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Since the inception of coherent waveforms, it has been realized that the effect of non-uniform motion of a non-point like object can induce structure in the return spectrum of the waveform that can be exploited. The non-uniform Doppler spectrum has useful information that can be found in the spreading of the Doppler spectrum for the motion models: acceleration, jerk, quadric, and exponential slowdown as examples well as a characteristic of periodic motion. We illustrate this with examples relevant to automotive radar, tracking meteors with ambient sources, characterizing moving sources and other relevant examples.

Camera calibration is one of the indispensable processes to obtain 3D depth information from 2D images in the field of computer vision. Camera self-calibration is more convenient and flexible, especially in the application of large depth of fields, wide fields of view, and scene conversion, as well as other occasions like zooms. In this paper, a self-calibration method based on two vanishing points is proposed, the geometric characteristic of disappear points formed by two groups of orthogonal parallel lines is applied to camera self-calibration. By using the vectors’ orthogonal properties of connection optical centers and the vanishing points, the constraint equations on the camera intrinsic parameters are established. By this method, four internal parameters of the camera can be solved though only four images taken from different viewpoints in a scene. Compared with the two other self-calibration methods with absolute quadric and calibration plate, the method based on two vanishing points does not require calibration objects, camera movement, the information on the size and location of parallel lines, without strict experimental equipment, and having convenient calibration process and simple algorithm. Compared with the experimental results of the method based on calibration plate, self-calibration method by using machine vision software Halcon, the practicability and effectiveness of the proposed method in this paper is verified.

A fast technique to calculate computer-generated holographic stereograms is proposed. We assume that the three-dimensional image generation by holographic stereograms might be similar to that by multi-view autostereoscopic displays; multiple parallax images are displayed with rays converging to corresponding viewpoints. Therefore, a wavefront whose amplitude is the square root of an intensity distribution of the parallax image and phase is a quadric phase distribution of a spherical wave converging to the viewpoint is considered. Multiple wavefronts are calculated for multiple viewpoints and are summed up to obtain an object wave. The proposed technique was verified experimentally.

Today aircraft attitude measurement technology plays an important role in an aircraft system because it can provide orientation for aircraft in action. Lately star sensor technology used in aircraft attitude measurement has become more and more popular because of its high accuracy, light weight, without attitude accumulation errors and other advantages. There are three main steps for star sensor to measure aircraft attitude, star image locating, star identification and attitude tracking. The latter two steps are based on the accuracy of star image locating. So it's critical to make efforts to advance the accuracy of star image locating. Some imaging errors, such as spherical aberration or coma aberration, also have negative effect on the accuracy of star image locating, of which the effect is necessarily reduced as well. At the beginning of this article, the structure of star sensor hardware is introduced. Secondly three methods for star image locating are described specifically, which are traditional centroid method, Gauss quadric fitting method and improved Gauss quadric fitting method. Subsequently an imaging calibration method is described for the purpose of reducing the effect of imaging errors. Finally the experiment shows that the accuracy of the star sensor is 2-arc-second.

In computer graphics applications, mesh coarsening is an important technique to alleviate the workload of visualization processing. Compared to the extensive works on static model approximation, very little attentions have been paid to animated models. In this paper, we propose a new method to approximate animated models with local area distortion and deformation degree control. Our method uses an improved quadric error metric guided by a local area distortion measurement as a basic hierarchy. Also, we define a deformation degree parameter to be embedded into the aggregated quadric errors, so areas with large deformation during the animation can be successfully preserved. Finally, a mesh optimization process is proposed to further reduce the geometric distortion for each frame. Our approach is fast, easy to implement, and as a result good quality dynamic approximations with well-preserved sharp features can be generated at any given frame.

The complexity of a polygonal mesh model is usually reduced by applying a simpli“cation method, resulting ina similar mesh having less vertices and faces. Although several such methods have been developed, only a fewobserver studies are reported comparing them regarding the perceived quality of the obtained simpli“ed meshes,and it is not yet clear how the choice of a given method, and the level of simpli“cation achieved, in”uence thequality of the resulting model, as perceived by the “nal users. Mesh quality indices are the obvious less costlyalternative to user studies, but it is also not clear how they relate to perceived quality, and which indices bestdescribe the users behavior.Following on earlier work carried out by the authors, but only for mesh models of the lungs, a comparisonamong the results of three simpli“cation methods was performed through (1) quality indices and (2) a controlledexperiment involving 65 observers, for a set of “ve reference mesh models of dierent kinds. These were simpli“edusing two methods provided by the OpenMesh library „ one using error quadrics, the other additionally usinga normal ”ipping criterion „ and also by the widely used QSlim method, for two simpli“cation levels: 50% and20% of the original number of faces. The main goal was to ascertain whether the “ndings previously obtainedfor lung models, through quality indices and a study with 32 observers, could be generalized to other types ofmodels and con“rmed for a larger number of observers. Data obtained using the quality indices and the resultsof the controlled experiment were compared and do con“rm that some quality indices (e.g., geometric distanceand normal deviation, as well as a new proposed weighted index) can be used, in speci“c circumstances, asreasonable estimators of the user perceived quality of mesh models.Keywords: Meshes, perceived quality, evaluation, user study, mesh simpli“cation.

Corneal topography has shown to be an essential tool in the ophthalmology clinic both in diagnosis and custom treatments (refractive surgery, keratoplastia), having also a strong potential in optometry. The post processing and analysis of corneal elevation, or local curvature data, is a necessary step to refine the data and also to extract relevant information for the clinician. In this context a parametric cornea model is proposed consisting of a surface described mathematically by two terms: one general ellipsoid corresponding to a regular base surface, expressed by a general quadric term located at an arbitrary position and free orientation in 3D space and a second term, described by a Zernike polynomial expansion, which accounts for irregularities and departures from the basic geometry. The model has been validated obtaining better adjustment of experimental data than other previous models. Among other potential applications, here we present the determination of the optical axis of the cornea by transforming the general quadric to its canonical form. This has permitted us to perform 3D registration of corneal topographical maps to improve the signal-to-noise ratio. Other basic and clinical applications are also explored.

In our earlier work, a group of error-compensating phase shifting algorithms with known phase step of (pi) /2 has been derived, and the optimal phase steps for Carre algorithm and Stoilov-Dragostinov algorithm were determined and a good and recommended choice is also (pi) /2. This paper gives a further evidence of error compensating merits of these algorithms. Theoretical analysis, as well as computer simulation is given for evaluating the phase errors due to the most common error sources, such as linear and quadric phase shifter errors, quadric detector error and additive random error.

Wide-Angle lenses are not often used for 3D reconstruction tasks, in spite of the potential advantages offered by their increased field-of-view, because existing algorithms for high-distortion lens compensation perform poorly at the image extremities. In this paper, a two-stage projection model based on quadric surfaces is developed which accurately characterizes the effect of wide-angle lenses across the entire image by incorporating the nonlinearity of the lens in the image projection transform. A comparison of this quadric projection model with an existing lens distortion correction technique based on spherical projection is presented to illustrate the increased accuracy of the pinhole images obtained using the new model.

Special class of all-optical holographic associative memories with a nonlinearity in the filter domain is represented. Natural nonlinearity, just a nonlinear part of a holographic recording, lies in the basis of auto- and heteroassociative processes. It is shown, that the developed here class of quadric hologram-based associative memories is the widest generalization of a holographic matched filter technique including informative properties of ghost-image holography, Vander Lugt's correlator, so-called 'second-order holography' using photorefractive oscillators, and nonlinear holographic associative processor to archival data storage and implementation of optical interconnections are discussed.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Special class of all-optical holographic associative memories with a nonlinearity in the filter domain is represented. Natural nonlinearity, just a nonlinear part of a holographic recording, lies in the basis of auto- and heteroassociative processes. It is shown, that the here developed class of quadric hologram-based associative memories is the widest generalization of a holographic matched filter technique including informative properties of ghost-image holography, Vander Lug's correlator, so-called 'second-order holography' using photorefractive oscillators, and nonlinear holographic associative memories based on resonator-like architectures. Potentialities of a quadric hologram-based associative processor to archival data storage and implementation of optical interconnections are discussed.

A robust segmentation scheme is one of the primary requirements for three-dimensional object recognition. The task of partitioning a given image into homogeneous regions has been the centerpiece of investigations of several major researchers all of these years. In this paper we propose a simplistic range image segmentation scheme for un-occluded cluttered three- dimensional objects in a scene. An assumption relating to the three-dimensional objects being quadric in nature, would further enable us to demonstrate an object recognition scheme which has been proposed in an earlier publication. The proposed method involves the extraction of jump edges which we refer to as global edges. After having median filtered the resultant image, a thinning algorithm is implemented which is subsequently followed by the blob determination algorithm thereby completing the segmentation process. Experiments have been conducted on range images of scenes consisting of several quadric surfaces with promising results. Application of the object recognition scheme subsequently successfully classified most of the objects in the scenes as either spherical, cylindrical, or planar in nature.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Techniques for the reconstruction of quadric surfaces (cones and cylinders) from disparity measurements obtained by a stereo vision system are presented. For the initial estimation of the geometrical parameters of cones, a regression based approach is adopted from [Newman, Flynn, and Jain, CVGIP: Image Understanding, Vol. 58, pp. 235-249]. A new method based on surface normal estimation is developed for the cylindrical case. For the refinement of the parameter estimates, the Levenberg-Marquardt nonlinear least squares algorithm is used as in [Flynn and Jain, Proc. 1988 IEEE Comput. Soc. Conf. Computer Vision and Pattern Recognition, pp. 261-267] but two mistaken formulas (one for a cone and the same for a cylinder) are corrected. The prior approaches for quadrics in stereo vision have been more or less approximative. Our contribution is to fit the exact quadric shape to disparity data using the existing methods for range data. The disparity space offers a convenient frame to analyze the differences between the measurements and the reconstructed model.

In this paper we describe the geometric components of our model-based approach to 3D rigid object recognition and positioning from range data that have potential applications in Graphics, Geometric Modeling, and Computer Aided Geometric Design. As in many other object recognition systems, due to occlusion, objects are recognized and located by comparing and geometrically matching small regions of the data set with corresponding regions of known models stored in a database. In our case, a known object is represented in the database as a hierarchical collection of regions, each of them approximated by an algebraic surface. The preliminary recognition and matching is based on comparing euclidean invariant functions of the coefficients of the corresponding polynomials. The final recognition and matching is based on determining how well the data fits a stored model. Although we have not implemented a complete system yet, towards the implementation of an object recognition and position estimation system based on this structure, a number of computational problems associated with algebraic curves and surfaces have been analyzed and solved. These problems, described in this paper, are: (1) how to fit unconstrained algebraic curve and surfaces to data, (2) how to fit bounded algebraic curves and surfaces, (3) how to efficiently compute Euclidean invariants of polynomials, and (4) how to define an intrinsic coordinate system of a polynomial, generalizing the notion of center and principal axes of a nonsingular quadric curve or surface. The intrinsic coordinate system of a polynomial can be used to transform its coefficients to a normal form. The coefficients of a polynomial in normal form constitute a complete set of Euclidean invariants.

Pose and orientation of an object are central issues in 3-D recognition problems. Most of today's available techniques require considerable pre-processing, such as detecting edges or joints, fitting curves or surfaces to segment images, and trying to extract higher order features from the input images. In this paper we present a method based on analytical geometry, whereby all the rotation parameters of any quadric surface are determined and subsequently eliminated. This procedure is iterative in nature and has been found to converge to the desired results in as few as three iterations. The approach enables us to position the quadric surface in a desired coordinate system, then, utilize the presented shape information to explicitly represent and recognize the 3-D surface. Experiments were conducted with simulated data for objects such as hyperboloid of one and two sheets, elliptic and hyperbolic paraboloid, elliptic and hyperbolic cylinders, ellipsoids, and quadric cones. Real data of quadric cones and cylinders were also utilized. Both of these sets yielded excellent results.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Algorithms are presented for constructing G' continuous meshes of degree two (quadric) and degree three (cubic) implicitly defined, piecewise algebraic surfaces, which exactly fit any given collection of points and algebraic space curves, of arbitrary degree. A combination of techniques are used from computational algebraic geometry and numerical approximation theory which reduces the problem to solving coupled systems of linear equations and low degree, polynomial equations.© (1990) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Nonuniform, rational B-splines (NUItBs) are the basis functions used to represent both free-form curves and surfaces and precise quadric primitives such as conics. NURBs are defined as ratios of linear combinations of nonuniform B-spline functions. In this paper, we present a new high-speed algorithm for the computation of nonuniform rational spline curves. We demonstrate this technique on a simple example and provide a computational complexity analysis.

Surface fitting allows for pose estimation and recognition of objects in range scenes. Unfortunately, surface fitting is computation-intensive. One way to speed-up this task is to use parallel processing, since its availability is on the increase. Mathematically, surface fitting can be formulated as an overdetermined linear system which can be solved in the least-square sense. Because of numerical stability and ease of implementation, the QR-factorization using the Givens transformation is best suited for the parallel solution of overdetermined systems. In this paper we present two algorithms to carry out a QR factorization on both distributed-memory and shared-memory parallel computers. These algorithms have been implemented and evaluated in terms of speed-up time.

An approach to 3-D surface estimation is introduced where surfaces are modelled as patches of primitive parameterized surfaces, and these parameters are estimated from images taken by cameras in two or more positions. Appropriate parameterized patches for modelling manufactured objects include planar, cylindrical, spherical and unrestricted quadric patches. Any parameterized function can be used. A complex 3-D object can be described as a collection of such patches. For more irregular surfaces such as outdoor terrain, we use a collection of primitive patches linked together as a stochastic process. More specifically, in this paper we use planar primitive patches, and describe their dependence by Markov Random Fields. We then treat 3-D terrain height estimation as stochastic pro-cess estimation given two or more image data sets. To the extent that the models used are appropriate, this should result in the most accurate surface height estimation, object recognition for objects such as boulders, crevices, mountains, etc, occulded surface height estimation, and other information extraction. A simple geometric explanation is given for the estimation algorithm. This paper is one aspect of a new Bayesian approach to stereo vision as presented in [4,5,6].

An infrared scene generator code has been developed for use in testing electro-optic systems. The scene generator combines sophisticated computer graphic techniques with first-principals background modeling. The code generates apparent radiance images of a scene composed of polygonal and/or quadric objects for a specified viewing geometry, spectral band, weather, time of day, location, season, and sensor field of view. Surfaces may be any one of 15 different materials and any surface can be given a texture to make the generated scene more realistic. The warming of surfaces caused by sunlight is also modeled. All parameters, including the effect of the intervening atmosphere, the weather, material type, material texture, and the system modulation transfer function, are contained in independent data bases. The use of data bases, combined with efficient programming, make the execution time short. This allows the user to quickly see the effects of different conditions on the scene of interest and how varying conditions will effect a sensor system.