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Found 18 papers, 4 papers with code
Point Cloud Compression via Constrained Optimal Transport
This paper presents a novel point cloud compression method COT-PCC by formulating the task as a constrained optimal transport (COT) problem.
Topology-Aware Latent Diffusion for 3D Shape Generation
By strategically incorporating topological features into the diffusion process, our generative module is able to produce a richer variety of 3D shapes with different topological structures.
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.
OT-Net: A Reusable Neural Optimal Transport Solver
With the widespread application of optimal transport (OT), its calculation becomes essential, and various algorithms have emerged.
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.
Global Consistent Point Cloud Registration Based on Lie-algebraic Cohomology
We present a novel, effective method for global point cloud registration problems by geometric topology.
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).
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.
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).
Ricci Curvature Based Volumetric Segmentation of the Auditory Ossicles
Compared to the state-of-the-art methods which usually use the gradient operator and some normalization terms, we propose to add a Ricci curvature term to the commonly employed energy function.
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.
Latent Space Optimal Transport for Generative Models
Experimental results on an eight-Gaussian dataset show that the proposed OT can handle multi-cluster distributions.
Geometric Understanding of Deep Learning
In this work, we give a geometric view to understand deep learning: we show that the fundamental principle attributing to the success is the manifold structure in data, namely natural high dimensional data concentrates close to a low-dimensional manifold, deep learning learns the manifold and the probability distribution on it.
A Geometric View of Optimal Transportation and Generative Model
In this work, we show the intrinsic relations between optimal transportation and convex geometry, especially the variational approach to solve Alexandrov problem: constructing a convex polytope with prescribed face normals and volumes.
Surface Registration via Foliation
This work introduces a novel surface registration method based on foliation.
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.
