arXiv subjects

Albert Chua

Publications and source records attributed to Albert Chua.

3 recordsLinked to original sources

arXiv2024

Generalizing Geometric Nonwindowed Scattering Transforms on Compact Riemannian Manifolds

Let $\mathcal{M}$ be a compact, smooth, $n$-dimensional Riemannian manifold without boundary. In this paper, we generalize nonwindowed geometric scattering transforms, which we formulate as $\mathbf{L}^q(\mathcal{M})$ norms of a cascade of geometric wavelet transforms and modulus operators. We then provide weighted measures for these operators, prove that these operators are well-defined under specific conditions on the manifold, invariant to the action of isometries, and stable to diffeomorphisms for $\lambda$-bandlimited functions.

math.FA↗

arXiv2022

Long Range Constraints for Neural Texture Synthesis Using Sliced Wasserstein Loss

In the past decade, exemplar-based texture synthesis algorithms have seen strong gains in performance by matching statistics of deep convolutional neural networks. However, these algorithms require regularization terms or user-added spatial tags to capture long range constraints in images. Having access to a user-added spatial tag for all situations is not always feasible, and regularization terms can be difficult to tune. Thus, we propose a new set of statistics for texture synthesis based on Sliced Wasserstein Loss, create a multi-scale method to synthesize textures without a user-added spatial tag, study the ability of our proposed method to capture long range constraints, and compare our results to other optimization-based, single texture synthesis algorithms.

cs.CV↗

arXiv2022

On Generalizations of the Nonwindowed Scattering Transform

In this paper, we generalize finite depth wavelet scattering transforms, which we formulate as $\Lb^q(\mathbb{R}^n)$ norms of a cascade of continuous wavelet transforms (or dyadic wavelet transforms) and contractive nonlinearities. We then provide norms for these operators, prove that these operators are well-defined, and are Lipschitz continuous to the action of $C^2$ diffeomorphisms in specific cases. Lastly, we extend our results to formulate an operator invariant to the action of rotations $R \in \text{SO}(n)$ and an operator that is equivariant to the action of rotations of $R \in \text{SO}(n)$.

math.FA↗