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Seeking informative projecting directions has been an important task in utilizing sliced Wasserstein distance in applications. However, finding these directions usually requires an iterative optimization procedure over the space of…
This paper focuses on a similarity measure, known as the Wasserstein distance, with which to compare images. The Wasserstein distance results from a partial differential equation (PDE) formulation of Monge's optimal transport problem. We…
We propose integrating optimal transport (OT) into operator learning for partial differential equations (PDEs) on complex geometries. Classical geometric learning methods typically represent domains as meshes, graphs, or point clouds. Our…
In the context of scene understanding, a variety of methods exists to estimate different information channels from mono or stereo images, including disparity, depth, and normals. Although several advances have been reported in the recent…
Recently, patch-deformation methods have exhibited significant effectiveness in multi-view stereo owing to the deformable and expandable patches in reconstructing textureless areas. However, such methods primarily emphasize broadening the…
Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely…
Assume that we observe i.i.d.~points lying close to some unknown $d$-dimensional $\mathcal{C}^k$ submanifold $M$ in a possibly high-dimensional space. We study the problem of reconstructing the probability distribution generating the…
Researches using margin based comparison loss demonstrate the effectiveness of penalizing the distance between face feature and their corresponding class centers. Despite their popularity and excellent performance, they do not explicitly…
Eliminating geometric distortion in semantically important regions remains an intractable challenge in image retargeting. This paper presents Object-IR, a self-supervised architecture that reformulates image retargeting as a learning-based…
In this paper, we propose a novel approach for manifold learning that combines the Earthmover's distance (EMD) with the diffusion maps method for dimensionality reduction. We demonstrate the potential benefits of this approach for learning…
This paper investigates the optimization of the long-standing probabilistically robust transmit beamforming problem with channel uncertainties in the multiuser multiple-input single-output (MISO) downlink transmission. This problem poses…
Approximate convex decomposition aims to decompose a 3D shape into a set of almost convex components, whose convex hulls can then be used to represent the input shape. It thus enables efficient geometry processing algorithms specifically…
Abdominal organ segmentation from CT and MRI is an essential prerequisite for surgical planning and computer-aided navigation systems. It is challenging due to the high variability in the shape, size, and position of abdominal organs.…
Deformation component analysis is a fundamental problem in geometry processing and shape understanding. Existing approaches mainly extract deformation components in local regions at a similar scale while deformations of real-world objects…
Surface registration plays an important role for anatomical shape analysis in medical imaging. Existing surface registration methods often face a trade-off between efficiency and robustness. Local point matching methods are computationally…
Permeability has a dominant influence on the flow properties of a natural fluid. Lattice Boltzmann simulator determines permeability from the nano and micropore network. The simulator holds millions of flow dynamics calculations with its…
Metasurfaces have become a promising means for manipulating optical wavefronts in flat and high-performance optical devices. Conventional metasurface device design relies on trial-and-error methods to obtain target electromagnetic (EM)…
Unsupervised learning of feature representations is a challenging yet important problem for analyzing a large collection of multimedia data that do not have semantic labels. Recently proposed neural network-based unsupervised learning…
Image segmentation is a fundamental and challenging problem in computer vision with applications spanning multiple areas, such as medical imaging, remote sensing, and autonomous vehicles. Recently, convolutional neural networks (CNNs) have…
In deep learning, it is usually assumed that the shape of the loss surface is fixed. Differently, a novel concept of deformation operator is first proposed in this paper to deform the loss surface, thereby improving the optimization.…