We propose a novel 3D morphable model for complete human heads based on hybrid neural fields. At the core of our model lies a neural parametric representation which disentangles identity and expressions in disjoint latent spaces. To this end, we capture a person's identity in a canonical space as a signed distance field (SDF), and model facial expressions with a neural deformation field. In addition, our representation achieves high-fidelity local detail by introducing an ensemble of local fields centered around facial anchor points. To facilitate generalization, we train our model on a newly-captured dataset of over 2200 head scans from 124 different identities using a custom high-end 3D scanning setup. Our dataset significantly exceeds comparable existing datasets, both with respect to quality and completeness of geometry, averaging around 3.5M mesh faces per scan. Finally, we demonstrate that our approach outperforms state-of-the-art methods by a significant margin in terms of fitting error and reconstruction quality.

生成的对抗网络（GANS）是在图像生成中最先进的驱动力。尽管他们能够合成高分辨率的照片真实图像，但在不同粒度的按需调节产生内容仍然是一个挑战。这一挑战通常是通过利用兴趣属性的大规模数据集，这是一个并不总是可行的选项的艰巨任务。因此，将控制进入无监督的生成模型的生成过程至关重要。在这项工作中，我们通过利用以无监督的时尚训练良好的GAN来专注于可控制的图像。为此，我们发现发电机的中间层的表示空间形成多个集群，该集群将数据分离为根据语义​​有意义的属性（例如，头发颜色和姿势）。通过在群集分配上调节，所提出的方法能够控制生成图像的语义类。我们的方法使通过隐式最大似然估计（IMLE）从每个集群中采样。我们使用不同的预先培训的生成模型展示我们对面孔（Celeba-HQ和FFHQ），动物（Imagenet）和物体（LSUN）的效果。结果突出了我们在面孔上像性，姿势和发型等属性的条件图像生成的能力，以及不同对象类别的各种功能。

本文解决了在预训练的生成对抗网络（GANS）的潜在空间中找到可解释方向的问题，以便于可控的图像合成。这种可解释的方向对应于可以影响合成图像的样式和几何体的变换。然而，利用线性技术来查找这些变换的现有方法通常无法提供直观的方式来分离这两个变化源。为了解决这个问题，我们建议a）对中间表示的张量进行多线性分解，b）使用基于张量的回归来利用该分解对潜在空间的映射方向。我们的方案允许与张量的各个模式相对应的线性编辑，并且非线性的编辑模型它们之间的乘法相互作用。我们通过实验显示我们可以利用前者与基于几何的转换更好的单独的风格，以及与现有作品相比，后者产生一组可能的变换。与目前的最先进，我们展示了我们的方法的效果和定性。

深度神经网络一直是分类任务成功的推动力，例如对象和音频识别。许多最近提出的架构似乎已经取得了令人印象深刻的结果和概括，其中大多数似乎是断开连接的。在这项工作中，我们在统一框架下对深层分类器进行了研究。特别是，我们以输入的不同程度多项式的形式表达最新的结构（例如残留和非本地网络）。我们的框架提供了有关每个模型的电感偏差的见解，并可以在其多项式性质上进行自然扩展。根据标准图像和音频分类基准评估所提出模型的功效。提出的模型的表达性既是在增加模型性能和模型压缩方面都突出的。最后，在存在有限的数据和长尾数据分布的情况下，此分类法所允许的扩展显示。我们希望这种分类法可以在现有特定领域的架构之间提供联系。源代码可在\ url {https://github.com/grigorisg9gr/polynomials-for-aigmenting-nns}中获得。

Mapping the seafloor with underwater imaging cameras is of significant importance for various applications including marine engineering, geology, geomorphology, archaeology and biology. For shallow waters, among the underwater imaging challenges, caustics i.e., the complex physical phenomena resulting from the projection of light rays being refracted by the wavy surface, is likely the most crucial one. Caustics is the main factor during underwater imaging campaigns that massively degrade image quality and affect severely any 2D mosaicking or 3D reconstruction of the seabed. In this work, we propose a novel method for correcting the radiometric effects of caustics on shallow underwater imagery. Contrary to the state-of-the-art, the developed method can handle seabed and riverbed of any anaglyph, correcting the images using real pixel information, thus, improving image matching and 3D reconstruction processes. In particular, the developed method employs deep learning architectures in order to classify image pixels to "non-caustics" and "caustics". Then, exploits the 3D geometry of the scene to achieve a pixel-wise correction, by transferring appropriate color values between the overlapping underwater images. Moreover, to fill the current gap, we have collected, annotated and structured a real-world caustic dataset, namely R-CAUSTIC, which is openly available. Overall, based on the experimental results and validation the developed methodology is quite promising in both detecting caustics and reconstructing their intensity.

Lipschitz regularized f-divergences are constructed by imposing a bound on the Lipschitz constant of the discriminator in the variational representation. They interpolate between the Wasserstein metric and f-divergences and provide a flexible family of loss functions for non-absolutely continuous (e.g. empirical) distributions, possibly with heavy tails. We construct Lipschitz regularized gradient flows on the space of probability measures based on these divergences. Examples of such gradient flows are Lipschitz regularized Fokker-Planck and porous medium partial differential equations (PDEs) for the Kullback-Leibler and alpha-divergences, respectively. The regularization corresponds to imposing a Courant-Friedrichs-Lewy numerical stability condition on the PDEs. For empirical measures, the Lipschitz regularization on gradient flows induces a numerically stable transporter/discriminator particle algorithm, where the generative particles are transported along the gradient of the discriminator. The gradient structure leads to a regularized Fisher information (particle kinetic energy) used to track the convergence of the algorithm. The Lipschitz regularized discriminator can be implemented via neural network spectral normalization and the particle algorithm generates approximate samples from possibly high-dimensional distributions known only from data. Notably, our particle algorithm can generate synthetic data even in small sample size regimes. A new data processing inequality for the regularized divergence allows us to combine our particle algorithm with representation learning, e.g. autoencoder architectures. The resulting algorithm yields markedly improved generative properties in terms of efficiency and quality of the synthetic samples. From a statistical mechanics perspective the encoding can be interpreted dynamically as learning a better mobility for the generative particles.

生成对抗网络（GAN）是基于生成器和歧视器之间的两种玩家游戏的一类分配学习方法，通常可以根据未知与生成的生成的差异表示的变异表示形式来表达为Minmax问题。分布。我们通过开发针对差异的新变分表示，将结构传播的gans作为学习分布的数据效率框架。我们的理论表明，我们可以利用与与基础结构相关的Sigma-algebra的条件期望，将歧视空间缩小为对不变歧视空间的投影。此外，我们证明了鉴别空间的缩小必须伴随着结构化发电机的仔细设计，因为有缺陷的设计很容易导致学习分布的灾难性的“模式崩溃”。我们通过构建具有对称性的gan来进行固有的群体对称性分布来使我们的框架背景化，并证明两个参与者，即epoiriant发电机和不变歧视者，都在学习过程中扮演重要但独特的角色。跨广泛的数据集的经验实验和消融研究，包括现实世界的医学成像，验证我们的理论，并显示我们所提出的方法可显着提高样品保真度和多样性 - 几乎是在FR \'Echet Intection中衡量的数量级距离 - 尤其是在小型数据制度中。