The Unbalanced Optimal Transport (UOT) problem plays increasingly important roles in computational biology, computational imaging and deep learning. Scaling algorithm is widely used to solve UOT due to its convenience and good convergence properties. However, this algorithm has lower accuracy for large regularization parameters, and due to stability issues, small regularization parameters can easily lead to numerical overflow. We address this challenge by developing an inexact Bregman proximal point method for solving UOT. This algorithm approximates the proximal operator using the Scaling algorithm at each iteration. The algorithm (1) converges to the true solution of UOT, (2) has theoretical guarantees and robust regularization parameter selection, (3) mitigates numerical stability issues, and (4) can achieve comparable computational complexity to the Scaling algorithm in specific practice. Building upon this, we develop an accelerated version of inexact Bregman proximal point method for solving UOT by using acceleration techniques of Bregman proximal point method and provide theoretical guarantees and experimental validation of convergence and acceleration.

Despite the promise of superior performance under challenging conditions, event-based motion estimation remains a hard problem owing to the difficulty of extracting and tracking stable features from event streams. In order to robustify the estimation, it is generally believed that fusion with other sensors is a requirement. In this work, we demonstrate reliable, purely event-based visual odometry on planar ground vehicles by employing the constrained non-holonomic motion model of Ackermann steering platforms. We extend single feature n-linearities for regular frame-based cameras to the case of quasi time-continuous event-tracks, and achieve a polynomial form via variable degree Taylor expansions. Robust averaging over multiple event tracks is simply achieved via histogram voting. As demonstrated on both simulated and real data, our algorithm achieves accurate and robust estimates of the vehicle's instantaneous rotational velocity, and thus results that are comparable to the delta rotations obtained by frame-based sensors under normal conditions. We furthermore significantly outperform the more traditional alternatives in challenging illumination scenarios. The code is available at \url{https://github.com/gowanting/NHEVO}.

In order to achieve it, we proposed and developed the classification framework EasiCS to obtain the relative stability The cervical spondylosis(CS), a common degenerative clustering results, which consists of dimension reduction, disease, harms human life and health, affects up clustering algorithm EasiSOM, spectral clustering algorithm to two-thirds of the population, and poses an serious EasiSC as shown in the Figure 1. To the best of our burden on individuals and society (Matz et al. 2009; knowledge, the EasiCS is the first effort to utilize the clustering Kotil and Bilge 2008; Cai et al. 2016; Nana Wang; algorithm and sEMG. Compared with the seven commonly Wang et al. 2018). Currently, the neck disability index used clustering algorithms, the novelty framework (Howard Vernon) is the most commonly used tool EasiCS provide the best overall performance. The cervical to assess the neck dysfunction (Vernon and Mior 1991), spondylosis(CS), a common degenerative disease, harms human The availability of which are mainly undermined by the life and health, affects up to two-thirds of the population, coarse-grained and unreasonable classification, despite that and poses an serious burden on individuals and society the NDI information is subjective and not accurate enough.

Cervical spondylosis (CS) is a common chronic disease that affects up to two-thirds of the population and poses a serious burden on individuals and society. The early identification has significant value in improving cure rate and reducing costs. However, the pathology is complex, and the mild symptoms increase the difficulty of the diagnosis, especially in the early stage. Besides, the time-consuming and costliness of hospital medical service reduces the attention to the CS identification. Thus, a convenient, low-cost intelligent CS identification method is imperious demanded. In this paper, we present an intelligent method based on the deep learning to identify CS, using the surface electromyography (sEMG) signal. Faced with the complex, high dimensionality and weak usability of the sEMG signal, we proposed and developed a multi-channel EasiCSDeep algorithm based on the convolutional neural network, which consists of the feature extraction, spatial relationship representation and classification algorithm. To the best of our knowledge, this EasiCSDeep is the first effort to employ the deep learning and the sEMG data to identify CS. Compared with previous state-of-the-art algorithm, our algorithm achieves a significant improvement.

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. This leads to a geometric interpretation to generative models, and leads to a novel framework for generative models. By using the optimal transportation view of GAN model, we show that the discriminator computes the Kantorovich potential, the generator calculates the transportation map. For a large class of transportation costs, the Kantorovich potential can give the optimal transportation map by a close-form formula. Therefore, it is sufficient to solely optimize the discriminator. This shows the adversarial competition can be avoided, and the computational architecture can be simplified. Preliminary experimental results show the geometric method outperforms WGAN for approximating probability measures with multiple clusters in low dimensional space.