Similarity Transformation Model Research Articles

A complete solution of an improved universal 3D coordinate similarity transformation model

When linearizing three-dimensional (3D) coordinate similarity transformation model with large rotations, we usually encounter the ill-posed normal matrix which may aggravate the instability of solutions. To alleviate the problem, a series of conversions are contributed to the 3D coordinate similarity transformation model in this paper. We deduced a complete solution for the 3D coordinate similarity transformation at any rotation with the nonlinear adjustment methodology, which involves the errors of the common and the non-common points. Furthermore, as the large condition number of the normal matrix resulted in an intractable form, we introduced the bary-centralization technique and a surrogate process for deterministic element of the normal matrix, and proved its benefit for alleviating the condition number. The experimental results show that our approach can obtain the smaller condition number to stabilize the convergence of the interested parameters. Especially, our approach can be implemented for considering the errors of the common and the non-common points, thus the accuracy of the transformed coordinates improves.

An Improved Image Registration Method Using E-SIFT Feature Descriptor with Hybrid Optimization Algorithm

Automatic image registration of the satellite images aids in the field of the computer-aided research. In the recent years, image registration is useful in the environment monitoring and the agriculture purpose. In this work, the automatic image registration model has been developed through the novel hybrid optimization algorithm. This work mainly concentrates in image registration of the hyperspectral images arriving from the satellite. The proposed automatic image registration model uses the input image and the reference image for the registration purpose. From both the images, the E-SIFT features are extracted and given to the point matching algorithm for the keypoint detection. Then, the similarity transformation model gets the keypoints and makes the input images to the original position. Here, the weighted average model is developed for the image fusion, and the weight score for the image fusion is selected optimally through the proposed salp swarm-crow search algorithm (SS-CSA). For the experimentation, the proposed scheme uses the standard database having the hyperspectral satellite images. The simulation results reveal that the proposed image registration scheme with the SS-CSA algorithm has progressed better than the existing techniques with 0.711788 and 0.993602 for the RMSE and NCC, respectively.

A novel extended phase correlation algorithm based on Log-Gabor filtering for multimodal remote sensing image registration

ABSTRACT Automatic registration of multimodal remote sensing images, which is a critical prerequisite in a range of applications (e.g. image fusion, image mosaic, and image analysis), continues to be a fundamental and challenging problem. In this paper, we propose a novel extended phase correlation algorithm based on Log-Gabor filtering (LGEPC) for the registration of images with nonlinear radiometric differences and geometric differences (e.g. rotation, scale, and translation). Our algorithm focuses on two problems that the traditional extended phase correlation algorithms cannot well handle: 1) significant nonlinear radiometric differences and 2) large-scale differences between image pairs. After an over-complete multi-scale atlas space of the original image is built based on the filtered magnitudes obtained by using Log-Gabor filters with different central frequencies, the phase correlation of the single scale images is extended by LGEPC to atlases phase correlation, which is conducive to solving the problem of large scale and rotation differences between the image pairs. Subsequently, LGEPC eliminates the interface of the significant nonlinear radiometric differences by superimposing multi-scale geometric structural spectra and carrying out the phase correlation module, so that the translation can be well determined. Our experiments on synthetic images demonstrated the rationality and effectiveness of LGEPC, and the experiments on a variety of multimodal images confirmed that LGEPC can ideally achieve pixel-wise registration accuracy for multimodal image pairs that conform to the similarity transformation model.

Iterative solution of Helmert transformation based on a unit dual quaternion

The rigid motion involving both rotation and translation in the 3D space can be simultaneously described by a unit dual quaternion. Considering this excellent property, the paper constructs the Helmert transformation (seven-parameter similarity transformation) model based on a unit dual quaternion and then presents a rigid iterative algorithm of Helmert transformation using a unit dual quaternion. Because of the singularity of the coefficient matrix of the normal equation, the nine parameter (including one scale factor and eight parameters of a dual quaternion) Helmert transformation model is reduced into five parameter (including one scale factor and four parameters of a unit quaternion which can represent the rotation matrix) Helmert transformation one. Besides, a good start estimate of parameter is required for the iterative algorithm, hence another algorithm employed to compute the initial value of parameter is put forward. The numerical experiments involving a case of small rotation angles i.e. geodetic coordinate transformation and a case of big rotation angles i.e. the registration of LIDAR points are studied. The results show the presented algorithms in this paper are correct and valid for the two cases, disregarding the rotation angles are big or small. And the accuracy of computed parameter is comparable to the classic Procrustes algorithm from Grafarend and Awange (J Geod 77:66–76, 2003), the orthonormal matrix algorithm from Zeng (Earth Planets Space 67:105, 2015), and the algorithm from Wang et al. (J Photogramm Remote Sens 94:63–69, 2014).

Coordinate transformation with variable number of parameters

Similarity transformation model does not provide a satisfactory solution for non-uniformly deformed systems because it allows only for a uniform scale and right angles. Instead, an affine model can be used, since it characterizes non-uniform dilatations and obliquity of the three axes. The general affine transformation contains 12 parameters. Nonetheless, it is not always necessary to use them all. The question of how many parameters should take part in the transformation and in what combinations is examined in the paper. In order to choose the proper transformation, a refined AIC is proposed. The paper also presents how to conduct the conversion of parameters between different coordinate systems with reference to the invariance property of coordinate transformation. To demonstrate the impact of using variable number of parameters and to observe the influence of coordinate systems on the transformation outcome, we use a network of 18 permanent GNSS stations in Israel as a case study.

THE ONE TO MULTIPLE AUTOMATIC HIGH ACCURACY REGISTRATION OF TERRESTRIAL LIDAR AND OPTICAL IMAGES

Abstract. The registration of ground laser point cloud and close-range image is the key content of high-precision 3D reconstruction of cultural relic object. In view of the requirement of high texture resolution in the field of cultural relic at present, The registration of point cloud and image data in object reconstruction will result in the problem of point cloud to multiple images. In the current commercial software, the two pairs of registration of the two kinds of data are realized by manually dividing point cloud data, manual matching point cloud and image data, manually selecting a two – dimensional point of the same name of the image and the point cloud, and the process not only greatly reduces the working efficiency, but also affects the precision of the registration of the two, and causes the problem of the color point cloud texture joint. In order to solve the above problems, this paper takes the whole object image as the intermediate data, and uses the matching technology to realize the automatic one-to-one correspondence between the point cloud and multiple images. The matching of point cloud center projection reflection intensity image and optical image is applied to realize the automatic matching of the same name feature points, and the Rodrigo matrix spatial similarity transformation model and weight selection iteration are used to realize the automatic registration of the two kinds of data with high accuracy. This method is expected to serve for the high precision and high efficiency automatic 3D reconstruction of cultural relic objects, which has certain scientific research value and practical significance.

The 2D time-dependent similarity transformation model as a tool for deformation monitoring

Besides the methodology of triangulation and geodetic networks nowadays, the permanent stations of satellite receivers exist, giving extra asset to geodetic daily practice. Permanent stations perform observations incessantly for the visible satellites. However, the coordinates of these stations are often changing over time due to geophysical and tectonic processes. Consequently, these changes are perceived to modern observations. So, along with the coordinates of geodetic points in a given epoch, their changes over time (e.g. the velocities of their movements) are also considered. Furthermore, any change to the reference system definition or/and to the network’s geometry can significantly impact the estimated coordinates and velocities. This paper investigates the reference datum definition problem (or datum problem, or zero order design problem) in a such network over time, which is later generalized for the study of the deformation control-networks. Emphasis is given to techniques of time-dependent 2D transformation models, with numerical tests on a simulation network.

Video stabilisation with total warping variation model

This study proposes a robust approach to stabilise videos with a new variational minimising model. In video stabilisation, accumulation error often occurs in cascaded transformation chain-based methods. To alleviate accumulation error, a new total warping variation (TWV) model is proposed, which describes the smoothness of stabilised camera motion and calculates all the warping transformations efficiently. After estimating original motion parameters based on a 2D similarity transformation model, the corresponding warping parameters are calculated under the TWV minimising framework, where the separable property of the motion parameters is utilised to obtain a closed-form solution. The proposed method provides robust, smooth and precise motion trajectories after stabilisation. Furthermore, an iterative TWV method is introduced to reduce high-frequency jitters as well as low-frequency motions. Moreover, an online TWV method is presented for a long video sequence streaming by adopting a sliding windowed approach. Experimental results on various shaky video sequences show the effectiveness of the proposed method.

Analysis of Methods for Ellipsoidal Height Estimation – The Case of a Local Geodetic Reference Network

Ghana’s local geodetic reference network is based on the War Office 1926 ellipsoid with data in latitude, longitude and orthometric height without the existence of ellipsoidal height. This situation makes it difficult to apply the standard forward transformation equation for direct conversion of curvilinear geodetic coordinates to its associated cartesian coordinates (X, Y, Z) in the Ghana local geodetic reference network. In order to overcome such a challenge, researchers resort to various techniques to obtain the ellipsoidal height for a local geodetic network. Therefore, this paper evaluates, compares, and discusses different methods for estimating ellipsoidal height for a local geodetic network. The investigated methods are the Abridged Molodensky transformation model, Earth Gravitational Model, and the Orthometric Height approach. To evaluate these methods, their estimated local ellipsoidal height values were implemented in the seven-parameter similarity transformation model of Bursa-Wolf. The performance of each of the methods was assessed based on statistical indicators of Mean Square Error (MSE), Mean Absolute Error (MAE), Horizontal Position Error (HE) and Standard Deviation (SD). The statistical findings revealed that, the Abridged Molodensky model produced more reliable transformation results compared with the other methods. It can be concluded that for Ghana’s local geodetic network, the most practicable method for estimating ellipsoidal height is the Abridged Molodensky transformation model. Keywords: Abridged Molodensky Model, Earth Gravitational Model, Orthometric Height, Geodetic Network

Hybridized centroid technique for 3D Molodensky-Badekas coordinate transformation in the Ghana geodetic reference network using total least squares approach

The Molodensky-Badekas model is one of the similarity transformation models used in Ghana for transferring Global Positioning System (GPS) coordinates from the geocentric World Geodetic System 1984 (WGS 84) ellipsoid to the local non-geocentric coordinate system, and vice versa. The objective of the Molodensky-Badekas model is to introduce a centroid to cater for the correlation that exists between the parameters when used over a small portion on the earth surface. However, the Molodensky-Badekas model performance depends on a particular centroid method adopted and the adjustment technique used. By virtue of literature covered, it was realised that the arithmetic mean centroid has been the most widely used. In view of this, the present study developed and tested two new hybrid centroid techniques known as the harmonic-quadratic mean and arithmetic-quadratic mean centroids. The proposed hybrid approaches were compared with the geometric mean, harmonic mean, median, quadratic mean and arithmetic mean. In addition, the Total Least Squares (TLS) technique was used to compute the transformation parameters with varying centroid techniques to investigate and assess their accuracies in precise GPS datum transformation parameters estimation within the Ghana Geodetic Reference Network. Statistical indicators such as Mean Error (ME), Mean Squared Error (MSE), Standard Deviation (SD), and Mean Horizontal Position Error (MHPE) were used to assess the centroid techniques performance. The results attained show that the Harmonic-Quadratic Mean produced reliable coordinate transformation results within the Ghana geodetic reference network and thus could serve as practical alternative technique to the frequently used arithmetic mean. Keywords: Coordinate transformation, Molodensky-Badekas model, Centroid, Total Least Squares

AUTOMATED MOSAICKING OF MULTIPLE 3D POINT CLOUDS GENERATED FROM A DEPTH CAMERA

Abstract. In this paper, we propose a method for automated mosaicking of multiple 3D point clouds generated from a depth camera. A depth camera generates depth data by using ToF (Time of Flight) method and intensity data by using intensity of returned signal. The depth camera used in this paper was a SR4000 from MESA Imaging. This camera generates a depth map and intensity map of 176 x 44 pixels. Generated depth map saves physical depth data with mm of precision. Generated intensity map contains texture data with many noises. We used texture maps for extracting tiepoints and depth maps for assigning z coordinates to tiepoints and point cloud mosaicking. There are four steps in the proposed mosaicking method. In the first step, we acquired multiple 3D point clouds by rotating depth camera and capturing data per rotation. In the second step, we estimated 3D-3D transformation relationships between subsequent point clouds. For this, 2D tiepoints were extracted automatically from the corresponding two intensity maps. They were converted into 3D tiepoints using depth maps. We used a 3D similarity transformation model for estimating the 3D-3D transformation relationships. In the third step, we converted local 3D-3D transformations into a global transformation for all point clouds with respect to a reference one. In the last step, the extent of single depth map mosaic was calculated and depth values per mosaic pixel were determined by a ray tracing method. For experiments, 8 depth maps and intensity maps were used. After the four steps, an output mosaicked depth map of 454x144 was generated. It is expected that the proposed method would be useful for developing an effective 3D indoor mapping method in future.

AUTOMATED MOSAICKING OF MULTIPLE 3D POINT CLOUDS GENERATED FROM A DEPTH CAMERA

In this paper, we propose a method for automated mosaicking of multiple 3D point clouds generated from a depth camera. A depth camera generates depth data by using ToF (Time of Flight) method and intensity data by using intensity of returned signal. The depth camera used in this paper was a SR4000 from MESA Imaging. This camera generates a depth map and intensity map of 176 x 44 pixels. Generated depth map saves physical depth data with mm of precision. Generated intensity map contains texture data with many noises. We used texture maps for extracting tiepoints and depth maps for assigning z coordinates to tiepoints and point cloud mosaicking. There are four steps in the proposed mosaicking method. In the first step, we acquired multiple 3D point clouds by rotating depth camera and capturing data per rotation. In the second step, we estimated 3D-3D transformation relationships between subsequent point clouds. For this, 2D tiepoints were extracted automatically from the corresponding two intensity maps. They were converted into 3D tiepoints using depth maps. We used a 3D similarity transformation model for estimating the 3D-3D transformation relationships. In the third step, we converted local 3D-3D transformations into a global transformation for all point clouds with respect to a reference one. In the last step, the extent of single depth map mosaic was calculated and depth values per mosaic pixel were determined by a ray tracing method. For experiments, 8 depth maps and intensity maps were used. After the four steps, an output mosaicked depth map of 454x144 was generated. It is expected that the proposed method would be useful for developing an effective 3D indoor mapping method in future.

External error modelling with combined model in terrestrial laser scanning

Terrestrial laser scanning (TLS) is a promising tool in geodetic applications. Data quality of outdoor TLS measurements is considerably limited by external errors caused by atmospheric variations and object related factors. In this study, external models related to atmospheric refraction, beam wander and incidence angle were introduced and integrated into a seven-parameter similarity transformation (7PST) model to compose a combined model. The combined model was rigorously adjusted by an iterative Gauss–Helmert (GH) model primarily to estimate external calibration parameters and transformation parameters simultaneously. In the application on a dam surface, a t-test showed that a significant external calibration parameter was the range scale, which mainly corresponded with the incidence angle model. The precision of estimated representative points was improved by approximately 50% with the proposed method. The presented models show a great potential for detecting external errors and registering multiple scans in outdoor applications.

A similarity transformation of velocity field and its application for an in-depth study on laminar free convection heat transfer of gases

An innovative similarity transformation of velocity field is reported for equivalent transformation of governing partial differential equations of laminar free convection. To demonstrate its rationality theoretically, its rigorous theoretical derivation is presented firstly in this work. On this basis, an example is presented with successful application for demonstration of its advantages in in-depth study on free convection heat transfer. The governing ordinary differential equations of laminar free convection equivalently transformed by the innovative similarity transformation are presented. It is seen that by the innovative similarity transformation the variable physical properties are transformed into the forms of the related physical property factors, which are organically coupled in the transformed governing ordinary differential equations. It proves that the innovative similarity transformation is very well suitable for consideration of variable physical properties. Then, a new algorithm is presented to calculate fluids flow and heat transfer of laminar free convection. It contains the theoretical and numerical models on laminar free convection, to consider the variable physical properties, to obtain the system of numerical solutions, and then, to create formalization equations for the convection heat transfer coefficient by means of an optimal curve-fitting approach based on the system of numerical solutions. A system of numerical calculations of the governing ordinary differential equations is presented for the gaseous laminar free convection. A temperature parameter model is induced for convenient and reliable treatment of variable physical properties of gases. The delivered formalization equations of heat transfer coefficient on gaseous free convection have strong theoretical and practical value for heat transfer applications because they are created based on the theoretically reasonable similarity transformation model combined with a better model of consideration of fluid's variable physical properties, accurate numerical solutions, and rigorous formalization equations combined with rigorous theoretical derivation. All these prove that the reported innovative similarity transformation is a better alternative applied for in-depth study on free convection heat transfer.

Fast Automatic Step Size Estimation for Gradient Descent Optimization of Image Registration

Fast automatic image registration is an important prerequisite for image-guided clinical procedures. However, due to the large number of voxels in an image and the complexity of registration algorithms, this process is often very slow. Stochastic gradient descent is a powerful method to iteratively solve the registration problem, but relies for convergence on a proper selection of the optimization step size. This selection is difficult to perform manually, since it depends on the input data, similarity measure and transformation model. The Adaptive Stochastic Gradient Descent (ASGD) method is an automatic approach, but it comes at a high computational cost. In this paper, we propose a new computationally efficient method (fast ASGD) to automatically determine the step size for gradient descent methods, by considering the observed distribution of the voxel displacements between iterations. A relation between the step size and the expectation and variance of the observed distribution is derived. While ASGD has quadratic complexity with respect to the transformation parameters, fast ASGD only has linear complexity. Extensive validation has been performed on different datasets with different modalities, inter/intra subjects, different similarity measures and transformation models. For all experiments, we obtained similar accuracy as ASGD. Moreover, the estimation time of fast ASGD is reduced to a very small value, from 40 s to less than 1 s when the number of parameters is 105, almost 40 times faster. Depending on the registration settings, the total registration time is reduced by a factor of 2.5-7 × for the experiments in this paper.

3D Model Based on Terrestrial Laser Scanning (TLS) Case study: The Cangkuang Temple, Garut District, West Java, Indonesia

The subject of the investigation reported in this paper is the visualization of three-dimensional (3D) surface models in a 3D mapping survey using terrestrial laser scanning (TLS). The Cangkuang Temple nearby Garut City was chosen as the object. The laser technology instruments used were a Topcon GLS-1000 (Geodetic Laser Scanner) and a Topcon IS (Image Station). Twelve points at the same position in each 3D surface model were selected. The coordinate system of the IS was then transformed into the coordinate system of the GLS-1000 using a 3D similarity transformation model. The 3D distances were calculated for each model. Differences in distance were considered as errors in the x, y, and z direction. The standard deviation of the distance differences was ±0.301 m. Some of the distance differences did not fall within the range of tolerances (about 15%). The 3D surface model visualization of the Cangkuang Temple that was created from the GLS-1000 data was more precise than the one created from the IS data. In the future, such 3D surface model visualizations could be used for documentation, preservation and reconstruction of heritage buildings.

REFINING GEOIDAL HEIGHTS COMPUTED BY FULLY-NORMALISED SPHERICAL HARMONICS COEFFICIENTS OF THE EARTH GRAVITATIONAL MODEL EGM2008 BY ADJUSTMENT OF COMBINED GPS/LEVELLING/GEOID NETWORK

The paper presents the combined adjustment of GPS/Levelling bservations on benchmarks with gravimetric geoid heights of the Earth Gravitational Model EGM2008 on both terms of theoretical and practical point of view. For the parametric models to be used, various choice have been tested, namely well-known four- and five-parameter similarity transformation models and 1st, 2nd, 3rd order polynomial ones.The geoid heights of GPS/Levelling points in Vietnam territory were computed by the use of fully-normalised spherical harmonic coefficients of the Earth Gravitational Model (EGM) 2008 up to degree 2190.All five models have been tested employing GPS/Levelling observations, geoid heights from EGM2008 with a uniform accuracy for all height types. The mean deviation can be attributed to some datum bias and other systematic errors which was eliminated by the mathematical models after the fit. From the results which are summarized in the paper, it becomes evident that the best fit is achieved when the 3rd order polynomial model is employed to model the residuals. After the fit by 3rd polynomial model, a reduction by 54 cm and 1cm correspoding to RMS and standard deviation is achieved while the range reduces from 1.783m to 1.714m.ReferencesChristian Hirt, 2012. Efficient and accurate high-degree spherical harmonic synthesis of gravity field functionals at the Earth’s surface using the gradient approach. Journal of Geodesy,Volume 86, pp 729-744, Springer-Verlag.G. Fotopoulos, 2005. Calibration of geoid error models via a combined adjustment of ellipsoidal, orthometric and gravimetric geoid height data.Journal of Geodesy, Volume 79,pp 111-123, Springer-Verlag.C. Kotsakis, M. G. Sideris, 1999. On the adjustment of combined GPS/Levelling/geoid networks.Journal of Geodesy, Volume 73, pp 412- 421, Springer-Verlag.Nikolaos K. Pavlis, Simon A. Holmes, Steve C. Kenyon and John K. Factor, 2012. The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). Journal of Geophysical Research, vol 117.Pavlis NK, Holmes SA, Kenyon SC, Factor JK, 2008. An Earth Gravitational Model to Degree 2160: EGM2008.Presented at the 2008 General Asembly of the European Geosciences Union, Vienna, Austria, April 13-18.N. Tziavos, G. S. Vergos, V. N. Grigoriadis, V. D. Andritsanos, 2012. Adjustment of collocated GPS, geoid and orthormetric height observations in Greece. Geoid or Orthometric height improvement?. International Association of Geodesy Symposia, Volume 136, pp 481-488, Springer Berlin Heidelberg.

Comparative evaluation of registration algorithms in different brain databases with varying difficulty: results and insights.

Evaluating various algorithms for the inter-subject registration of brain magnetic resonance images (MRI) is a necessary topic receiving growing attention. Existing studies evaluated image registration algorithms in specific tasks or using specific databases (e.g., only for skull-stripped images, only for single-site images, etc.). Consequently, the choice of registration algorithms seems task- and usage/parameter-dependent. Nevertheless, recent large-scale, often multi-institutional imaging-related studies create the need and raise the question whether some registration algorithms can 1) generally apply to various tasks/databases posing various challenges; 2) perform consistently well, and while doing so, 3) require minimal or ideally no parameter tuning. In seeking answers to this question, we evaluated 12 general-purpose registration algorithms, for their generality, accuracy and robustness. We fixed their parameters at values suggested by algorithm developers as reported in the literature. We tested them in 7 databases/tasks, which present one or more of 4 commonly-encountered challenges: 1) inter-subject anatomical variability in skull-stripped images; 2) intensity homogeneity, noise and large structural differences in raw images; 3) imaging protocol and field-of-view (FOV) differences in multi-site data; and 4) missing correspondences in pathology-bearing images. Totally 7,562 registrations were performed. Registration accuracies were measured by (multi-)expert-annotated landmarks or regions of interest (ROIs). To ensure reproducibility, we used public software tools, public databases (whenever possible), and we fully disclose the parameter settings. We show evaluation results, and discuss the performances in light of algorithms' similarity metrics, transformation models and optimization strategies. We also discuss future directions for the algorithm development and evaluations.

Comparison of Several Techniques for Fitting of the EGM08 to GPS/Leveling Datum

This paper aims to provide a precise transformation model for the geoid heights between earth geopotential models and regional vertical datum in geodetic applications. With this purpose, Earth Gravitational Model 2008 (EGM08), which is ultra-high-resolution geopotential model, that is complete spherical harmonic degree and order 2190 is considered and fitted to the local vertical datum in three local test areas in west and south of Turkey. The observations at GPS/leveling benchmarks were used for fitting the EGM08 to the local height reference surface and a couple of mathematical methods were evaluated, namely similarity transformation model (STM), polynomial regression model (PRM), least squares collocation (LSC), spline interpolation model (SIM). They are commonly used for corrector surface fitting approaches in height datum studies. Their performances were assessed depending on the statistics at test benchmarks. The results show that fitting of the differences between the GPS/leveling, EGM08-derived geoid heights with LSC, and SIM supplies more accurate solutions than STM and PRM. The accuracies of the achieved models (improved from EGM08 global model) are tested in the several GPS/leveling benchmarks throughout Turkey; the external model accuracy has been estimated as ±4–5 cm. In this aspect, this study will provide benefits as both representing the performance of EGM08 model in given local areas and clarifying the modeling performances of the applied transformation approaches for fitting of EGM08 geoid models to GPS/leveling defined vertical datum.

Model Parameters Estimation for Image Motion Compensation

Fast and optimal motion estimation method is proposed for electronic image stabilization. First, an approach for macro-block judgment is presented. Before motion vectors calculation, gradient information is analyzed, only useful reference blocks that are indispensable for accurate motion estimation are selected, by which the number of macro-blocks for subsequent calculation is reduced. Second, in the block matching, an improved SSDA is used to reduce computing cost. Finally, the affine transformation model and similarity transformation model of image motion are created and using least squares method for solving the optimal estimation of model parameters. Experimental results show the accuracy and fast computing speed of the proposed method.