Most of existing manifold learning methods rely on Mean Squared Error (MSE) or norm. However, for the problem of image quality assessment, these are not promising measure. In this paper, we introduce the concept of an image structure manifold which captures image structure features and discriminates image dist…
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48 results for “image manifolds”
Generative modeling over natural images is one of the most fundamental machine learning problems. However, few modern generative models, including Wasserstein Generative Adversarial Nets (WGANs), are studied on manifold-valued images that are frequently encountered in real-world applications. To fill the gap, this pape…
Boomerang generates nonidentical images similar to input on image manifolds.
problem Generating nonidentical images similar to input on image manifolds.
method Adding noise to input image, moving closer to latent space, and mapping back through partial reverse diffusion.
result Boomerang generates nonidentical images similar to input on image manifolds.
We consider the problem of selecting an optimal mask for an image manifold, i.e., choosing a subset of the pixels of the image that preserves the manifold's geometric structure present in the original data. Such masking implements a form of compressive sensing through emerging imaging sensor platforms for which the pow…
The paper proposes a method to learn 3D object pose manifolds using GANs and elasticae.
problem Learning image manifolds of 3D objects with limited data.
method Geom-SGAN and elasticae for geometry-preserving image interpolation.
result The method outperforms state-of-the-art GANs and VAEs in learning rotation paths.
Wassmap reduces image complexity while preserving key features.
problem Global nonlinear dimensionality reduction in imaging.
method Wassmap uses Wasserstein space and pairwise distances to create isometric embeddings.
result Wassmap can recover parameters of image manifolds like translations and dilations.
Proves elliptic operator images are closed on Hilbert bundles.
problem Closedness of images of elliptic operators on Hilbert bundles.
method Analyzes tensor product of elliptic operators and compares images.
result Establishes closedness of images with respect to natural topology.
Proves Thurston's bounded image theorem for Haken manifolds.
problem Proving Thurston's bounded image theorem for Haken manifolds.
method Using recent developments in Kleinian group theory.
result A proof of Thurston's original bounded image theorem.
We describe all affine maps from a Riemannian manifold to a metric space and all possible image spaces.
This paper addresses the morphing of manifold-valued images based on the time discrete geodesic paths model of Berkels, Effland and Rumpf 2015. Although for our manifold-valued setting such an interpretation of the energy functional is not available so far, the model is interesting on its own. We prove the existence of…
Study slopes of direct images in complex manifolds, proving a Mehta-Ramanathan type theorem.
problem Distribution of Harder-Narasimhan slopes in direct image sheaves.
method Analyzing asymptotic distributions of slopes under base changes of families of complex projective manifolds.
result Asymptotic distribution of slopes can be recovered from base changes over generic curves.
Many tasks in computer vision can be cast as a "label changing" problem, where the goal is to make a semantic change to the appearance of an image or some subject in an image in order to alter the class membership. Although successful task-specific methods have been developed for some label changing applications, to da…
We define submersions f between manifolds M and N modelled on locally convex spaces. If the range N is finite-dimensional or a Banach manifold, then these coincide with the naive notion of a submersion. We study pre-images of submanifolds under submersions and pre-images under mappings whose differentials have dense im…
mFI-PSO: A Flexible and Effective Method in Adversarial Image Generation for Deep Neural Networkscs.LG
mFI-PSO generates effective adversarial images for DNNs.
problem Vulnerability of DNNs to small perturbations in images.
method Uses mFI for pixel selection and PSO for objective functions.
result mFI-PSO effectively designs flexible adversarial images.
Generates high-resolution images from low-resolution inputs.
problem Generating realistic images from low-resolution inputs.
method Latent Adversarial Generator (LAG) using perceptual loss.
result Samples of high-resolution images from low-resolution inputs.
The paper refutes the manifold hypothesis for image data and proposes the union of manifolds hypothesis.
problem The manifold hypothesis fails to capture the structure of image data.
method Empirical verification of the union of manifolds hypothesis on image datasets.
result Image data lies on a disconnected set with varying intrinsic dimensions.
RGI improves robustness of GAN-inversion for image restoration and anomaly detection.
problem Robustness of GAN-inversion to unknown gross corruptions.
method Proposes RGI and R-RGI methods with provable robustness guarantees.
result Restored images and corrupted region masks converge to ground truth under mild assumptions.
We obtain conditions on the Lee form under which a holomorphic map between almost Hermitian manifolds is a harmonic map or morphism. Then we discuss under what conditions (i) the image of a holomorphic map from a cosymplectic manifold is also cosymplectic, (ii) a holomophic map with Hermitian image defines a Hermitian …
Minimal surfaces can be mapped to 3D with bounded images.
problem Mapping minimal surfaces to 3D with bounded images.
method Analyzes various types of minimal immersions into and complex manifolds.
result Every surface contains a Cantor set allowing bounded conformal minimal immersions.
New model separates images into independent factors quickly and easily.
problem Separating high-dimensional data like images into independent latent factors.
method Combines bijective feature maps with linear ICA model on the Stiefel manifold.
result Models converge quickly and achieve better unsupervised latent factor discovery.
Cohomology fractalsmath.GT
Cohomology fractals are visual representations of cohomology classes on hyperbolic 3-manifolds.
problem Visualizing cohomology classes on hyperbolic 3-manifolds.
method Cohomology fractals are images associated to cohomology classes. They are related to limit sets of Kleinian groups but differ in key aspects. An implementation using ideal triangulations and ray-casting is presented.
result Cohomology fractals allow for real-time zooming in any direction at arbitrary depth.
Localized curvature bounds ensure harmonic maps are constant.
problem Ensuring harmonic maps are constant under localized curvature constraints.
method Localized Bochner-type rigidity theorem for harmonic maps with image-dependent curvature bounds.
result Harmonic maps are constant if minimal Ricci curvature dominates image-dependent curvature bounds.
GEM learns a manifold for cross-modal data, capturing structure without modality dependence.
problem Modality-specific neural models limit flexibility and custom architecture.
method Casts learning as manifold inference, enforcing coverage, linearity, and isometry.
result GEM learns latent structure across image, shape, audio, and cross-modal domains.
Study on the parity of fold map singular points, showing non-invariance for odd-dimensional manifolds.
problem Parity of connected components of fold map singular points for odd-dimensional manifolds.
method Constructive proofs using open book decompositions, round fold maps, and allowable moves.
result Parity of connected components is not a homotopy invariant for odd-dimensional manifolds.
This paper proposes a method to generate realistic test cases for image classifiers.
problem Ensuring neural networks for image classification are correct with adequate realistic test data.
method Captures patterns in a large input data space using a manifold, then generates fault-revealing test cases.
result Generates thousands of realistic yet fault-revealing test cases efficiently for well-trained models.
MimicGAN improves robustness of image projections under corruption.
problem Robust projection onto image manifolds is challenging due to corruptions.
method Proposes corruption mimicking to robustly project images.
result Significantly more robust than PGD under various corruptions.
We develop a new purely combinatorial approach to N. Steenrod's problem on realisation of cycles. We prove that every n-dimensional homology class of every topological space can be realised with some multiplicity by an image of a finite-fold covering over the manifold M^n, where M^n is the isospectral manifold of real …
Let K be a connected Lie group and M a Hamiltonian K-manifold. In this paper, we introduce the notion of convexity of M. It implies that the momentum image is convex, the moment map has connected fibers, and the total moment map is open onto its image. Conversely, the three properties above imply convexity. We show tha…
Most content-based image retrieval systems consider either one single query, or multiple queries that include the same object or represent the same semantic information. In this paper we consider the content-based image retrieval problem for multiple query images corresponding to different image semantics. We propose a…
This paper presents a novel framework for generating texture mosaics with convolutional neural networks. Our method is called GANosaic and performs optimization in the latent noise space of a generative texture model, which allows the transformation of a content image into a mosaic exhibiting the visual properties of t…
In computer vision, image datasets used for classification are naturally associated with multiple labels and comprised of multiple views, because each image may contain several objects (e.g. pedestrian, bicycle and tree) and is properly characterized by multiple visual features (e.g. color, texture and shape). Currentl…
Paper proves certain closed affine manifolds without invariant lines don't exist.
problem Proving non-existence of closed affine manifolds with invariant lines.
method Developing map, holonomy, invariant line, large open subsets, modified proof.
result Developing image cannot meet invariant line if affine holonomy acts purely by translations.
Proposes a normalization technique for manifold valued data.
problem Instability in optimization for manifold valued data.
method Develops a general normalization technique for manifold valued data.
result Demonstrates performance gain in synthetic and real datasets.
We consider a classical N. Steenrod's problem on realization of homology classes by images of the fundamental classes of manifolds. It is well-known that each integral homology class can be realized with some multiplicity as an image of the fundamental class of a manifold. Our main result is an explicit purely combinat…
We improve autoencoder image interpolation by shaping latent space.
problem Incongruities in autoencoder interpolation leading to artifacts or unrealistic results.
method Propose a regularization technique to shape latent space to follow a smooth, locally convex manifold consistent with training images.
result Faithful interpolation between data points achieved.
We show that every effective smooth action of a Lie group G on a manifold M is a diffeomorphism from G onto its image in Diff(M), where the image is equipped with the subset diffeology of the functional diffeology.
We study the compactness of sequences of diffeomorphisms in almost complex manifolds in terms of the direct images of the standard integrable structure.
Despite the advances of deep learning in specific tasks using images, the principled assessment of image fidelity and similarity is still a critical ability to develop. As it has been shown that Mean Squared Error (MSE) is insufficient for this task, other measures have been developed with one of the most effective bei…
New submanifolds found in toric manifolds with specific actions.
problem Understanding submanifolds in toric manifolds with complex subtorus actions.
method Analyzing the closure of a complex subtorus in a toric manifold and its Hamiltonian action.
result The image of the moment map for the Hamiltonian subtorus action coincides with the image of the Delzant polytope.
A new method tracks retinal vessels more accurately than existing methods.
problem Tracking retinal vessels accurately in spherical images.
method Computing cusp-free, crossing-preserving geodesics on spherical positions and orientations.
result Crossing-preserving tracking shows clear advantages over non-crossing-preserving tracking.
We compute the first and second homotopy groups of a class of contact toric manifolds in terms of the images of the associated moment map.
In this paper we propose a novel augmentation technique that improves not only the performance of deep neural networks on clean test data, but also significantly increases their robustness to random transformations, both affine and projective. Inspired by ManiFool, the augmentation is performed by a line-search manifol…
The image of the branch set of a PL branched cover between PL -manifolds is a simplicial -complex. We demonstrate that the reverse implication also holds: an open and discrete map with the image of the branch set contained in a simplicial -complex is equivalent …
In this paper, we propose Generative Adversarial Network (GAN) architectures that use Capsule Networks for image-synthesis. Based on the principal of positional-equivariance of features, Capsule Network's ability to encode spatial relationships between the features of the image helps it become a more powerful critic in…
Generative Adversarial Networks are powerful generative models that are able to model the manifold of natural images. We leverage this property to perform manifold regularization by approximating a variant of the Laplacian norm using a Monte Carlo approximation that is easily computed with the GAN. When incorporated in…
Bayesian Imaging With Data-Driven Priors Encoded by Neural Networks: Theory, Methods, and Algorithmsstat.ME
Bayesian imaging uses neural networks to learn prior knowledge from data.
problem Performing Bayesian inference in imaging problems with limited prior knowledge.
method Constructs a data-driven prior on a sub-manifold of the image space using neural networks, and performs Bayesian computation on this manifold.
result Established the existence and well-posedness of the posterior distribution and moments, and demonstrated superior performance compared to existing methods.
Cohomology fractals illustrate complex 3-manifold properties.
problem Visualizing complex cohomology classes in hyperbolic 3-manifolds.
method Ray-tracing cohomology fractals and proving their distribution.
result Cohomology fractals converge to a distribution on the sphere at infinity.
Research on unique continuation principles in medical and seismic imaging.
problem Understanding unique continuation principles for inverse problems.
method Integral geometry and fractional calculus methods applied to various imaging problems.
result Developed new techniques for solving inverse problems with partial data.