A General Framework of Remote Sensing Epipolar Image Generation

Epipolar images can improve the efficiency and accuracy of dense matching by restricting the search range of correspondences from 2-D to 1-D, which play an important role in 3-D reconstruction. As most of the satellite images in archives are incidental collections, which do not have rigorous stereo properties, in this paper, we propose a general framework to generate epipolar images for both in-track and cross-track stereo images. We first investigate the theoretical epipolar constraints of single-sensor and multi-sensor images and then introduce the proposed framework in detail. Considering large elevation changes in mountain areas, the publicly available digital elevation model (DEM) is applied to reduce the initial offsets of two stereo images. The left image is projected into the image coordinate system of the right image using the rational polynomial coefficients (RPCs). By dividing the raw images into several blocks, the epipolar images of each block are parallel generated through a robust feature matching method and fundamental matrix estimation, in which way, the horizontal disparity can be drastically reduced while maintaining negligible vertical disparity for epipolar blocks. Then, stereo matching using the epipolar blocks can be easily implemented and the forward intersection method is used to generate the digital surface model (DSM). Experimental results on several in-track and cross-track images, including optical-optical, SAR-SAR, and SAR-optical pairs, demonstrate the effectiveness of the proposed framework, which not only has obvious advantages in mountain areas with large elevation changes but also can generate high-quality epipolar images for flat areas. The generated epipolar images of a ZiYuan-3 pair in Songshan are further utilized to produce a high-precision DSM.

Linear Barycentric Rational Method for Solving Schrodinger Equation

A linear barycentric rational collocation method (LBRCM) for solving Schrodinger equation (SDE) is proposed. According to the barycentric interpolation method (BIM) of rational polynomial and Chebyshev polynomial, the matrix form of the collocation method (CM) that is easy to program is obtained. The convergence rate of the LBRCM for solving the Schrodinger equation is proved from the convergence rate of linear barycentric rational interpolation. Finally, a numerical example verifies the correctness of the theoretical analysis.

Orthorectification of WorldView-3 Satellite Image Using Airborne Laser Scanning Data

Satellite images have been widely used to produce land use and land cover maps and to generate other thematic layers through image processing. However, images acquired by sensors onboard various satellite platforms are affected by a systematic sensor and platform-induced geometry errors, which introduce terrain distortions, especially when the sensor does not point directly at the nadir location of the sensor. To this extent, an automated processing chain of WorldView-3 image orthorectification is presented using rational polynomial coefficient (RPC) model and laser scanning data. The research is aimed at analyzing the effects of varying resolution of the digital surface model (DSM) derived from high-resolution laser scanning data, with a novel orthorectification model. The proposed method is validated on actual data in an urban environment with complex structures. This research suggests that a DSM of 0.31 m spatial resolution is optimum to achieve practical results (root-mean-square error = 0.69 m ) and decreasing the spatial resolution to 20 m leads to poor results (root-mean-square error = 7.17 ). Moreover, orthorectifying WorldView-3 images with freely available digital elevation models from Shuttle Radar Topography Mission (SRTM) (30 m) can result in an RMSE of 7.94 m without correcting the distortions in the building. This research can improve the understanding of appropriate image processing and improve the classification for feature extraction in urban areas.

Optimal Regularization Method Based on the L-Curve for Solving Rational Function Model Parameters

Rational polynomial coefficients in a rational function model (<small>RFM</small>) have high correlation and redundancy, especially in high-order <small>RFMs</small>, which results in ill-posed problems of the normal equation. For this reason, this article presents an optimal regularization method with the L-curve for solving rational polynomial coefficients. This method estimates the rational polynomial coefficients of an <small>RFM</small> using the L-curve and finds the optimal regularization parameter with the minimum mean square error, then solves the parameters of the <small>RFM</small> by the Tikhonov method based on the optimal regularization parameter. The proposed method is validated in both terrain-dependent and terrain-independent cases using Gaofen-1 and aerial images, respectively, and compared with the least-squares method, L-curve method, and generalized cross-validation method. The experimental results demonstrate that the proposed method can solve the <small> RFM</small> parameters effectively, and their accuracy is increased by more than 85% on average relative to the other methods.

Reducing Rational Polynomial: A Proposition of a Strategy to Deal With Floating Points Numbers Using SVD

In this article, we present a new strategy to reduce rational polynomial based on the kernel of a linear map defined by the matrix's Sylvester. The strategy does not hold the computation of the Greatest common divisors (GCD) of two polynomials, as other algorithms do, but produce the reduced fraction directly. This strategy was inspired when we consider elements of Padé approximant as a basis is the Proper Generalised Decomposition for solving Partial Differential equation. The algorithm can use the Singular value decomposition technique when dealing with a polynomial with floating-point arithmetic. We compare it with Brown's algorithm in two wedges: multiplication for finite fields and large integers. Results are shown in term of time computation and robustness. The proposed algorithm shows that the time accuracy of computing the reduced fractional is at the same order as the Brown algorithm for finite field and large integers when the GCD of both polynomials has a small degree and an improving when the GCD's degree increase with the degree of polynomials. Also, robustness is more dynamic when arithmetic with the floating-point operation.

Automatic rational approximation and linearization of nonlinear eigenvalue problems

We present a method for solving nonlinear eigenvalue problems (NEPs) using rational approximation. The method uses the Antoulas–Anderson algorithm (AAA) of Nakatsukasa, Sète and Trefethen to approximate the NEP via a rational eigenvalue problem. A set-valued variant of the AAA algorithm is also presented for building low-degree rational approximations of NEPs with a large number of nonlinear functions. The rational approximation is embedded in the state-space representation of a rational polynomial by Su and Bai. This procedure perfectly fits the framework of the compact rational Krylov methods (CORK and TS-CORK), allowing solve large-scale NEPs to be efficiently solved. One advantage of our method, compared to related techniques such as NLEIGS and infinite Arnoldi, is that it automatically selects the poles and zeros of the rational approximations. Numerical examples show that the presented framework is competitive with NLEIGS and usually produces smaller linearizations with the same accuracy but with less effort for the user.