In the paper A Neural Algorithm of Artistic Style, Leon A. Gatys et all. describe a process of extracting the content and style vectors from an image separately. They use this technique to generate new images that have the content from one image and style from another, it's called neural style transfer here's what it looks like:

enter image description here

Are there any existing implementations for version 11 of Mathematica?


  • 1
    $\begingroup$ oops, what is your trial...? $\endgroup$
    – mma
    Feb 1, 2017 at 15:33
  • 1
    $\begingroup$ Do you think someone will help you implement that algorithm? $\endgroup$
    – mma
    Feb 1, 2017 at 15:38

2 Answers 2


Example from NetTrain documentation (Applications - Computer Vision - Style Transfer):

enter image description here

vggNet = NetModel["VGG-16 Trained on ImageNet Competition Data"];

Take a subnet that will be used as a feature extractor for the style and content images:

featureNet = Take[vggNet, {1, "relu4_1"}]

enter image description here

There are three loss functions used. The first loss ensures that the "content" is similar in the synthesized image and the content image:

contentLoss = NetGraph[{MeanSquaredLossLayer[]}, {1 -> NetPort["LossContent"]}]

enter image description here

The second loss ensures that the "style" is similar in the synthesized image and the style image. Style similarity is defined as the mean-squared difference between the Gram matrices of the input and target:

gramMatrix = 
  NetGraph[{FlattenLayer[-1], TransposeLayer[1 -> 2], 
    DotLayer[]}, {1 -> 3, 1 -> 2 -> 3}];

styleLoss = NetGraph[{gramMatrix, gramMatrix, MeanSquaredLossLayer[]},
  {NetPort["Input"] -> 1, NetPort["Target"] -> 2, {1, 2} -> 3, 
   3 -> NetPort["LossStyle"]}]

enter image description here

The third loss ensures that the magnitude of intensity changes across adjacent pixels in the synthesized image is small. This helps the synthesized image look more natural:

l2Loss = NetGraph[{ThreadingLayer[(#1 - #2)^2 &], 
    SummationLayer[]}, {{NetPort["Input"], NetPort["Target"]} -> 
     1 -> 2}];

tvLoss = NetGraph[<|
   "dx1" -> 
    PaddingLayer[{{0, 0}, {1, 0}, {0, 0}}, "Padding" -> "Fixed" ],
   "dx2" -> 
    PaddingLayer[{{0, 0}, {0, 1}, {0, 0}}, "Padding" -> "Fixed"],
   "dy1" -> 
    PaddingLayer[{{0, 0}, {0, 0}, {1, 0}}, "Padding" -> "Fixed" ],
   "dy2" -> 
    PaddingLayer[{{0, 0}, {0, 0}, {0, 1}}, "Padding" -> "Fixed"],
   "lossx" -> l2Loss, "lossy" -> l2Loss, "tot" -> TotalLayer[]|>, {
   {"dx1", "dx2"} -> "lossx", {"dy1", "dy2"} -> "lossy",
   {"lossx", "lossy"} -> "tot" -> NetPort["LossTV"]}]

enter image description here

Define a function that creates the final training net for any content and style image. This function also creates a random initial image:

createTransferNet[net_, content_Image, styleFeatSize_] := Module[
  {dims = Prepend[3]@Reverse@ImageDimensions[content]},
    "Image" -> 
     ConstantArrayLayer["Array" -> RandomReal[{-0.1, 0.1}, dims]],
    "imageFeat" -> NetReplacePart[net, "Input" -> dims],
    "content" -> contentLoss,
    "style" -> styleLoss,
    "tv" -> tvLoss|>,
   {"Image" -> "imageFeat",
    {"imageFeat", NetPort["ContentFeature"]} -> "content",
    {"imageFeat", NetPort["StyleFeature"]} -> "style",
    "Image" -> "tv"},
   "StyleFeature" -> styleFeatSize

Define a NetDecoder for visualizing the predicted image:

meanIm = NetExtract[featureNet, "Input"][["MeanImage"]]

{0.48502, 0.457957, 0.407604}

decoder = NetDecoder[{"Image", "MeanImage" -> meanIm}]

enter image description here

The training data consists of features extracted from the content and style images. Define a feature extraction function:

extractFeatures[img_] := 
    "Input" -> 
     NetEncoder[{"Image", ImageDimensions[img], 
       "MeanImage" -> meanIm}]][img];

Create a training set consisting of a single example of a content and style feature:

trainingdata = <|
   "ContentFeature" -> {extractFeatures[contentImg]}, 
   "StyleFeature" -> {extractFeatures[styleImg]}

Create the training net whose input dimensions correspond to the content and style image dimensions:

net = createTransferNet[featureNet, contentImg, 

When training, the three losses are weighted differently to set the relative importance of the content and style. These values might need to be changed with different content and style images. Create a loss specification that defines the final loss as a combination of the three losses:

perPixel = 1/(3*Apply[Times, ImageDimensions[contentImg]]);
lossSpec = {"LossContent" -> Scaled[6.*10^-5], 
   "LossStyle" -> Scaled[0.5*10^-14], 
   "LossTV" -> Scaled[20.*perPixel]};

Optimize the image using NetTrain. LearningRateMultipliers are used to freeze all parameters in the net except for the ConstantArrayLayer. The training is best done on a GPU, as it will take up to an hour to get good results with CPU training.

trainedNet = NetTrain[net,
  trainingdata, lossSpec,
  LearningRateMultipliers -> {"Image" -> 1, _ -> None},
  TrainingProgressReporting -> 
   Function[decoder[#Weights[{"Image", "Array"}]]],
  MaxTrainingRounds -> 300, BatchSize -> 1,
  Method -> {"ADAM", "InitialLearningRate" -> 0.05},
  TargetDevice -> "GPU"

enter image description here

decoder[NetExtract[trainedNet, {"Image", "Array"}]]

enter image description here


Yes, Mathematica 11.2 has implemented this with the new function ImageRestyle.

Here is an example from Wolfram Blog:

An example from Wolfram's Blog

Another example:

Another example input Another example output

You can refer to these for more details:


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.