arXiv subjects
Publications and source records attributed to Shuhui Yang.
In this paper, the weighted Lp boundedness of multilinear commutators and iterated commutators of multilinear singular integral operators with generalized kernels is established, where the weight is multiple weight. Our results are generalizations of the corresponding results for multilinear singular integral operators with standard kernels and Dini kernels.
The fractional Hilbert transform was introduced by Zayed [30, Zayed, 1998] and has been widely used in signal processing. In view of is connection with the fractional Fourier transform, Chen, the first, second and fourth authors of this paper in [6, Chen et al., 2021] studied the fractional Hilbert transform and other fractional multiplier operators on the real line. The present paper is concerned with a natural extension of the fractional Hilbert transform to higher dimensions: this extension is the fractional Riesz transform which is defined by multiplication which a suitable chirp function on the fractional Fourier transform side. In addition to a thorough study of the fractional Riesz transforms, in this work we also investigate the boundedness of singular integral operators with chirp functions on rotation invariant spaces, chirp Hardy spaces and their relation to chirp BMO spaces, as well as applications of the theory of fractional multipliers in partial differential equations. Through numerical simulation, we provide physical and geometric interpretations of high-dimensional fractional multipliers. Finally, we present an application of the fractional Riesz transforms in edge detection which verifies a hypothesis insinuated in [26, Xu et al., 2016]. In fact our numerical implementation confirms that amplitude, phase, and direction information can be simultaneously extracted by controlling the order of the fractional Riesz transform.
Domain adaptation has received a lot of attention in recent years, and many algorithms have been proposed with impressive progress. However, it is still not fully explored concerning the joint probability distribution (P(X, Y)) distance for this problem, since its empirical estimation derived from the maximum mean discrepancy (joint maximum mean discrepancy, JMMD) will involve complex tensor-product operator that is hard to manipulate. To solve this issue, this paper theoretically derives a unified form of JMMD that is easy to optimize, and proves that the marginal, class conditional and weighted class conditional probability distribution distances are our special cases with different label kernels, among which the weighted class conditional one not only can realize feature alignment across domains in the category level, but also deal with imbalance dataset using the class prior probabilities. From the revealed unified JMMD, we illustrate that JMMD degrades the feature-label dependence (discriminability) that benefits to classification, and it is sensitive to the label distribution shift when the label kernel is the weighted class conditional one. Therefore, we leverage Hilbert Schmidt independence criterion and propose a novel MMD matrix to promote the dependence, and devise a novel label kernel that is robust to label distribution shift. Finally, we conduct extensive experiments on several cross-domain datasets to demonstrate the validity and effectiveness of the revealed theoretical results.
Facial expression manipulation aims at editing facial expression with a given condition. Previous methods edit an input image under the guidance of a discrete emotion label or absolute condition (e.g., facial action units) to possess the desired expression. However, these methods either suffer from changing condition-irrelevant regions or are inefficient for fine-grained editing. In this study, we take these two objectives into consideration and propose a novel method. First, we replace continuous absolute condition with relative condition, specifically, relative action units. With relative action units, the generator learns to only transform regions of interest which are specified by non-zero-valued relative AUs. Second, our generator is built on U-Net but strengthened by Multi-Scale Feature Fusion (MSF) mechanism for high-quality expression editing purposes. Extensive experiments on both quantitative and qualitative evaluation demonstrate the improvements of our proposed approach compared to the state-of-the-art expression editing methods. Code is available at \url{https://github.com/junleen/Expression-manipulator}.