Orthonormal Convolutions for the Rotation Based Iterative Gaussianization

• URL: http://arxiv.org/abs/2206.03860v1
• Date: Wed, 8 Jun 2022 12:56:34 GMT
• Title: Orthonormal Convolutions for the Rotation Based Iterative Gaussianization
• Authors: Valero Laparra, Alexander Hepburn, J. Emmanuel Johnson, Jes\'us Malo
• Abstract summary: This paper elaborates an extension of rotation-based iterative Gaussianization, RBIG, which makes image Gaussianization possible. In images its application has been restricted to small image patches or isolated pixels, because rotation in RBIG is based on principal or independent component analysis. We present the emphConvolutional RBIG: an extension that alleviates this issue by imposing that the rotation in RBIG is a convolution.
• Score: 64.44661342486434
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper we elaborate an extension of rotation-based iterative Gaussianization, RBIG, which makes image Gaussianization possible. Although RBIG has been successfully applied to many tasks, it is limited to medium dimensionality data (on the order of a thousand dimensions). In images its application has been restricted to small image patches or isolated pixels, because rotation in RBIG is based on principal or independent component analysis and these transformations are difficult to learn and scale. Here we present the \emph{Convolutional RBIG}: an extension that alleviates this issue by imposing that the rotation in RBIG is a convolution. We propose to learn convolutional rotations (i.e. orthonormal convolutions) by optimising for the reconstruction loss between the input and an approximate inverse of the transformation using the transposed convolution operation. Additionally, we suggest different regularizers in learning these orthonormal convolutions. For example, imposing sparsity in the activations leads to a transformation that extends convolutional independent component analysis to multilayer architectures. We also highlight how statistical properties of the data, such as multivariate mutual information, can be obtained from \emph{Convolutional RBIG}. We illustrate the behavior of the transform with a simple example of texture synthesis, and analyze its properties by visualizing the stimuli that maximize the response in certain feature and layer.

Related papers

• RLE: A Unified Perspective of Data Augmentation for Cross-Spectral Re-identification [59.5042031913258]
  Non-linear modality discrepancy mainly comes from diverse linear transformations acting on the surface of different materials. We propose a Random Linear Enhancement (RLE) strategy which includes Moderate Random Linear Enhancement (MRLE) and Radical Random Linear Enhancement (RRLE) The experimental results not only demonstrate the superiority and effectiveness of RLE but also confirm its great potential as a general-purpose data augmentation for cross-spectral re-identification.
  arXiv  Detail & Related papers  (2024-11-02T12:13:37Z)
• PixelGaussian: Generalizable 3D Gaussian Reconstruction from Arbitrary Views [116.10577967146762]
  PixelGaussian is an efficient framework for learning generalizable 3D Gaussian reconstruction from arbitrary views. Our method achieves state-of-the-art performance with good generalization to various numbers of views.
  arXiv  Detail & Related papers  (2024-10-24T17:59:58Z)
• MGAug: Multimodal Geometric Augmentation in Latent Spaces of Image Deformations [2.711740183729759]
  We propose a novel model that generates augmenting transformations in a multimodal latent space of geometric deformations. Experimental results show that our proposed approach outperforms all baselines by significantly improved prediction accuracy.
  arXiv  Detail & Related papers  (2023-12-20T21:30:55Z)
• Dual-Octave Convolution for Accelerated Parallel MR Image Reconstruction [75.35200719645283]
  We propose the Dual-Octave Convolution (Dual-OctConv), which is capable of learning multi-scale spatial-frequency features from both real and imaginary components. By reformulating the complex operations using octave convolutions, our model shows a strong ability to capture richer representations of MR images.
  arXiv  Detail & Related papers  (2021-04-12T10:51:05Z)
• The Geometry of Deep Generative Image Models and its Applications [0.0]
  Generative adversarial networks (GANs) have emerged as a powerful unsupervised method to model the statistical patterns of real-world data sets. These networks are trained to map random inputs in their latent space to new samples representative of the learned data. The structure of the latent space is hard to intuit due to its high dimensionality and the non-linearity of the generator.
  arXiv  Detail & Related papers  (2021-01-15T07:57:33Z)
• Learnable Gabor modulated complex-valued networks for orientation robustness [4.024850952459758]
  Learnable Gabor Convolutional Networks (LGCNs) are parameter-efficient and offer increased model complexity. We investigate the robustness of complex valued convolutional weights with learned Gabor filters to enable orientation transformations.
  arXiv  Detail & Related papers  (2020-11-23T21:22:27Z)
• Rotated Ring, Radial and Depth Wise Separable Radial Convolutions [13.481518628796692]
  In this work, we address trainable rotation invariant convolutions and the construction of nets. On the one hand, we show that our approach is rotationally invariant for different models and on different public data sets. The rotationally adaptive convolution models presented are more computationally intensive than normal convolution models.
  arXiv  Detail & Related papers  (2020-10-02T09:01:51Z)
• Deeply Learned Spectral Total Variation Decomposition [8.679020335206753]
  We present a neural network approximation of a non-linear spectral decomposition. We report up to four orders of magnitude ($times 10,000$) speedup in processing of mega-pixel size images.
  arXiv  Detail & Related papers  (2020-06-17T17:10:43Z)
• Region adaptive graph fourier transform for 3d point clouds [51.193111325231165]
  We introduce the Region Adaptive Graph Fourier Transform (RA-GFT) for compression of 3D point cloud attributes. The RA-GFT achieves better complexity-performance trade-offs than previous approaches.
  arXiv  Detail & Related papers  (2020-03-04T02:47:44Z)
• Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data [52.78581260260455]
  We propose a general method to construct a convolutional layer that is equivariant to transformations from any specified Lie group. We apply the same model architecture to images, ball-and-stick molecular data, and Hamiltonian dynamical systems.
  arXiv  Detail & Related papers  (2020-02-25T17:40:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.