Least-squares Matching Research Articles

Measurement of Surface Displacement and Deformation of Mass Movements Using Least Squares Matching of Repeat High Resolution Satellite and Aerial Images

Displacement and deformation are fundamental measures of Earth surface mass movements such as glacier flow, rockglacier creep and rockslides. Ground-based methods of monitoring such mass movements can be costly, time consuming and limited in spatial and temporal coverage. Remote sensing techniques, here matching of repeat optical images, are increasingly used to obtain displacement and deformation fields. Strain rates are usually computed in a post-processing step based on the gradients of the measured velocity field. This study explores the potential of automatically and directly computing velocity, rotation and strain rates on Earth surface mass movements simultaneously from the matching positions and the parameters of the geometric transformation models using the least squares matching (LSM) approach. The procedures are exemplified using bi-temporal high resolution satellite and aerial images of glacier flow, rockglacier creep and land sliding. The results show that LSM matches the images and computes longitudinal strain rates, transverse strain rates and shear strain rates reliably with mean absolute deviations in the order of 10−4 (one level of significance below the measured values) as evaluated on stable grounds. The LSM also improves the accuracy of displacement estimation of the pixel-precision normalized cross-correlation by over 90% under ideal (simulated) circumstances and by about 25% for real multi-temporal images of mass movements.

Development of 3D Image Measurement System and Stereo-matching Method, and Its Archeological Measurement

The three dimensional measurement & modeling system with digital cameras on PC is now making progress and its need and hope is increasingly felt in terrestrial (close-range) photogrammetry for such sectors as cultural heritage preservation, architecture, civil engineering, manufacturing, measurement etc. Therefore, we have developed a system to improve the accuracy of stereo-matching, which is the very core of 3D measurement. As for stereo-matching method, in order to minimize the mismatching and to be robust in geometric distortions, occlusion, as well as brightness change, we invented Coarse-to-Fine Strategy Method by integrating OCM (Orientation Code Matching) with LSM (Least Squares Matching). Thus this system could attain the accuracy of 0.26mm, when we experimented on a mannequin. And when we actually experimented on the archeological ruins in Greece and Turkey, the accuracy was within the range of 1cm, compared with their blue-print plan. Besides, formally workers used to take at least 1.5 month for this kind of survey operation with the existing method, but now workers need only 3 or 4 days. Thus, its practicality and efficiency was confirmed.This paper demonstrates our new system of 3D measurement and stereo-matching with some concrete examples as its practical application.

Interpolation of near offset using surface-related multiples

In this research, we present a seismic trace interpolation method which uses seismic data with surface-related multiples. It is different from conventional seismic data interpolation using information transformation or extrapolation of adjacent channels for reconstruction of missing seismic data. In this method there are two steps, first, we construct pseudo-primaries by cross-correlation of surface multiple data to extract the missing nearoffset information in multiples, which are not displayed in the acquired seismic record. Second, we correct the pseudo-primaries by applying a Least-squares Matching Filter (LMF) and RMS amplitude correction method in time and space sliding windows. Then the corrected pseudo-primaries can be used to fill the data gaps. The method is easy to implement, without the need to separate multiples and primaries. It extracts the seismic information contained by multiples for filling missing traces. The method is suitable for seismic data with surfacerelated multiples.

Optimum estimator for SPOT-pan and ALS-lidar intensity image registration via tie points

The characteristics of a Système Pour d’Observation de la Terre (SPOT) panchromatic image of a geographic area such as an airfield are different from those of an airborne laser scanner lidar intensity image of the same area. This study investigates the feasibility of locating tie points shared by the target (airborne lidar-intensity) and search (spaceborne SPOT-pan) images. At an approximate point position, image segmentation and enhancement are employed so that a pair of target and search window images tend to resemble each other. The similarity is then measured by utilizing a least-squares image matching algorithm which involves variance-component estimation. The proposed method has a 3–15% higher success rate than an equal-weight matching method. Coordinate differences of the conjugate image points serve as reference value to be used in the least-squares collocation method for pixel-by-pixel transformation. The image registration accuracy from a SPOT-pan to a lidar intensity image is estimated to be ±1.0 pixel.

Least-squares Matching with Advanced Geometric Transformation Models

The least-squares matching algorithm (LSM) for area-based image matching is a well known technique in photogrammetry and computer vision since more than two decades. Differences between two or more images can be modelled by estimating geometric and radiometric transformation functions within the functional model. Commonly the affine transformation is used as geometric transformation. Since this approach is not strict in terms of the projective imaging model, it is worthwhile to investigate alternative transformation models. This paper presents an advanced least-squares matching algorithm that uses the projective transformation model and polynomial transformations to handle geometric distortions between the images. The projective approach is geometrically strict as long as object surface and image sensors are planes. The polynomial approach is supposed to be geometrically strict for plane image sensors and non-plane object surfaces. The possibility of this kind of expansions has been mentioned in several papers but up to now no publicly available investigation is known. First results of the new geometric model have been published by the authors in 2008, showing promising effects on non-planar object patches. * Corresponding author

Model-based interferometric interpolation method

We have proposed a two-stage model-based interferometric interpolation method for filling in gaps in marine seismic data. The first stage is creating virtual traces and the second stage is utilizing modified virtual traces for interpolation. There are three steps for creating a virtual trace. First, set the virtual trace’s source and receiver coordinates and retrieve two common-receiver gathers (CRG) from existing data. At least one CRG should be obtained, otherwise, our method cannot be performed. Second, if only one CRG is obtained, then a synthetic CRG should be generated using known velocity model (e.g., water-layer model). Third, the virtual trace is created by summing correlated trace pairs over all identical source positions in two CRGs. When all virtual traces are created, a least-squares matching filter or a nonstationary prediction error filter (PEF) should be used together with virtual traces to do the interpolation. If the trace gap is small or the subsurface geology is simple, the local matching filter is preferred for the improvement of signal-to-noise ratio, otherwise, we need to estimate a PEF from virtual traces and then use this PEF for interpolation. A simple velocity model and Sigsbee2b velocity model are used to validate the effectiveness of our method. Results show that the trace gaps can be kinematically interpolated, but there are still artifacts that are due to the approximations made in our theory.

Comparison of Matching Algorithms for DSM Generation in Urban Areas from Ikonos Imagery

The extraction of the third dimension from remote sensing data is a well known technique. Since in a number of countries aerial images and laser scanner data are unavailable, expensive or classified, stereoscopic high-resolution optical satellite images provide a viable alternative for generating digital surface and digital terrain models. Especially the automatic extraction of highly accurate 3D surface models in urban areas is still a very complicated task due to occlusions, large differences in height and the variety of objects and surface material. In this paper an analysis and a visual and quantitative comparison of three different matching algorithms for generating urban DSMs based on very high-resolution satellite images is presented. The three algorithms are least squares matching (LSM) in a region growing fashion, dynamic programming (DP) and semiglobal matching (SGM). The characteristics of the three algorithms as applied to four different Ikonos stereo pairs with a ground sampling distance of 1 m are shown. The following results were obtained: visually, in the LSM results the shape of the buildings is considerably smoothed. While in the DP results the building shape is sharper, only little detail is visible on the building roofs, and streaking along the epipolar lines causes problems. With SGM more details can be extracted and the results visually have the best quality. Based on reference data for the different test sites, the standard deviation of the building heights determined by LSM and DP is in the range of one pixel or slightly better, while it is in the range of half a pixel for SCM.

Human Body Measurement by Robust Stereo-Matching

We have developed a digital photogrammetry system, which enables us to make all-around 3D measurement using the object pictures obtained through the integrated works of digital cameras, projectors and our specific PC software. The system consists of units, each of which is again consists of two synchronized digital cameras and projectors with PC program.The measuring process is now simplified by making all the operations of orientation and measurement analysis automatic; and this, with a single push of a button. Automation of orientation was realized by creating a calibration box covered by color-coded targets, which enables us to make exterior orientation parameters of the cameras automatically.For stereo-matching, in order to minimize the mismatching, we invented Coarse-to Fine Strategy Method by integrating OCM (Orientation Code Matching) or robust matching with LSM (Least Square Matching). Therefore, improving the accuracy of the initial values of OCM, using LSM for fine measurement and making the involved operations automatic, we enhanced the quality of surface measurement and succeeded to shorten the measuring time considerably.In this paper we are presenting the report on our system of human body measurement and its processing method of stereo-matching, as well as on the result of comparing assessment of each matching method.

円形ターゲットの中心位置の計測手法の比較

A circular target on a plane is projected as an ellipse onto an oblique image. This paper reports an experiment conducted to evaluate measuring methods of elliptical target location by using simulated images of various sizes, eccentricities, and rotation angles of elliptical targets. Three popular measuring methods in digital photogrammetry : unweighted centroid method using a binary image created by thresholding (BCM), weighted centroid method (WCM), and least squares matching (LSM) were investigated. The experiment results show that BCM is robust against flatness and rotation of a target, and image noise. However, BCM cannot produce more accurate measuring results than WCM and LSM. Meanwhile, the results demonstrate that WCM is robust against flatness and rotation of a target, and WCM can achieve the most accurate measurement when a target image has no image noise. However, the measuring error of WCM would be proportional to the magnitude of image noises, and WCM would be unable to provide the best measuring results when a target image has larger image noises. The results indicate that LSM is rather robust against image noise, but very sensitive to flatness and rotation of a target. Moreover, the results show that BCM using an enlarged target image by bi-linear interpolation should be a good measuring method on accuracy and robustness against flatness and rotation of a target, and image noise.

Comparison of information and variance maximization strategies for characterizing neural feature selectivity

This paper compares several statistical methods for analyzing neural feature selectivity with natural stimuli. Despite the non-Gaussian character of correlations in natural stimuli, several relevant stimulus dimensions can be found by maximizing either information or, as is demonstrated here, variance. In the case of information, the relevance of each dimension is quantified by a Kullback-Leibler divergence between the full input probability distribution and that across inputs associated with positive neural responses, both projected onto that dimension. We demonstrate that least-square matching of the nonlinear prediction based on several dimensions relevant to the recorded spike trains yields an optimization scheme similar to information maximization. The relevant dimensions are found as those that capture the most variance in neural response. The variance along a stimulus dimension is given by a Rényi divergence of order 2 instead of the Kullback-Leibler divergence used for maximizing information. Statistical errors expected for the two schemes are shown to be similar through both analytical and numerical calculations. However, in the asymptotic limit of large spike numbers, maximizing information results in smaller errors than variance optimization. Numerical simulations for model cells with different noise levels show that this trend persists, and possibly increases, when the number of spikes decreases. This makes the problem of finding relevant dimensions one of the examples where information-theoretic approaches are no more data limited than the variance-based measures. Variance and information optimization also outperform methods based on the spike-triggered average for all numbers of spikes and neural noise levels.

テンプレートマッチングにおけるサブピクセル推定法の精度比較

Precise results of matching are required to obtain the precise locations of objects using stereo images. Accordingly, sub-pixel estimation of the corresponding position in area-based matching is often conducted. Several methods to obtain sub-pixel estimation in area-based matching have been proposed. However, there are few reports on accuracy comparison of those methods. Therefore, we performed an experiment in order to investigate accuracy of sub-pixel estimation methods in area-based matching by using 54 diverse images. Our study focused on two popular methods in digital photogrammetry: cross correlation method with fitting a second order surface by using normalized cross correlation coefficients (CMF), and least squares matching (LSM) . The experiment results demonstrate that the accuracy of sub-pixel estimation methods in area-based matching varies considerably with the properties of the image. Furthermore, the experiment results show that LSM can estimate the corresponding position more accurately than CMF. The estimation error of LSM would be average half of that of CMF.

CLASSIFICATION OF OBJECTS IN AN ACOUSTIC WAVEGUIDE BY INVERSION OF THE FARFIELD DATA

In this paper we investigate the unknown body problem in a waveguide. The Rayleigh conjecture states that every point on an illuminated body radiates sound from that point as if the point lies on its tangent sphere. This conjecture is the cornerstone of the intersecting canonical body approximation ICBA for solving the unknown body inverse problem. Therefore, the use of the ICBA requires that an analytical solution be known exterior to the sphere in the waveguide, which leads us to analytically compute the exterior solution for a sphere between two parallel plates. A least-squares matching of theoretical acoustic fields against the measured, scattered field permits a reconstruction of the unknown object.

Stereo cloud‐top height retrieval with ASTER and MISR

The combined multi‐view photogrammetric retrieval of cloud‐top height (CTH) from the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) and the Multi‐angle Imaging SpectroRadiometer (MISR) is discussed. Although ASTER was designed mainly for land applications, the synergistic use of MISR and ASTER is shown to be valuable for 3D cloud analysis. A new cloud‐adapted matching algorithm based on least‐squares matching (LSM) was used for the photogrammetric processing of both MISR and ASTER. The methods were applied to an ASTER scene over Zürich‐Kloten, Switzerland, in April 2002, which was acquired on‐demand. This case study, with coincident ASTER, MISR and Meteosat‐6 10‐minute Rapid Scans, is treated in detail. As a matching validation option it is shown that, by chance, the cloud motion error for the MISR An‐Aa and ASTER stereo CTHs is approximately the same, independent of the actual cloud height and cloud motion. It was therefore possible to evaluate the accuracy of the MISR An‐Aa matching versus the ASTER matching, independent of artefacts due to the subsequent wind correction. The results were also compared to the operational MISR L2TC stereo CTH results. The results obtained by each of these methods yield consistent values for CTH (uncorrected for wind motion).

Numerical analysis of surface plasmons excited on a thin metal grating

The authors numerically investigated the characteristics of surface plasmons excited on a thin metal grating placed in planer or conical mounting. After formulating the problem, the solution method, Yasuura’s method (a modal expansion approach with least-squares boundary matching) was described. Although the grating is periodic in one direction, coupling between TE and TM waves occurs because arbitrary incidence is assumed. This requires the employment of both TE and TM vector modal functions in the analysis. Numerical computations showed: (1) the excitation of surface plasmons with total or partial absorption of incident light; (2) the resonance character of the coefficient of an evanescent order that couples the plasmon surface wave; (3) the field profile and Poynting’s vector. The plasmons excited on the surfaces of a thin metal grating are classified into three types: SISP, SRSP, and LRSP, different from each other in the feature of field profile and energy flow. In addition, the eigenvalue of a plasmon mode was obtained by solving a sequence of diffraction problems with complex-valued angles of incidence and using the quasi-Newton algorithm to predict the real angle of incidence at which the absorption occurs.

Automatic Registration of INSAR Data Based on Least-Square Matching and Multi-Step Strategy

Interferometric Synthetic Aperture Radar (INSAR) allows for production of high resolution DEM and detection of small earth deformation using multiple-pass SAR data sets. The automatic algorithm for registration of the INSAR data is one of the key points for improving both accuracy and efficiency. In this paper, an automatic approach based on multi-step matching strategy is presented and only intensity components of SLC images are involved in relevant computation. Both probability relaxation and Least-Square Matching (LSM) algorithms have been introduced to maintain reliability and improve accuracy. All the procedures could be automatically implemented. Primary results are promising and reveal the potential for operational INSAR data processing.

平面ステレオマッチング手法

This paper proposes a new type of stereo matching algorithm called “Stereo Plane Matching”. Stereo plane matching adopts least square matching (LSM) method under the constraint that all points in an area specified by a polygon should lie on a same plane. This algorithm stands on the fact that correspondence between stereo images becomes 2-D projective transformation (homography) within an area where a common plane is projected. Three corresponding point pairs on stereo image pair are used for parameterization of geometry of a target plane, which allows computation of homography within the polygon. The most powerful feature of this algorithm is that it can impose geometrical constraint in planar direction and position. For example, the target plane can be fixed in horizontal or vertical direction, as well as in other specified direction in 3-D space. Another feature is that it can be applied to unrectified stereo pair, so far as its orientation parameters are known. Experimental results show that this algorithm can measure oblique roof or vertical wall of a building.

Estimate of the three-loop [formula omitted] contribution to σ( WL+WL−→ ZLZL)

The three-loop contribution to the MS single-Higgs-doublet standard-model cross-section σ( W L + W L −→ Z L Z L ) at s=(5 M H ) 2 is estimated via least-squares matching of the asymptotic Padé-approximant prediction of the next order term, a procedure that has been previously applied to QCD corrections to correlation functions and decay amplitudes. In contrast to these prior applications, the expansion parameter for the W L + W L −→ Z L Z L process is the non-asymptotically-free quartic scalar-field coupling of the standard model, suggesting that the least-squares matching be performed over the “infrared” μ 2⩽ s region of the scale parameter. All three coefficients of logarithms within the three-loop term obtained by such matching are found to be within 6.6% relative error of their true values, as determined via renormalization-group methods. Surprisingly, almost identical results are obtained by performing the least squares matching over the μ 2⩾ s region.

Fully automatic 3D feature-based registration of multi-modality medical images

In this paper, we present an automated multi-modality registration algorithm based on hierarchical feature extraction. The approach, which has not been used previously, can be divided into two distinct stages: feature extraction (edge detection, surface extraction), and geometric matching. Two kinds of corresponding features — edge and surface — are extracted hierarchically from various image modalities. The registration then is performed using least-squares matching of the automatically extracted features. Both the robustness and accuracy of feature extraction and geometric matching steps are evaluated using simulated and patient images. The preliminary results show the error is on the average of one voxel. We have shown the proposed 3D registration algorithm provides a simple and fast method for automatic registering of MR-to-CT and MR-to-PET image modalities. Our results are comparable to other techniques and require no user interaction.

Simultaneous measurement of particle and fluid velocities in a plane mixing layer with dispersion

An optical method is presented to measure simultaneously and separately the velocity field of both phases in particle-laden flows. The fluid is seeded with flow markers which are fluorescent at a specific wavelength and thus can be distinguished from the sediment particles by applying an optical filter. The motion of each phase is recorded by two CCD cameras, which are triggered such that a high correlation between subsequent images is guaranteed. The velocity fields are determined by means of least-square matching of a group of particles. The whole set-up was applied to study the sedimentation of particles through a rapidly evolving mixing layer.

Measurement of velocity and velocity derivatives based on pattern tracking in 3D LIF images

Pattern tracking in consecutive 3D LIF images based on least squares matching (LSM) of grey levels has been developed recently for velocity and velocity gradient measurements. The shortcomings of this method are clearly shown. The present article presents an improvement on this method by introducing a local multi-patch (LMP) technique through the LSM approach. The method is validated using the flow field of a turbulent channel flow obtained by direct numerical simulation (DNS) and a synthetic image with grey-level patterns. The results show that LMP matching allows the determination of the velocity and the velocity gradient fields with high accuracy including the second derivatives. Measurements of a round non-buoyant jet are presented which demonstrate the good performance of the method when applied under laboratory conditions. This method can also be applied on two-dimensional images provided that the flow is strictly two-dimensional.