From a smooth, strictly convex function phi: Rn --> R, a parametric family of divergence function Dphi(alpha) may be introduced: [ equation: see text] for x, y epsilon int dom (Phi) subset Rn, and for alpha in R, with Dphi(+/-1) defined through taking the limit of alpha. Each member is shown to induce an alpha-independent Riemannian metric, as well as a pair of dual alpha-connections, which are generally nonflat, except for alpha = +/-1. In the latter case, Dphi(+/-1) reduces to the (nonparametric) Bregman divergence, which is representable using phi and its convex conjugate phi* and becomes the canonical divergence for dually flat spaces (Amari, 1982, 1985; Amari & Nagaoka, 2000). This formulation based on convex analysis naturally extends the informationgeometric interpretation of divergence functions (Eguchi, 1983) to allow the distinction between two different kinds of duality: referential duality (alpha <--> -alpha) and representational duality (phi <--> phi*). When applied to (not necessarily normalized) probability densities, the concept of conjugated representations of densities is introduced, so that +/-alpha-connections defined on probability densities embody both referential and representational duality and are hence themselves bidual. When restricted to a finite-dimensional affine submanifold, the natural parameters of a certain representation of densities and the expectation parameters under its conjugate representation form biorthogonal coordinates. The alpha representation (indexed by beta now, beta epsilon [-1, 1]) is shown to be the only measure-invariant representation. The resulting two-parameter family of divergence functionals D(alpha,beta), (alpha, beta) epsilon [-1, 1] x [-1, 1] induces identical Fisher information but bidual alpha-connection pairs; it reduces in form to Amari's alpha-divergence family when alpha = +/-1 or when beta = 1, but to the family of Jensen difference (Rao, 1987) when beta = -1.

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Objective The goal of this paper is to automatically digitize craniomaxillofacial (CMF) landmarks efficiently and accurately from cone-beam computed tomography (CBCT) images, by addressing the challenge caused by large morphological variations across patients and image artifacts of CBCT images. Methods We propose a Segmentation-guided Partially-joint Regression Forest (S-PRF) model to automatically digitize CMF landmarks. In this model, a regression voting strategy is first adopted to localize each landmark by aggregating evidences from context locations, thus potentially relieving the problem caused by image artifacts near the landmark. Second, CBCT image segmentation is utilized to remove uninformative voxels caused by morphological variations across patients. Third, a partially-joint model is further proposed to separately localize landmarks based on the coherence of landmark positions to improve the digitization reliability. In addition, we propose a fast vector quantization (VQ) method to extract high-level multi-scale statistical features to describe a voxel's appearance, which has low dimensionality, high efficiency, and is also invariant to the local inhomogeneity caused by artifacts. Results Mean digitization errors for 15 landmarks, in comparison to the ground truth, are all less than 2mm. Conclusion Our model has addressed challenges of both inter-patient morphological variations and imaging artifacts. Experiments on a CBCT dataset show that our approach achieves clinically acceptable accuracy for landmark digitalization. Significance Our automatic landmark digitization method can be used clinically to reduce the labor cost and also improve digitalization consistency.

Calibrating the extrinsic parameters on a system of 3D Light Detection And Ranging (LiDAR) and the monocular camera is a challenging task, because accurate 3D-2D or 3D-3D point correspondences are hard to establish from the sparse LiDAR point clouds in the calibration procedure. In this paper, we propose a geometric calibration method for estimating the extrinsic parameters of the LiDAR-camera system. In this method, a novel combination of planar boards with chessboard patterns and auxiliary calibration objects are proposed. The planar chessboard provides 3D-2D and 3D-3D point correspondences. Auxiliary calibration objects provide extra constraints for stable calibration results. After that, a novel geometric optimization framework is proposed to utilize these point correspondences, thus leading calibration results robust to LiDAR sensor noise. Besides, we contribute an automatic approach to extract point clouds of calibration objects. In the experiments, our method has a superior performance over state-of-the-art calibration methods. Furthermore, we verify our method by computing depth map and improvements can also be found. These results demonstrate that our method performance on the LiDAR-camera system is applicable for future advanced visual applications.

SUMMARYA precorrected fast Fourier transform (pFFT) accelerated boundary element method (BEM) for large-scale transient elastodynamic analysis is developed and described in this paper. The frequency-domain approach is used. To overcome the 'wrap-around' problem associated with the discrete Fourier transform, the exponential window method (EWM) is employed and incorporated in the frequency-domain BEM. An improved implementation scheme of the pFFT method based on polynomial interpolation technique is developed and applied to accelerate the elastodynamic BEM. This new scheme reduces the memory required to save the convolution matrix by a factor of 8. To further improve the efficiency of the code, a newly developed linear system solver based on the induced dimension reduction method is employed. Its performance is investigated and compared with that of the well-known GMRES. The accuracy and computational efficiency of the method are evaluated and demonstrated by three examples: a classical benchmark, a plate subject to an impact loading and a porous cube with nearly half million DOFs subject to a step traction loading. Both analytical and experimental results are employed to validate the method. It has been found that the EWM can effectively resolve the wrap-around problem and accurate time responses for an arbitrarily chosen time period can be obtained.

Low-light image enhancement is an important challenge in computer vision. Most of the low-light images taken in low-light conditions usually look noisy and dark, which makes it more difficult for subsequent computer vision tasks. In this paper, inspired by multi-scale retinex, we present a low-light image enhancement pipeline network based on an end-to-end fully convolutional networks and discrete wavelet transformation (DWT). First, we show that multiscale retinex (MSR) can be considered as a convolutional neural network with Gaussian convolution kernel, and blending the result of DWT can improve the image produced by MSR. Second, we propose our pipeline neural network, consisting of denoising net and low-light image enhancement net, which learns a function from a pair of dark and bright images. Finally, we evaluate our method both in the synthetic dataset and public dataset. The experiments reveal that in comparison with other state-of-the-art methods, our methods achieve a better performance in the perspective of qualitative and quantitative analyses. INDEX TERMS Convolutional neural network, low-light image enhancement, LLIE-Net. II. RELATED WORK Based on retinex theory [1], several methods were proposed. Single scale retinex (SSR) [2], multiscale scale retinex (MSR) [3] and multiscale retinex with color restoration (MSRCR) [4] enhance images in frequency domains. HE algorithms [5], [6] mainly focus on enhancing

Linear three-dimensional instabilities of nonlinear two-dimensional uniform gravitycapillary waves are studied using numerical methods. The eigenvalue system for the stability problem is generated using a Galerkin method and differs in detail from techniques used to study the stability of pure gravity waves (McLean 1982) and pure capillary waves (Chen & Saffman 1985). It is found that instabilities develop in the neighbourhood of the linear (triad, quartet and quintet) resonance curves. Further, both sum and difference triad ressonances are unstable for sufficiently steep waves in consequence of which Hasselmann's (1967) theorem is restricted to weakly nonlinear waves. The appearance of a superharmonic two-dimensional instability and bifurcation to three-dimensional waves are noted.