching)  # (bs, 4, 4, 1024)
      x11 <- self$up3(record(x10, x5), coaching = coaching) # (bs, 8, 8, 1024)
      x12 <- self$up4(record(x11, x4), coaching = coaching) # (bs, 16, 16, 1024)
      x13 <- self$up5(record(x12, x3), coaching = coaching) # (bs, 32, 32, 512)
      x14 <- self$up6(record(x13, x2), coaching = coaching) # (bs, 64, 64, 256)
      x15 <-self$up7(record(x14, x1), coaching = coaching)  # (bs, 128, 128, 128)
      x16 <- self$final(x15)                               # (bs, 256, 256, 3)
      x16
    }
  })
}

How can spatial info be preserved if we downsample all the way in which right down to a single pixel? The generator follows the final precept of a U-Internet (Ronneberger, Fischer, and Brox 2015), the place skip connections exist from layers earlier within the downsampling course of to layers in a while the way in which up.

Figure from (Ronneberger, Fischer, and Brox 2015)

Let’s take the road

x15 <-self$up7(record(x14, x1), coaching = coaching)

from the name technique.

Right here, the inputs to self$up are x14, which went via the entire down- and upsampling, and x1, the output from the very first downsampling step. The previous has decision 64×64, the latter, 128×128. How do they get mixed?

That’s taken care of by upsample, technically a customized mannequin of its personal.
As an apart, we comment how customized fashions allow you to pack your code into good, reusable modules.

upsample <- operate(filters,
                     dimension,
                     apply_dropout = FALSE,
                     title = "upsample") {
  
  keras_model_custom(title = NULL, operate(self) {
    
    self$apply_dropout <- apply_dropout
    self$up_conv <- layer_conv_2d_transpose(
      filters = filters,
      kernel_size = dimension,
      strides = 2,
      padding = "similar",
      kernel_initializer = initializer_random_normal(),
      use_bias = FALSE
    )
    self$batchnorm <- layer_batch_normalization()
    if (self$apply_dropout) {
      self$dropout <- layer_dropout(fee = 0.5)
    }
    
    operate(xs, masks = NULL, coaching = TRUE) {
      
      c(x1, x2) %<-% xs
      x <- self$up_conv(x1) %>% self$batchnorm(coaching = coaching)
      if (self$apply_dropout) {
        x %>% self$dropout(coaching = coaching)
      }
      x %>% layer_activation("relu")
      concat <- k_concatenate(record(x, x2))
      concat
    }
  })
}

x14 is upsampled to double its dimension, and x1 is appended as is.
The axis of concatenation right here is axis 4, the characteristic map / channels axis. x1 comes with 64 channels, x14 comes out of layer_conv_2d_transpose with 64 channels, too (as a result of self$up7 has been outlined that method). So we find yourself with a picture of decision 128×128 and 128 characteristic maps for the output of step x15.

Downsampling, too, is factored out to its personal mannequin. Right here too, the variety of filters is configurable.

downsample <- operate(filters,
                       dimension,
                       apply_batchnorm = TRUE,
                       title = "downsample") {
  
  keras_model_custom(title = title, operate(self) {
    
    self$apply_batchnorm <- apply_batchnorm
    self$conv1 <- layer_conv_2d(
      filters = filters,
      kernel_size = dimension,
      strides = 2,
      padding = 'similar',
      kernel_initializer = initializer_random_normal(0, 0.2),
      use_bias = FALSE
    )
    if (self$apply_batchnorm) {
      self$batchnorm <- layer_batch_normalization()
    }
    
    operate(x, masks = NULL, coaching = TRUE) {
      
      x <- self$conv1(x)
      if (self$apply_batchnorm) {
        x %>% self$batchnorm(coaching = coaching)
      }
      x %>% layer_activation_leaky_relu()
    }
  })
}

Now for the discriminator.

Discriminator

Once more, let’s begin with a birds-eye view.
The discriminator receives as enter each the coarse segmentation and the bottom fact. Each are concatenated and processed collectively. Identical to the generator, the discriminator is thus conditioned on the segmentation.

What does the discriminator return? The output of self$final has one channel, however a spatial decision of 30×30: We’re outputting a chance for every of 30×30 picture patches (which is why the authors are calling this a PatchGAN).

The discriminator thus engaged on small picture patches means it solely cares about native construction, and consequently, enforces correctness within the excessive frequencies solely. Correctness within the low frequencies is taken care of by an extra L1 element within the discriminator loss that operates over the entire picture (as we’ll see under).

discriminator <- operate(title = "discriminator") {
  
  keras_model_custom(title = title, operate(self) {
    
    self$down1 <- disc_downsample(64, 4, FALSE)
    self$down2 <- disc_downsample(128, 4)
    self$down3 <- disc_downsample(256, 4)
    self$zero_pad1 <- layer_zero_padding_2d()
    self$conv <- layer_conv_2d(
      filters = 512,
      kernel_size = 4,
      strides = 1,
      kernel_initializer = initializer_random_normal(),
      use_bias = FALSE
    )
    self$batchnorm <- layer_batch_normalization()
    self$zero_pad2 <- layer_zero_padding_2d()
    self$final <- layer_conv_2d(
      filters = 1,
      kernel_size = 4,
      strides = 1,
      kernel_initializer = initializer_random_normal()
    )
    
    operate(x, y, masks = NULL, coaching = TRUE) {
      
      x <- k_concatenate(record(x, y)) %>%            # (bs, 256, 256, channels*2)
        self$down1(coaching = coaching) %>%         # (bs, 128, 128, 64)
        self$down2(coaching = coaching) %>%         # (bs, 64, 64, 128)
        self$down3(coaching = coaching) %>%         # (bs, 32, 32, 256)
        self$zero_pad1() %>%                        # (bs, 34, 34, 256)
        self$conv() %>%                             # (bs, 31, 31, 512)
        self$batchnorm(coaching = coaching) %>%
        layer_activation_leaky_relu() %>%
        self$zero_pad2() %>%                        # (bs, 33, 33, 512)
        self$final()                                 # (bs, 30, 30, 1)
      x
    }
  })
}

And right here’s the factored-out downsampling performance, once more offering the means to configure the variety of filters.

disc_downsample <- operate(filters,
                            dimension,
                            apply_batchnorm = TRUE,
                            title = "disc_downsample") {
  
  keras_model_custom(title = title, operate(self) {
    
    self$apply_batchnorm <- apply_batchnorm
    self$conv1 <- layer_conv_2d(
      filters = filters,
      kernel_size = dimension,
      strides = 2,
      padding = 'similar',
      kernel_initializer = initializer_random_normal(0, 0.2),
      use_bias = FALSE
    )
    if (self$apply_batchnorm) {
      self$batchnorm <- layer_batch_normalization()
    }
    
    operate(x, masks = NULL, coaching = TRUE) {
      x <- self$conv1(x)
      if (self$apply_batchnorm) {
        x %>% self$batchnorm(coaching = coaching)
      }
      x %>% layer_activation_leaky_relu()
    }
  })
}

Losses and optimizer

As we mentioned within the introduction, the concept of a GAN is to have the community study the price operate.
Extra concretely, the factor it ought to study is the stability between two losses, the generator loss and the discriminator loss.
Every of them individually, after all, needs to be supplied with a loss operate, so there are nonetheless choices to be made.

For the generator, two issues issue into the loss: First, does the discriminator debunk my creations as pretend?
Second, how huge is absolutely the deviation of the generated picture from the goal?
The latter issue doesn’t must be current in a conditional GAN, however was included by the authors to additional encourage proximity to the goal, and empirically discovered to ship higher outcomes.

lambda <- 100 # worth chosen by the authors of the paper
generator_loss <- operate(disc_judgment, generated_output, goal) {
    gan_loss <- tf$losses$sigmoid_cross_entropy(
      tf$ones_like(disc_judgment),
      disc_judgment
    )
    l1_loss <- tf$reduce_mean(tf$abs(goal - generated_output))
    gan_loss + (lambda * l1_loss)
  }

The discriminator loss appears as in a typical (un-conditional) GAN. Its first element is set by how precisely it classifies actual photos as actual, whereas the second is dependent upon its competence in judging pretend photos as pretend.

discriminator_loss <- operate(real_output, generated_output) {
  real_loss <- tf$losses$sigmoid_cross_entropy(
    multi_class_labels = tf$ones_like(real_output),
    logits = real_output
  )
  generated_loss <- tf$losses$sigmoid_cross_entropy(
    multi_class_labels = tf$zeros_like(generated_output),
    logits = generated_output
  )
  real_loss + generated_loss
}

For optimization, we depend on Adam for each the generator and the discriminator.

discriminator_optimizer <- tf$practice$AdamOptimizer(2e-4, beta1 = 0.5)
generator_optimizer <- tf$practice$AdamOptimizer(2e-4, beta1 = 0.5)

The sport

We’re able to have the generator and the discriminator play the sport!
Beneath, we use defun to compile the respective R features into TensorFlow graphs, to hurry up computations.

generator <- generator()
discriminator <- discriminator()

generator$name = tf$contrib$keen$defun(generator$name)
discriminator$name = tf$contrib$keen$defun(discriminator$name)

We additionally create a tf$practice$Checkpoint object that may enable us to save lots of and restore coaching weights.

checkpoint_dir <- "./checkpoints_pix2pix"
checkpoint_prefix <- file.path(checkpoint_dir, "ckpt")
checkpoint <- tf$practice$Checkpoint(
    generator_optimizer = generator_optimizer,
    discriminator_optimizer = discriminator_optimizer,
    generator = generator,
    discriminator = discriminator
)

Coaching is a loop over epochs with an internal loop over batches yielded by the dataset.
As ordinary with keen execution, tf$GradientTape takes care of recording the ahead move and figuring out the gradients, whereas the optimizer – there are two of them on this setup – adjusts the networks’ weights.

Each tenth epoch, we save the weights, and inform the generator to have a go on the first instance of the take a look at set, so we are able to monitor community progress. See generate_images within the companion code for this performance.

practice <- operate(dataset, num_epochs) {
  
  for (epoch in 1:num_epochs) {
    total_loss_gen <- 0
    total_loss_disc <- 0
    iter <- make_iterator_one_shot(train_dataset)
    
    until_out_of_range({
      batch <- iterator_get_next(iter)
      input_image <- batch[[1]]
      goal <- batch[[2]]
      
      with(tf$GradientTape() %as% gen_tape, {
        with(tf$GradientTape() %as% disc_tape, {
          
          gen_output <- generator(input_image, coaching = TRUE)
          disc_real_output <-
            discriminator(input_image, goal, coaching = TRUE)
          disc_generated_output <-
            discriminator(input_image, gen_output, coaching = TRUE)
          gen_loss <-
            generator_loss(disc_generated_output, gen_output, goal)
          disc_loss <-
            discriminator_loss(disc_real_output, disc_generated_output)
          total_loss_gen <- total_loss_gen + gen_loss
          total_loss_disc <- total_loss_disc + disc_loss
        })
      })
      
      generator_gradients <- gen_tape$gradient(gen_loss,
                                               generator$variables)
      discriminator_gradients <- disc_tape$gradient(disc_loss,
                                                    discriminator$variables)
      
      generator_optimizer$apply_gradients(transpose(record(
        generator_gradients,
        generator$variables
      )))
      discriminator_optimizer$apply_gradients(transpose(
        record(discriminator_gradients,
             discriminator$variables)
      ))
      
    })
    
    cat("Epoch ", epoch, "n")
    cat("Generator loss: ",
        total_loss_gen$numpy() / batches_per_epoch,
        "n")
    cat("Discriminator loss: ",
        total_loss_disc$numpy() / batches_per_epoch,
        "nn")
    
    if (epoch %% 10 == 0) {
      test_iter <- make_iterator_one_shot(test_dataset)
      batch <- iterator_get_next(test_iter)
      enter <- batch[[1]]
      goal <- batch[[2]]
      generate_images(generator, enter, goal, paste0("epoch_", i))
    }
    
    if (epoch %% 10 == 0) {
      checkpoint$save(file_prefix = checkpoint_prefix)
    }
  }
}

if (!restore) {
  practice(train_dataset, 200)
} 

The outcomes

What has the community discovered?

Right here’s a fairly typical consequence from the take a look at set. It doesn’t look so dangerous.

Right here’s one other one. Curiously, the colours used within the pretend picture match the earlier one’s fairly properly, despite the fact that we used an extra L1 loss to penalize deviations from the unique.

This decide from the take a look at set once more exhibits comparable hues, and it would already convey an impression one will get when going via the entire take a look at set: The community has not simply discovered some stability between creatively turning a rough masks into an in depth picture on the one hand, and reproducing a concrete instance however. It additionally has internalized the principle architectural model current within the dataset.

For an excessive instance, take this. The masks leaves an unlimited lot of freedom, whereas the goal picture is a fairly untypical (maybe essentially the most untypical) decide from the take a look at set. The result is a construction that would symbolize a constructing, or a part of a constructing, of particular texture and colour shades.

Conclusion

After we say the community has internalized the dominant model of the coaching set, is that this a nasty factor? (We’re used to pondering when it comes to overfitting on the coaching set.)

With GANs although, one might say all of it is dependent upon the aim. If it doesn’t match our goal, one factor we might attempt is coaching on a number of datasets on the similar time.

Once more relying on what we need to obtain, one other weak point might be the dearth of stochasticity within the mannequin, as acknowledged by the authors of the paper themselves. This shall be arduous to keep away from when working with paired datasets as those utilized in pix2pix. An attention-grabbing different is CycleGAN(Zhu et al. 2017) that allows you to switch model between full datasets with out utilizing paired cases:

Figure from Zhu et al. (2017)

Lastly closing on a extra technical word, you will have observed the outstanding checkerboard results within the above pretend examples. This phenomenon (and methods to deal with it) is fantastically defined in a 2016 article on distill.pub (Odena, Dumoulin, and Olah 2016).
In our case, it is going to principally be as a consequence of using layer_conv_2d_transpose for upsampling.

As per the authors (Odena, Dumoulin, and Olah 2016), a greater different is upsizing adopted by padding and (customary) convolution.
Should you’re , it must be simple to change the instance code to make use of tf$picture$resize_images (utilizing ResizeMethod.NEAREST_NEIGHBOR as advisable by the authors), tf$pad and layer_conv2d.

Isola, Phillip, Jun-Yan Zhu, Tinghui Zhou, and Alexei A. Efros. 2016. “Picture-to-Picture Translation with Conditional Adversarial Networks.” CoRR abs/1611.07004. http://arxiv.org/abs/1611.07004.
Odena, Augustus, Vincent Dumoulin, and Chris Olah. 2016. “Deconvolution and Checkerboard Artifacts.” Distill. https://doi.org/10.23915/distill.00003.
Ronneberger, Olaf, Philipp Fischer, and Thomas Brox. 2015. “U-Internet: Convolutional Networks for Biomedical Picture Segmentation.” CoRR abs/1505.04597. http://arxiv.org/abs/1505.04597.
Zhu, Jun-Yan, Taesung Park, Phillip Isola, and Alexei A. Efros. 2017. “Unpaired Picture-to-Picture Translation Utilizing Cycle-Constant Adversarial Networks.” CoRR abs/1703.10593. http://arxiv.org/abs/1703.10593.

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