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Found 26 papers, 5 papers with code
Modeling the Space of Point Landmark Constrained Diffeomorphisms
Based on Teichm\""uller theory, this mapping space is generated by the Beltrami coefficients, which are infinitesimally Teichm\""uller equivalent to $0$.
Backdoor Attack with Mode Mixture Latent Modification
Backdoor attacks become a significant security concern for deep neural networks in recent years.
DPM-OT: A New Diffusion Probabilistic Model Based on Optimal Transport
Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image.
Large language models improve Alzheimer's disease diagnosis using multi-modality data
In diagnosing challenging conditions such as Alzheimer's disease (AD), imaging is an important reference.
What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives
This paper also underscores several promising future research directions and challenges in IMG.
Efficient Optimal Transport Algorithm by Accelerated Gradient descent
Basically, the non-smooth c-transform of the Kantorovich potential is approximated by the smooth Log-Sum-Exp function, which finally smooths the original non-smooth Kantorovich dual functional (energy).
Cortical Surface Shape Analysis Based on Alexandrov Polyhedra
Shape analysis has been playing an important role in early diagnosis and prognosis of neurodegenerative diseases such as Alzheimer's diseases (AD).
FFT-OT: A Fast Algorithm for Optimal Transportation
First, solving Monge-Ampere equation is converted to a fixed point problem; Second, the obliqueness property of optimal transportation maps are reformulated as Neumann boundary conditions on rectangular domains; Third, FFT is applied in each iteration to solve a Poisson equation in order to improve the efficiency.
AE-OT: A NEW GENERATIVE MODEL BASED ON EXTENDED SEMI-DISCRETE OPTIMAL TRANSPORT
In order to tackle the both problems, we explicitly separate the manifold embedding and the optimal transportation; the first part is carried out using an autoencoder to map the images onto the latent space; the second part is accomplished using a GPU-based convex optimization to find the discontinuous transportation maps.
AE-OT-GAN: Training GANs from data specific latent distribution
Though generative adversarial networks (GANs) areprominent models to generate realistic and crisp images, they often encounter the mode collapse problems and arehard to train, which comes from approximating the intrinsicdiscontinuous distribution transform map with continuousDNNs.
Mode Collapse and Regularity of Optimal Transportation Maps
This work builds the connection between the regularity theory of optimal transportation map, Monge-Amp\`{e}re equation and GANs, which gives a theoretic understanding of the major drawbacks of GANs: convergence difficulty and mode collapse.
Corresponding Supine and Prone Colon Visualization Using Eigenfunction Analysis and Fold Modeling
The use of Fiedler vectors and the segmented folds presents a precise way of visualizing corresponding regions across datasets and visual modalities.
LMap: Shape-Preserving Local Mappings for Biomedical Visualization
In this paper, we present a shape-preserving local mapping technique for resolving occlusions locally while preserving the overall geometric context.
Latent Space Optimal Transport for Generative Models
Experimental results on an eight-Gaussian dataset show that the proposed OT can handle multi-cluster distributions.
A Two-Step Computation of the Exact GAN Wasserstein Distance
In this paper, we propose a two-step method to compute the Wasserstein distance in Wasserstein Generative Adversarial Networks (WGANs): 1) The convex part of our objective can be solved by linear programming; 2) The non-convex residual can be approximated by a deep neural network.
Classification of lung nodules in CT images based on Wasserstein distance in differential geometry
The Wasserstein distance between the nodules is calculated based on our new spherical optimal mass transport, this new algorithm works directly on sphere by using spherical metric, which is much more accurate and efficient than previous methods.
Variational Wasserstein Clustering
We propose a new clustering method based on optimal transportation.
Brenier approach for optimal transportation between a quasi-discrete measure and a discrete measure
Correctly estimating the discrepancy between two data distributions has always been an important task in Machine Learning.
Intrinsic 3D Dynamic Surface Tracking Based on Dynamic Ricci Flow and Teichmuller Map
In this paper, we propose a novel automatic method for non-rigid 3D dynamic surface tracking with surface Ricci flow and Teichmuller map methods.
An Optimal Transportation Based Univariate Neuroimaging Index
We compute the OT from each image to a template and measure the Wasserstein distance between them.
Surface Registration via Foliation
This work introduces a novel surface registration method based on foliation.
Surface Registration by Optimization in Constrained Diffeomorphism Space
The physically plausible constraints, in terms of feature landmarks and deformation types, define subspaces in the Beltrami coefficient space.
Area Preserving Brain Mapping
Experimental results on caudate nucleus surface mapping and cortical surface mapping demonstrate the efficacy and efficiency of the proposed method.
Hyperbolic Harmonic Mapping for Constrained Brain Surface Registration
This work conquer this problem by changing the Riemannian metric on the target surface to a hyperbolic metric, so that the harmonic mapping is guaranteed to be a diffeomorphism under landmark constraints.
Variational Principles for Minkowski Type Problems, Discrete Optimal Transport, and Discrete Monge-Ampere Equations
In this paper, we develop several related finite dimensional variational principles for discrete optimal transport (DOT), Minkowski type problems for convex polytopes and discrete Monge-Ampere equation (DMAE).
Geometric Topology Differential Geometry Metric Geometry 52-XX I.3.5
Kernel Estimation from Salient Structure for Robust Motion Deblurring
One effective way to eliminate these details is to apply image denoising model based on the Total Variation (TV).
