Neural Style Transfer .

Introduction

This project reproduces the results from the famous paper A Neural Algorithm of Artistic Style (Gatys et al.). By defining a content loss and a style loss, we can iteratively update a noise image to match the content of one photo and the artistic style of another.

Loss Functions

The magic happens in how we define "style". The style representation is computed using the Gram Matrix of the feature maps from intermediate layers of a VGG-19 network.

The Gram Matrix

$$G_{ij}^l = \sum_k F_{ik}^l F_{jk}^l$$

Where $F$ represents the feature map.

def gram_matrix(input):
    a, b, c, d = input.size() 
    # a=batch size(=1)
    # b=number of feature maps
    # (c,d)=dimensions of a f. map (N=c*d)

    features = input.view(a * b, c * d)
    G = torch.mm(features, features.t())

    return G.div(a * b * c * d)

Implementation Details

• Framework: PyTorch
• Model: Pre-trained VGG-19 (features only)
• Optimizer: L-BFGS (converges faster than Adam for this specific task)

Gallery

I experimented with various style images, including Starry Night (Van Gogh) and The Great Wave off Kanagawa. The results show how the network captures textures—swirls, brush strokes, and geometric patterns—and applies them to photographs.