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A discrete quaternion filtering algorithm following high-density uncertainty matching-based deterministic sampling scheme is proposed for IMU attitude estimation. Existing quaternion filters rely on the specific distributions directly or the on-tangent-plane Gaussian distribution indirectly to model the underlying uncertainty. The key idea of this paper is to apply a Dirac mixture at few deterministic weighted samples for non-parametric interpreting the high-density uncertainty of unit quaternion manifold. In contrast to standard Monte Carlo techniques based on random sampling, the proposed approach is deterministic. Furthermore, the deterministic quaternion particles are obtained by projecting on-sphere uniform points to the unit quaternion manifold via an exponential map. The on-manifold quaternions are then exploited in a discrete Bayesian filtering procedure. We compare the new filter with the genetic algorithm embedded quaternion particle filter (GA-QPF) and the unscented quaternion estimator (USQUE) for accuracy and computation cost by using simulated and practical IMU data. The results illustrate that the proposed estimator possesses lower computational cost than the GA-QPF while providing a comparable accuracy, higher accuracy than the USQUE, as well as more effective against large initialization error.

A linear frequency modulation (LFM)-Costas waveform generation scheme is proposed and experimentally demonstrated based on a Fourier domain mode locking (FDML) optoelectronic oscillator (OEO). The FDML OEO is established based on stimulated Brillouin scattering (SBS) effect, where the Costas-coded probe light is realized by employing an open-loop voltage controlled oscillator (VCO) via electro-optic frequency shift. In the experiment, an LFM-Costas waveform with a 12-bit Costas sequence, a chirp rate of 39.234 MHz/μs and a period of 20.390 μs is generated in the frequency range of 8.020 GHz to 8.820 GHz. The generated LFM-Costas waveform has good pulse-to-pulse coherence according to the correlation results, and has been used to detect two targets with a distance difference of 0.30 m and 0.20 m

A Fourier domain mode locking (FDML) optoelectronic oscillator (OEO) based on stimulated Brillouin scattering is demonstrated to optimize the signal performance from a voltage controlled oscillator (VCO). Experimental results indicate that the signal from the FDML OEO has a much lower phase noise and a better coherence than the signal output from the VCO.

Metaflumizone is a novel semicarbazone insecticide. It functions as a sodium channel blocker insecticide (SCBI) with excellent insecticidal activity on most economically important lepidopterous pests. This study assessed the resistance risk of Spodoptera exigua (Hübner) (Lepidoptera: Noctuidae) to metaflumizone in the laboratory and the effects of metaflumizone selection on toxicities to other insecticides. Spodoptera exigua collected from a field population at Huizhou in 2012 were successively challenged by metaflumizone to evaluate the risk of resistance evolution. Twelve generations of selection increased resistance to metaflumizone by 3.4-fold and threshold trait analysis revealed that the realized heritability (h2) of this resistance was 0.086. When h2 was equal to 0.086 and 90% of individuals were killed at each generation, LC50 to metaflumizone increased by 10-fold after 15 generations. The selection by metaflumizone did not increase the resistance to indoxacarb, chlorantraniliprole, spinosad, methomyl, or endosulfan, suggesting a lack of cross-resistance. However, metaflumizone challenge upheld the recession of resistance to emamectin benzoate, chlorfluazuron, and tebufenozide. The block of resistance drops by metaflumizone exposure implied a possible cross-resistance between metaflumizone and these three insecticides. These results contribute to integrated resistance management of S. exigua.

Background Glutathione S-transferases (GSTs) are a superfamily of multifunctional dimeric proteins existing in both prokaryotic and eukaryotic organisms. They are involved in the detoxification of both endogenous and exogenous electrophiles, including insecticides. However, the molecular mechanisms underlying the regulation of GST genes in insects are poorly understood. Results We first identified at least three GST genes involved in resistance to the insecticides chlorpyrifos and cypermethrin. Analysis of upstream sequences revealed that three GSTs (SeGSTo2, SeGSTe6 and SeGSTd3) harbor the same cap 'n' collar C/muscle aponeurosis fibromatosis (CncC/Maf) binding site, and SeGSTo2 and SeGSTe6 contain the aryl hydrocarbon receptor/aryl hydrocarbon receptor nuclear translocator (AhR/ARNT) binding site. Luciferase reporter assay showed co-transfection of reporter plasmid containing the SeGSTe6 promoter with CncC and/or Maf expressing constructs significantly boosted transcription. Similarly, AhR and/or ARNT expressing constructs also significantly increased the promoter activities. The co-transfection of mutated reporter plasmid with CncC/Maf or AhR/ARNT did not increase transcription activity anymore. Constitutive over-expression of CncC, Maf and AhR was also found in the HZ16 strain, which might be the molecular mechanism for up-regulated expression of multiple detoxification genes conferring resistance to insecticides. Conclusion These results suggest that CncC/Maf and AhR/ARNT coordinately regulate the expression of multiple GST genes involved in insecticide resistance in Spodoptera exigua. © 2019 Society of Chemical Industry.

A recursively indirect quaternion estimator based on the Gaussian particle filter (GPF) is proposed for nonlinear attitude estimation. The key idea is to estimate an on-tangent-plane Gaussian distribution in the GPF scheme for interpreting the uncertainty of the unit quaternion manifold. The unit quaternion is provided with a global nonsingular attitude description in the prediction step, and the three-dimensional attitude error is estimated in the update step. Based on the framework of the GPF, the proposed filter does not need resampling and regularization compared with the PF. The performance of the proposed filter is verified theoretically and evaluated by experiments. The results show that the proposed filter has a faster convergence speed, lower complexity, and lower computational cost than the existing quaternion PF under a comparable accuracy.

The evolution of insect resistance to insecticides is frequently associated with overexpression of one or more cytochrome P450 enzyme genes. Although overexpression of CYP450 genes is a well-known mechanism of insecticide resistance, the underlying regulatory mechanisms are poorly understood. Here we uncovered the mechanisms of overexpression of the P450 gene, CYP321A8 in a major pest insect, Spodoptera exigua that is resistant to multiple insecticides. CYP321A8 confers resistance to organophosphate (chlorpyrifos) and pyrethroid (cypermethrin and deltamethrin) insecticides in this insect. Constitutive upregulation of transcription factors CncC/Maf are partially responsible for upregulated expression of CYP321A8 in the resistant strain. Reporter gene assays and site-directed mutagenesis analyses demonstrated that CncC/Maf enhanced the expression of CYP321A8 by binding to specific sites in the promoter. Additional cis-regulatory elements resulting from a mutation in the CYP321A8 promoter in the resistant strain facilitates the binding of the orphan nuclear receptor, Knirps, and enhances the promoter activity. These results demonstrate that two independent mechanisms; overexpression of transcription factors and mutations in the promoter region resulting in a new cis-regulatory element that facilitates binding of the orphan nuclear receptor are involved in overexpression of CYP321A8 in insecticide-resistant S. exigua., Author summary Insect pests developing resistance to insecticides used for their control is a major problem in agriculture. Many pests including the beet armyworm, Spodoptera exigua have developed resistance to insecticides used for their control. Information on the mechanisms of resistance would help in resistance management programs. Overexpression of detoxifying enzymes were associated with insecticide resistance, but their functions and regulatory mechanisms are still unidentified. The expression levels of P450 genes between susceptible and resistant strains of S. exigua were compared and CYP321A8 was identified as the major contributor to resistance to organophosphate and pyrethroid insecticides. Further studies uncovered two independent but synergistic mechanisms; constitutive upregulation of b-Zip transcription factors and mutations in the promoter that facilitates the binding of an orphan nuclear receptor, Knirps contributing to increase in the expression of CYP321A8 and resistance to multiple insecticides in S. exigua.

Spodoptera exigua has developed very high resistance to pyrethroid insecticides; however, the mode-of-action target of pyrethroids has not been studied, and the mechanism for target resistance remains elusive in this insect. In this study the resistance level of a field collected population from Huizhou, China was assayed with leaf-dip method and further selected in laboratory. The transcripts of voltage-gated sodium channel gene from S. exigua were cloned and analyzed for the structural characteristics, the relative expression levels of transcripts were measured by quantitative RT-PCR. Finally, detection of the point mutations was performed. The bioassay indicated that Huizhou population had developed 309.5-fold resistance to lambda-cyhalothrin, and the selection in laboratory led to the resistant strain (HZ14-sel) with increased resistance of 423-fold. Nine transcripts of sodium channel with 4517–6149 bp nucleotides were identified from S. exigua, among which only one transcript (SeNav4) encode the functional protein with complete domains, and other eight transcripts were observed to lost some transmembrane segments. The L834F mutation in IIS6 corresponding for the typical kdr mutation “L1014F”, was detected in 50% individuals of HZ14-sel strain. These results suggested that lambda-cyhalothrin resistance is associated with point mutations and expression level changes of sodium channel transcripts in HZ14-sel strain.

Enhanced detoxification is one of the important mechanisms for insecticide resistance. Most research in this field to date has focused on the role of cytochrome P450s. Our previous work revealed that flavin-dependent monooxygenases (FMOs) were involved in metabolic resistance of Spodoptera exigua. In the present study we investigated the molecular characteristics, expression patterns and oxidative activities of SeFMO on insecticides. Three FMO genes, which encode proteins with the typical FMO motifs, were cloned from S. exigua. The oxidative activities of eukaryotically expressed SeFMO enzymes were verified with the model substrate of FMO. Importantly, the SeFMOs had significantly higher oxidative activities on metaflumizone and lambda-cyhalothrin than on model substrates and other insecticides tested. The three SeFMOs were mainly expressed in the midgut, fat body and Malpighian tubules. The tissues responsible for xenobiotic metabolism and their expression characteristics were similar to those of P450s acting as detoxification genes. The study also revealed that the expression of SeFMOs could be induced by insecticide exposure, and that SeFMOs were over-expressed in a metaflumizone-resistant strain of S. exigua. These results suggest that SeFMOs are important insecticide detoxifying enzymes, and that over-expression of FMO genes may be one of the mechanisms for metabolic resistance in S. exigua.

Cytochrome P450 and UDP‐glucosyltransferase (UGT) as phase I and phase II metabolism enzymes, respectively, play vital roles in the breakdown of endobiotics and xenobiotics. Insects can increase the expression of detoxification enzymes to cope with the stress from xenobiotics including insecticides. However, the molecular mechanisms for insecticide detoxification in Spodoptera exigua remain elusive, and the genes conferring insecticide metabolisms in this species are less well reported. In this study, 68 P450 and 32 UGT genes were identified. Phylogenetic analysis showed gene expansions in CYP3 and CYP4 clans of P450 genes and UGT33 family of this pest. P450 and UGT genes exhibited specific tissue expression patterns. Insecticide treatments in fat body cells of S. exigua revealed that the expression levels of P450 and UGT genes were significantly influenced by challenges of abamectin, lambda‐cyhalothrin, chlorantraniliprole, metaflumizone and indoxacarb. Multiple genes for detoxification were affected in expression levels after insecticide exposures. The results demonstrated that lambda‐cyhalothrin, chlorantraniliprole, metaflumizone and indoxacarb induced similar responses in the expression of P450 and UGT genes in fat body cells; eight P450 genes and four UGT genes were co‐up‐regulated significantly, and no or only a few CYP/UGT genes were down‐regulated significantly by these four insecticides. However, abamectin triggered a distinct response for P450 and UGT gene expression; more P450 and UGT genes were down‐regulated by abamectin than by the other four compounds. In conclusion, P450 and UGT genes from S. exigua were identified, and different responses to abamectin suggest a different mechanism for insecticide detoxification.

A method for determination of attitude of the airborne remote sensing platform is proposed. In this method, the attitude of airborne platform can be obtained on-line by following four steps: (i) recording the attitude of the platform at time t 0 , which serves as the initial attitude; (ii) starting from t 0 , taking aerial images using the dedicated camera fixed on the airborne platform at time t k ( k = 0, 1, 2, ...) regularly and noting as the k th ( k = 0, 1, 2, ...) aerial image; (iii) calculating the attitude change between every two adjacent images; (iv) determining the attitude of the platform at a time according to the initial attitude and the related attitude change. Simulation results proves the theoretical feasibility of the method. The attitude error sources are also be analysed. The attitude accuracy is proportional to focal length, field angle and matching accuracy of the corresponding points. Physical experiments were carried out to illustrate the feasibility and effectiveness of the proposed method.

Loop closure detection is one of the important components of Visual SLAM. It can reduce the accumulating drift of visual odometer if the loops are detected correctly. Traditional loop closure detection mainly relies on the traditional algorithms to extract feature points. However, these algorithms are difficult to adapt to the complex and dynamic environment, e.g. illumination changes. In this paper, a new approach of loop closure detection is proposed. It learns inner structures from raw data using neural networks named SuperPoint. SuperPoint is designed to detect interest points and corresponding descriptors at the same time. The method clusters the feature descriptors as words using K-means and converts descriptors of each tested image into a vector by comparing the similarity between the descriptors and words. It measures the similarity of the images by calculating the cosine similarity of the corresponding vectors. A series of experiments on New College and City Center are demonstrated to evaluate the performance of the proposed method. The average precision of loop closure detection based on SuperPoint increases by 28% and 122% respectively compared with that based on SIFT and ORB under the same conditions. It is proved that the method based on SuperPoint is possible to detecti loops at a satisfactory precision compared with the traditional method based on ORB or SIFT.

An adaptive quaternion particle filter (QPF) based on the generalized likelihood ratio test (GLRT) is proposed for aircraft attitude estimation in the presence of an anomalous measurement. The framework of the QPF is employed to guarantee quaternion normalization. To cope with an anomalous measurement when interference occurs, the proposed algorithm uses the GLRT to detect an anomalous measurement and determine the interference source. An adaptation scheme is used to tune the measurement noise covariance matrix after the interference source has been determined so that the algorithm can remain robust against interference. Numerical simulations are carried out to evaluate the performance of the proposed algorithm and compare it with the QPF algorithm. The results show that the proposed algorithm outperforms the standard one in attitude estimation accuracy under anomalous measurement conditions.

Glutathione S-transferases (GSTs) are a family of multifunctional enzymes that are involved in detoxification of electrophilic toxic compounds. Although the co-induced expression of GST genes by insecticides in insects has been documented in recent years, the underlying regulatory mechanisms are not understood. In this study, a total of thirty-one cytosolic S. exigua GSTs (SeGSTs) was cloned and identified. The bioinformatics and gene expression patterns were also analyzed. Out of them, SeGSTe9, SeGSTs6, SeGSTe1, SeGSTe6, SeGSTe8, SeGSTe14, and SeGSTd1 were significantly co-expressed following exposure to three insecticides (lambda-cyhalothrin, chlorpyrifos and chlorantraniliprole). The analysis of upstream sequences revealed that all of these seven SeGSTs harbored CncC/Maf binding site. The luciferase reporter assay showed that the pGL3-SeGST promoter construct exhibited a significant increase in luciferase activities after exposure to insecticides, and mutation of CncC/Maf binding site diminish the induction effect. These data indicate that CncC/Maf pathway regulates the co-expression of GST genes in response to different insecticides in S. exigua. Insecticides significantly enhanced the ROS content and treatment with the ROS inhibitor N-acetylcysteine (NAC) decreased the insecticide-induced luciferase activities of the PGL3-GSTe6 promoter construct, but not the CncC-mutated construct. These results indicate that ROS mediates GST gene expression after exposure to insecticides through CncC/Maf pathway. Overall, these data show that insecticides induce the co-expression of glutathione S-transferases through the ROS/CncC pathway in S. exigua.

An improved Quaternion Particle Filter (QPF) algorithm is developed to cope with the interference of the acceleration in attitude measurement system of the self-balancing robot. The improved QPF algorithm is built based on the framework of standard QPF. The state and measurement model established by quaternion can avoid the linearization procedure, and thus increase the accuracy of estimation. By calculating the residual, the adaptive factor is constructed to adjust the measurement noise covariance of accelerometer and eliminate the interference of acceleration. The characteristics and advantages of the improved QPF algorithm are investigated numerically and experimentally in both static and dynamic scenarios. The results show that the improved QPF performs better in accuracy than the traditional method in attitude estimation when the robot is under an accelerated phase.

The metaflumizone, which belongs to the class of voltage-dependent sodium channel blockers, was registered to control Spodoptera exigua on vegetables in China in 2009. The present study revealed S. exigua has developed high resistance to this novel chemistry insecticide shortly after 2-3 years application in Guangdong Province of China. The metabolic mechanisms for metaflumizone resistance in this insect were analysed. The inhibitor of esterases greatly potentiates the toxicity of this chemical against the field resistant populations. The synergism ratio is 5.7 and 3.4-fold for S. exigua collected from Huizhou, Guangdong Province in 2011 and 2012, respectively. The activity of esterases in field populations (HZ12) is also significantly greater than that in the susceptible strain, and further significantly increased by challenge with metaflumizone for 3 generations. However, the inhibitor of P450s or GSTs only has slight synergism on metaflumizone toxicity against resistant populations, and there are no obvious differences in activities of P450s or GSTs between resistant populations and the susceptible strain. These results suggest that esterases might take pivotal role in conferring metabolic resistance to metaflumizone in the field populations of S. exigua, and P450s or GSTs are not involved in this resistance. Moreover, flavin-dependent monooxygenases (FMOs) are discovered to involve in metaflumizone resistance in the field populations of S. exigua. The FMO inhibitor, methimazole, potentiates metaflumizone toxicity in resistant larva of this species substantially. The synergism ratios for methimazole in resistant populations HZ11 and HZ12 were 3.1 and 1.9, respectively. Enzymatic assays also revealed higher FMO activities in resistant populations than in the susceptible strain, and successive selection with metaflumizone further increased the FMO activity in the field resistant population, but not significantly. The higher FMO activities in the older larval stages and in the larval midgut signify the importance of FMO in the detoxification of xenobiotic from food sources. The synergism assay and FMO activity analysis suggest that FMO contributes to metaflumizone detoxification in resistant populations of S. exigua and conferred metaflumizone resistance in S. exigua. A novel mechanism for insecticide resistance by insect was proposed.

Attitude measurement error is one of the main factors that deteriorates the imaging accuracy of laser scanning. In view of the fact that the inertial navigation system (INS) with high accuracy is very costly, a low-cost but effective GPS-aided method based on the target images is proposed to measure the platform attitude angles in this paper. Based on the relationship between the attitude change of the platform and the displacement of two adjacent images, the attitude change can be derived by the proposed method. To quantitatively evaluate the accuracy of the platform attitude angles measured by the proposed method, an outdoor experiment was carried out in comparison with the GPS/INS method. The preliminary results demonstrated that the measurement accuracy using the proposed method was better than 0.05° (RMSE).

In order to analyze the impact of attitude measurement errors (roll, pitch and yaw errors) on the positioning accuracy of laser footprints, the positioning principle of airborne Light Detection And Ranging (LiDAR) was analyzed and the transformation relationship between the attitude measurement errors and the positioning errors of laser footprints was deduced. Considering the actual complex terrain, three different terrains were simulated to analyze the influence of attitude measurement errors on the positioning accuracy of laser footprints. After simulating calculations, some conclusions can be obtained, such as the impact of the roll angle error on the positioning accuracy of laser footprints is the most significant, the impact of the yaw angle error is minimal. And the results of the study will offer a theory foundation for the study of the positioning accuracy of laser footprints and practical application.

According to the attitude determination method based on aerial images, an INS/GPS/aerial-image integrated attitude determination system solutions was proposed to improve the airborne platform attitude determination accuracy and reliability. A federal Unscented Kalman Filter (UKF) algorithm based on optimization information distribution factor was used in the INS/GPS/aerial-image integrated system. The integrated system included INS/GPS and INS/aerial-image two subsystems, the outputs from two subsystems were fused in the main filter. Finally, optimal parameters of the system state estimation were obtained. Experimental results show that the proposed method well solves the error divergence problem over time with INS, and prevents the truncation error generated by EKF algorithm. The integrated attitude determination system can get higher precision and reliability.

In this paper, an improved image matching methods based on Speeded Up Robust Features (SURF) algorithm was proposed to calculate the attitudes of the aircraft platform. Firstly, SURF algorithm was used to extract series of the interest points of two selected images. Then the improved nearest neighbor matching method based on KD-tree was used to get the pairs of the matching interest points. And the RANdom SAmple Consensus (RANSAC) algorithm was used to remove the error pairs of matching interest points. Finally, the transformation matrix between the two selected images was established to obtain the attitude angles. In order to validate the effectiveness, two images were utilized to implement the proposed methods. The experimental results show that the algorithm has the advantage in both accuracy and time-consuming, which is helpful to improve the performance of image navigation.

An outlier detection method is proposed based on the kernel density estimation for removing the outliers in airborne LiDAR point clouds. The point cloud is divided into many blocks. Then, in each block, the kernel probability density of the height values of all points is estimated. Two elevation thresholds, one for low outliers and one for high outliers, are selected based on the values of the probability density and the values of elevation. The computation is simplified in complexity for the method doses not focus on the calculation of individual points. Two datasets were utilized to test our method. This method combines distance-based method with density-based method. Experiments showed that our proposed method had good performance.

The impacts of various control errors and measurement errors of airborne LiDAR on laser point cloud were studied. Firstly, the principle of the Palmer-scan airborne LiDAR was analyzed. Then the transformation formulas, from the control errors and measurement errors of various parameters, such as attitude angles, flight trajectory and scan angle in airborne LiDAR system, to the three-dimensional (3D) coordinate errors of the point cloud, were derived. Finally, by numerical simulation, two terrain models (planar and hemisphere terrains) were established, and the impacts of the control errors and measurement errors of flight trajectory and attitude angles on the laser point cloud were analyzed. Results show that the control errors mainly cause the distribution region shifting and the point density decreasing of the laser point cloud, while the measurement errors mainly result in the 3D coordinate accuracy decreasing of the laser point cloud. The combining impact of the control errors and measurement errors results in the distortion increasing of the reconstructed 3D surface models relative to the surveyed terrain.

A new method of parameters design for aerial survey based on the laser footprint distribution of airborne LiDAR was proposed. In order to implement the method of parameters design, the relationship maps between the distribution of laser footprints and different parameters, respective the parameters of laser beam, flight and laser scanning system were created. Using the actual parameters and the independent variable of the number of scanning strips, the best aerial survey parameters and flight routes were designed. It is an important method to achieve the least scanning time cost as a dependent variable.

The influence of random attitude measurement errors of the GPS/INS integrated system on the laser point cloud and the three-dimensional (3D) surface image reconstructed by the airborne laser scanner was studied. The mapping relationship between the attitude measurement errors and the positioning errors of the laser footprints was derived. By numerical simulation, three common terrains, i.e. a planar, a rectangular, and a hemisphere terrain, were simulated, and the impacts of the random attitude measurement errors on the laser point clouds and the reconstructed 3D surface images of the three terrains were analyzed, respectively. Simulation results show that the random attitude measurement errors decrease the positioning accuracy of the laser point clouds, further directly deteriorating the 3D surface image. The greater the random attitude measurement errors are, the greater the caused 3D imaging distortion.

In this paper, the impacts of the random measurement errors on airborne laser scanning (ALS) accuracy were studied. Firstly, the transformation formulas from measurement parameters to the coordinates of laser footprints were derived and the factors affecting ALS accuracy were analyzed. According to the actual characteristics of these factors, 2000 sets of experimental data of the random measurement errors were simulated and the errors of three-dimensional (3D) coordinates of the laser footprints were calculated. Then, the simulated experimental error data were processed by using the linear least squares regression method to get the standardized regression coefficients. According to the obtained standardized regression coefficients, the impacts of various random measurement errors on the 3D coordinate errors were evaluated quantitatively, and the variation of the impacts with increasing flight height was studied. Analysis results provide an important basis for error budget of ALS system and improvement of ALS accuracy.

A method for correcting the geometric distortion of the images scanned sinusoidally by an atomic force microscope (AFM) was proposed. The generation mechanism of the geometric distortion in sinusoidally scanned AFM images was analyzed. Based on the relationship between the coordinates of uniformly scanned points and those of sinusoidally scanned points, a transformation formula was obtained for correcting the geometric distortion when the sampling frequency is a constant. By comparing the forward method with the backward method, a hybrid method for correcting the geometric distortion of the sinusoidally scanned images was proposed. This method takes advantages of both the forward method and the backward method, and was proven to be better than either of them. In addition, it is a universal approach to correct the geometric distortion of the images scanned in the sinusoidal mode.

A novel method for measuring the aerodynamic deformation of wings during fluttering in real-time by using a two-laser rangefinder is proposed for the first time, in which one laser is fixed above the plane and the other is fixed below the plane. Based on the distances between lasers and the diffuse reflector on wingtip, the wingtip displacement is geometrically calculated. The displacement of a certain point on the surface of the wing is acquired from the database formed in wind tunnel test, including the function of the aerodynamics deformation of wing. The method mentioned above and error analysis is explained by giving a simple two-dimensional example. The method is useful and all-pervading for real-time measurement of deformation of wing during fluttering.

A method for correcting the geometric distortion of sinusoidally scanned images was proposed. The generation mechanism of the geometric distortion in sinusoidally scanned images was analyzed. Based on the relationship between the coordinates of uniformly scanned points and those of sinusoidally scanned points, a transformation formula was obtained for correcting the geometric distortion when the sampling rate was a constant. By comparing the forward method with the inverse method, a hybrid method for correcting the geometric distortion of sinusoidally scanned images was proposed. This method takes advantage of both the forward and inverse methods and was proven to be better than either of them in terms of peak signal-to-noise ratio (PSNR). The time consumed by the hybrid method was between the other two. When a higher PSNR is desired, the hybrid method is recommended if time permits. In addition, it is a universal approach to the correction of geometric distortion of the images scanned in the sinusoidal mode.