Exploring Invariance in Images through One-way Wave Equations
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914973851058176 |
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| author | Chen, Yinpeng Chen, Dongdong Dai, Xiyang Liu, Mengchen Feng, Yinan Lin, Youzuo Yuan, Lu Liu, Zicheng |
| author_facet | Chen, Yinpeng Chen, Dongdong Dai, Xiyang Liu, Mengchen Feng, Yinan Lin, Youzuo Yuan, Lu Liu, Zicheng |
| contents | In this paper, we empirically reveal an invariance over images-images share a set of one-way wave equations with latent speeds. Each image is uniquely associated with a solution to these wave equations, allowing for its reconstruction with high fidelity from an initial condition. We demonstrate it using an intuitive encoder-decoder framework where each image is encoded into its corresponding initial condition (a single vector). Subsequently, the initial condition undergoes a specialized decoder, transforming the one-way wave equations into a first-order norm + linear autoregressive process. This process propagates the initial condition along the x and y directions, generating a high-resolution feature map (up to the image resolution), followed by a few convolutional layers to reconstruct image pixels. The revealed invariance, rooted in the shared wave equations, offers a fresh perspective for comprehending images, establishing a promising avenue for further exploration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_12976 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Exploring Invariance in Images through One-way Wave Equations Chen, Yinpeng Chen, Dongdong Dai, Xiyang Liu, Mengchen Feng, Yinan Lin, Youzuo Yuan, Lu Liu, Zicheng Computer Vision and Pattern Recognition Machine Learning In this paper, we empirically reveal an invariance over images-images share a set of one-way wave equations with latent speeds. Each image is uniquely associated with a solution to these wave equations, allowing for its reconstruction with high fidelity from an initial condition. We demonstrate it using an intuitive encoder-decoder framework where each image is encoded into its corresponding initial condition (a single vector). Subsequently, the initial condition undergoes a specialized decoder, transforming the one-way wave equations into a first-order norm + linear autoregressive process. This process propagates the initial condition along the x and y directions, generating a high-resolution feature map (up to the image resolution), followed by a few convolutional layers to reconstruct image pixels. The revealed invariance, rooted in the shared wave equations, offers a fresh perspective for comprehending images, establishing a promising avenue for further exploration. |
| title | Exploring Invariance in Images through One-way Wave Equations |
| topic | Computer Vision and Pattern Recognition Machine Learning |
| url | https://arxiv.org/abs/2310.12976 |