Kernel Cross-Correlator

Cross-correlator plays a significant role in many visual perception tasks, such as object detection and tracking. Beyond the linear cross-correlator, this paper proposes a kernel cross-correlator (KCC) that breaks traditional limitations. First, by introducing the kernel trick, the KCC extends the linear cross-correlation to non-linear space, which is more robust to signal noises and distortions. Second, the connection to the existing works shows that KCC provides a unified solution for correlation filters. Third, KCC is applicable to any kernel function and is not limited to circulant structure on training data, thus it is able to predict affine transformations with customized properties. Last, by leveraging the fast Fourier transform (FFT), KCC eliminates direct calculation of kernel vectors, thus achieves better performance yet still with a reasonable computational cost. Comprehensive experiments on visual tracking and human activity recognition using wearable devices demonstrate its robustness, flexibility, and efficiency. The source codes of both experiments are released at https://github.com/wang-chen/KCCComment: The Thirty-Second AAAI Conference on Artificial Intelligence (AAAI-18

Correlation Flow: Robust Optical Flow Using Kernel Cross-Correlators

Robust velocity and position estimation is crucial for autonomous robot navigation. The optical flow based methods for autonomous navigation have been receiving increasing attentions in tandem with the development of micro unmanned aerial vehicles. This paper proposes a kernel cross-correlator (KCC) based algorithm to determine optical flow using a monocular camera, which is named as correlation flow (CF). Correlation flow is able to provide reliable and accurate velocity estimation and is robust to motion blur. In addition, it can also estimate the altitude velocity and yaw rate, which are not available by traditional methods. Autonomous flight tests on a quadcopter show that correlation flow can provide robust trajectory estimation with very low processing power. The source codes are released based on the ROS framework.Comment: 2018 International Conference on Robotics and Automation (ICRA 2018

Subleading-N_c corrections in non-linear small-x evolution

We explore the subleading-N_c corrections to the large-N_c Balitsky-Kovchegov (BK) evolution equation by comparing its solution to that of the all-N_c Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) equation. In earlier simulations it was observed that the difference between the solutions of JIMWLK and BK is unusually small for a quark dipole scattering amplitude, of the order of 0.1%, which is two orders of magnitude smaller than the naively expected 1/N_c^2 or 11%. In this paper we argue that this smallness is not accidental. We show that saturation effects and correlator coincidence limits fixed by group theory constraints conspire with the particular structure of the dipole kernel to suppress subleading-N_c corrections reducing the difference between the solutions of JIMWLK and BK to 0.1%. We solve the JIMWLK equation with improved numerical accuracy and verify that the remaining 1/N_c corrections, while small, still manage to slow down the rapidity-dependence of JIMWLK evolution compared to that of BK. We demonstrate that a truncation of JIMWLK evolution in the form of a minimal Gaussian generalization of the BK equation captures some of the remaining 1/N_c contributions leading to an even better agreement with JIMWLK evolution. As the 1/N_c corrections to BK include multi-reggeon exchanges one may conclude that the net effect of multi-reggeon exchanges on the dipole amplitude is rather small.Comment: discussion of phase space regions streamlined, version to be published in NP

Improved real-time dynamics from imaginary frequency lattice simulations

The computation of real-time properties, such as transport coefficients or bound state spectra of strongly interacting quantum fields in thermal equilibrium is a pressing matter. Since the sign problem prevents a direct evaluation of these quantities, lattice data needs to be analytically continued from the Euclidean domain of the simulation to Minkowski time, in general an ill-posed inverse problem. Here we report on a novel approach to improve the determination of real-time information in the form of spectral functions by setting up a simulation prescription in imaginary frequencies. By carefully distinguishing between initial conditions and quantum dynamics one obtains access to correlation functions also outside the conventional Matsubara frequencies. In particular the range between $\omega_0$ and $\omega_1=2\pi T$, which is most relevant for the inverse problem may be more highly resolved. In combination with the fact that in imaginary frequencies the kernel of the inverse problem is not an exponential but only a rational function we observe significant improvements in the reconstruction of spectral functions, demonstrated in a simple 0+1 dimensional scalar field theory toy model.Comment: 8 pages, 5 figures, Talk given at the XXXVth International Symposium on Lattice Field Theory, June 18-24, 2017, Granada, Spai