於本文首先回顧風格轉換的發展、2016年Gatys等人所提出 的風格轉換演算法及其使用的卷積神經網路架構。我們應用一種 稱為理查森外插法的技術，已提高Gatys風格轉換演算法的計算 效率及有效性，大多數基於CNN的風格轉換模型旨在提高計算效 率。而本文從泰勒展開式衍生的理查森外插法用於估計損失函數 對於輸入至CNN圖像的梯度，藉助理查森外插梯度，我們的風格 轉換方法可以節省通過CNN前向傳遞來計算損失函數的時間，以 及反向傳遞計算損失函數相對於輸入梯度之時間。由數值模擬顯 示，透過我們提出的算法於加快轉換效率中顯示驚艷的結果。

In this thesis, we first review the development of style transfer, including the style-transfer algorithm proposed of Gatys et al and the used convolutional neural network(CNN) architecture. This work applies an extrapolation technique, termed as Richardson extrapolation(RE), to improve the Gatys style transfer algorithm both in computational efficiency and effectiveness. Most of the style transfer model based on CNNs is aimed at enhancing computational efficiency. Richardson Extrapolation derived from Taylor expansion is employed to estimate the gradient of the loss function with respect to an input image to a CNN. With Richardson gradients extrapolation, our style transfer approach could save time for computing the total loss function through CNN forward pass and the gradient of the total loss function with respect to input through CNN backward pass. Numerical simulations show encouraging results of speeding up the transfer efficiency by our algorithm.

Acknowledgments i
摘要 iii
Abstract v
Contents vii
List of Figure ix
List of Table xi
1. Introduction 1
2. Style Transfer using Convolutional Neural Networks 3
2.1 Model Architecture and Feature Extraction 3
2.2 Derivation of Loss function and Gradients 4
3. Richardson Extrapolation 7
3.1 Richardson Extrapolation (RE) 7
3.2 Applied Richardson Extrapolation to Style Transfer 8
3.3 Style Transfer with backward pass and Richardson Extrapolation 10
4. Experiences 15
4.1 Fixed style 16
4.2 Style Revolution 16
5. Conclusions
References

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