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Effectively modeling a collection of three-dimensional (3-D) faces is an important task in various applications, especially facial expression-driven ones, e.g., expression generation, retargeting, and synthesis. These 3-D faces naturally form a set of second-order tensors--one modality for identity and the other for expression. The number of these second-order tensors is three times of that of the vertices for 3-D face modeling. As for algorithms, Bayesian data modeling, which is a natural data analysis tool, has been widely applied with great success; however, it works only for vector data. Therefore, there is a gap between tensor-based representation and vector-based data analysis tools. Aiming at bridging this gap and generalizing conventional statistical tools over tensors, this paper proposes a decoupled probabilistic algorithm, which is named Bayesian tensor analysis (BTA). Theoretically, BTA can automatically and suitably determine dimensionality for different modalities of tensor data. With BTA, a collection of 3-D faces can be well modeled. Empirical studies on expression retargeting also justify the advantages of BTA. Index Terms--Bayesian inference, Bayesian tensor analysis, face expression synthesis, 3-D face.

Face recognition based on 3D surface matching is promising for overcoming some of the limitations of current 2D image-based face recognition systems. The 3D shape is generally invariant to the pose and lighting changes, but not invariant to the nonrigid facial movement such as expressions. Collecting and storing multiple templates to account for various expressions for each subject in a large database is not practical. We propose a facial surface modeling and matching scheme to match 2.5D facial scans in the presence of both nonrigid deformations and pose changes (multiview) to a stored 3D face model with neutral expression. A hierarchical geodesic-based resampling approach is applied to extract landmarks for modeling facial surface deformations. We are able to synthesize the deformation learned from a small group of subjects (control group) onto a 3D neutral model (not in the control group), resulting in a deformed template. A user-specific (3D) deformable model is built for each subject in the gallery with respect to the control group by combining the templates with synthesized deformations. By fitting this generative deformable model to a test scan, the proposed approach is able to handle expressions and pose changes simultaneously. A fully automatic and prototypic deformable model based 3D face matching system has been developed. Experimental results demonstrate that the proposed deformation modeling scheme increases the 3D face matching accuracy in comparison to matching with 3D neutral models by 7 and 10 percentage points, respectively, on a subset of the FRGC v2.0 3D benchmark and the MSU multiview 3D face database with expression variations. Index Terms--Deformation modeling, 3D face recognition, facial expression, deformable model, expression transfer, nonrigid.

An autostereoscopic display using a directional backlight with a fast-switching liquid-crystal (LC) display was designed and fabricated to obtain a better perception of 3D images by enhanced resolution and brightness. A grooved light guide in combination with an asymmetric focusing foil was utilized to redirect the emitting cones of light to the left and right eyes, respectively. By designing the groove structures of the focusing foil with rotation from - 1.5[degrees] to 1.5[degrees] in the gradient and having the pitch ratio of the grooved light guide to the focusing foil of less than 3, the boundary angle then shifts from normal viewing and the moire phenomenon can be suppressed. Cross talk of less than 6% and a LC response time of faster than 7.1 ms further improve the stereoscopic image perception. Additionally, 2D-3D compatibility is provided. OCIS codes: 230.3720, 330.1400.

Creating three-dimensional (3-D) models of real urban objects is an important goal in a wide variety of applications. This paper describes a method that utilizes airborne laser elevation images and aerial images for the 3-D reconstruction of urban objects. Our modeling approach uses the vertical geometric pattern analysis of elevation images. These patterns correspond to object contours and, thus, enable the extraction of the object. In addition, to provide realistic textured details, textures are cut from aerial images and mapped onto 3-D models. Our texture-mapping approach can avoid geometry mismatching and enable the automatic registration to determine the most reliable correspondence between projected outlines of 3-D models and contours of real objects shown in aerial images. Edge pairs, which are matched with projected outlines, are detected from aerial images. In order to minimize mismatching, we apply the voting technique based on the generalized Hough transform. Experimental results show that 3-D reconstruction of urban objects is generally successful. Index Terms--Generalized Hough transform, geometric feature classification, image registration, three-dimensional reconstruction.

The high computational cost of data processing in volume PET imaging is still hindering the routine application of this successful technique, especially in the case of dynamic studies. This paper describes two new algorithms based on an exact rebinning equation, which can be applied to accelerate the processing of three-dimensional (3-D) PET data. The first algorithm, FOREPRO J, is a fast-forward projection algorithm that allows calculation of the 3-D attenuation correction factors (ACF's) directly from a two-dimensional (2-D) transmission scan, without first reconstructing the attenuation map and then performing a 3-D forward projection. The use of FOREPROJ speeds up the estimation of the 3-D ACF's by more than a factor five. The second algorithm, FOREX, is a rebinning algorithm that is also more than five times faster, compared to the standard reprojection algorithm (3DRP) and does not suffer from the image distortions generated by the even faster approximate Fourier rebinning (FORE) method at large axial apertures. However, FOREX is probably not required by most existing scanners, as the axial apertures are not large enough to show improvements over FORE with clinical data. Both algorithms have been implemented and applied to data simulated for a scanner with a large axial aperture (30 degrees), and also to data acquired with the ECAT HR and the ECAT HR+ scanners. Results demonstrate the excellent accuracy achieved by these algorithms and the important speedup when the sinogram sizes are powers of two. Index Terms: Forward projection, PET, rebinning, 3-D reconstruction.

This paper discusses novel techniques and methodologies suitable for automated electromagnetic (EM) design of arbitrary three-dimensional (3-D) structures. In the context of parameterization of arbitrary 3-D structures, the authors outline the concept of the geometry capture technique. The authors present efficient response interpolation with respect to optimizable parameters - the key to effective automation. The authors' formulation is based on the maximally flat quadratic interpolation (MFQI) technique and provides gradient estimation essential to efficient optimization. The authors address the issue of storing the results of expensive EM simulations in a dynamically updated database, integrated with the interpolation technique. The automated EM optimization process is illustrated by the design of waveguide mitered bends. The authors also apply the aggressive space mapping (SM) technique to the optimization of multistep waveguide transformers. Index Terms - Design automation, electromagnetic analysis, finite-element methods, optimization methods, waveguide bends.

A novel compact holographic crossbar architecture based on planar optics is presented. It consists of a pair of identical planar holographic elements, a two-dimensional array (N x N) transmission mask, a one-dimensional array (N) of input light sources, and a one-dimensional array (N) of detectors. Each planar element contains two cylindrical holographic lenses, both of which are recorded on a single glass substrate. The design of the overall compact configuration is presented along with experimental results.

We describe a polarization-controlled free-space optical multistage interconnection network based on polarization-selective computer-generated holograms: optical elements that are capable of imposing arbitrary, independent phase functions on horizontally and vertically polarized monochromatic light. We investigate the design of a novel nonblocking space-division photonic switch architecture. The multistage-switch architecture uses a fan-out stage, a single stage of 2 x 2 switching elements, and a fan-in stage. The architecture is compatible with several control strategies that use 1 x 2 and 2 x 2 polarization-controlled switches to route the input light beams. One application of the switch is in a passive optical network in which data is optically transmitted through the switch with a time-of-flight delay but without optical-to-electrical conversions at each stage. We have built and characterized a proof-of-principle 4 x 4 free-space switching network using three cascaded stages of arrayed birefringent computer-generated holographic elements. Data modulated at 20 MHz/channel were transmitted through the network to demonstrate transparent operation.

A new three-dimensional (3-D) 12-lead electrocardiogram (ECG) display method is presented which employs a 3-D rectangular coordinate system to display the 12-lead cardiac electric signals in two 3-D graphs. The 3-D graph consists of a temporal axis representing the time domain of the cardiac signals, a spatial axis representing the lead positions, and an amplitude axis representing the voltages of the cardiac signals. The six horizontal plane leads and the other six frontal plane leads were displayed in two 3-D graphs, respectively. The voltages of the cardiac signals were represented in rainbow-like colors. Cubic interpolation was employed to insert interconnecting points between neighboring leads on each plane and to smooth the surface of the 3-D ECG graphs. The 3-D ECG graphs of a normal subject, a patient with myocardial infarction, and a patient with left bundle branch block were presented in this paper. This new display method could not only be used as a complementary display method to the 12-lead ECG, but also provide physicians with an overall integral view about the spatial distribution of the cardiac signals. Index Terms--Cardiac signals, three-dimensional (3-D) display method, 12-lead ECG.

An efficient procedure for the generation of synthetic near-field hologram structures for display purposes is presented. The formation process requires virtually no computation effort. [C] 2001 Optical Society of America OCIS codes: 090.1760, 100.3010, 090.0090.

Coordination of design changes is important because, if the design changes are not properly managed, design conflicts will result in more expensive design or even failure in the design-construction process. Geometric modification has been a routine for design activities. However, the facility of existing systems for managing changes in multiview models is still inadequate. This paper presents a novel parametric approach using a knowledge-based constraint solving method to incorporate the projection knowledge and graphic inference to address the issue of design changes for multiview models. A corresponding multiview constraint solver has been developed. This knowledge-based constraint solver can be combined with the linking knowledge between building components to facilitate the coordination of design information for multiview models. Illustrative examples are presented to demonstrate the feasibility of the proposed parametric approach for design change management.

A new type of electro-optical three-dimensional (3-D) correlator is proposed and demonstrated. A 3-D object scene, observed by multiple cameras from several points of view, is correlated with a 3-D complex computer-generated function. This correlator is a hybridization of the joint transform and the VanderLugt correlators, and, as such, it allows correlations to be made between 3-D real-world objects and 3-D general complex functions. Experimental results are presented. [C] 2000 Optical Society of America OCIS codes: 070.4450, 070.2580, 070.5010, 070.6110, 100.5090.

In this paper, we propose a novel and practical stereo camera system that uses only one camera and a biprism placed in front of the camera. The equivalent of a stereo pair of images is formed as the left and right halves of a single charge coupled device (CCD) image using a biprism. The system is therefore cheap and extremely easy to calibrate since it requires only one CCD camera. An additional advantage of the geometrical setup is that corresponding features lie on the same scanline automatically. The single camera and biprism have led to a simple stereo system for which correspondence is very easy and accurate for nearby objects in a small field of view. Since we use only a single lens, calibration of the system is greatly simplified. Given the parameters in the biprism-stereo camera system, we can reconstruct the three-dimensional structure using only the disparity between the corresponding points. Index Terms--Biprism stereo, calibration, disparity, disparity map, Euclidean structure.

Software for categorizing a cloud of more than 300000 three-dimensional (3-D) surface data points, captured from a human subject, is presented. The software is part of an incremental approach that progressively refines the identification of human anthropometric landmarks. The first phase of identification is to orient and segment the human body data points. A step-by-step method for these tasks is presented. One of the algorithms, a discrete point cusp detector, plays a fundamental role in separating the data cloud. The theory and operation of the algorithm is explained. The discrete cusp detector can be used to separate any two cylindrical objects, in (3-D) data, whose boundaries touch. The software has been tested on over a hundred different body scan data sets and shown to be robust. Index Terms--Anthropometry, cusp, segmentation, surface scanning.

In many medical applications, the number of available two-dimensional (2-D) images is always insufficient. Therefore, the three-dimensional (3-D) reconstruction must be accomplished by appropriate interpolation methods to fill gaps between available image slices. In this paper, we propose a morphology-based algorithm to interpolate the missing data. The proposed algorithm consists of several steps. First, the object or hole contours are extracted using conventional image-processing techniques. Second, the object or hole matching issue is evaluated. Prior to interpolation, the centroids of the objects are aligned. Next, we employ a dilation operator to transform digital images into distance maps and we correct the distance maps if required. Finally, we utilize an erosion operator to accomplish the interpolation. Furthermore, if multiple objects or holes are interpolated, we blend them together to complete the algorithm. We experimentally evaluate the proposed method against various synthesized cases reported in the literature. Experimental results show that the proposed method is able to handle general object interpolation effectively. Index Terms--Blending, dilation and erosion, distance-maps, interpolation, morphology, object centralization.

We present an inversion procedure for electromagnetic scattering, based on the powerful and flexible technique called the coupled-dipole method combined with an optimization algorithm. This method permits us to realize imaging of dielectric objects whose dimensions are comparable with the incident wavelength and is shown to be efficient with corrupted data (scattered electric field). The feasibility of this method is shown in a synthetic example in which the scattered field is corrupted with Gaussian noise. Two methods are used to invert the scattered field to recover the refractive index of the medium: a conventional matrix inversion and an iterative method. [C] 2000 Optical Society of America OCIS codes: 100.3190, 290.3200, 100.3010.

A system for the automatic reconstruction of real-world objects from multiple uncalibrated camera views is presented. The camera position and orientation for all views, the 3-D shape of the rigid object, as well as the associated color information, are recovered from the image sequence. The system proceeds in four steps. First, the internal camera parameters describing the imaging geometry are calibrated using a reference object. Second, an initial 3-D description of the object is computed from two views. This model information is then used in a third step to estimate the camera positions for all available views using a novel linear 3-D motion and shape estimation algorithm. The main feature of this third step is the simultaneous estimation of 3-D camera-motion parameters and object shape refinement with respect to the initial 3-D model. The initial 3-D shape model exhibits only a few degrees of freedom and the object shape refinement is defined as flexible deformation of the initial shape model. Our formulation of the shape deformation allows the object texture to slide on the surface, which differs from traditional flexible body modeling. This novel combined shape and motion estimation using sliding texture considerably improves the calibration data of the individual views in comparison to fixed-shape model-based camera-motion estimation. Since the shape model used for model-based camera-motion estimation is only approximate, a volumetric 3-D reconstruction process is initiated in the fourth step that combines the information from all views simultaneously. The recovered object consists of a set of voxels with associated color information that describes even fine structures and details of the object. New views of the object can be rendered from the recovered 3-D model, which has potential applications in virtual reality or multimedia systems and the emerging field of video coding using 3-D scene models. Index Terms--Shape and motion estimation, view calibration, 3-D reconstruction.

An autostereoscopic 3-D displaying technique that uses fan-likely placed multiple light beams in a light array with 2-D raster scanning is proposed. This technique is capable of displaying multiple perspective views at high resolution because the number of views only depends on the number of light beams, while the number of light beams does not depend on the resolution of each view. Moreover, dozens or hundreds of perspective views at an angular interval narrower than one degree can be produced if small light sources are used. On the basis of this technique, an experimental 3-D display system capable of producing 45-view video images at an angular interval of 0.5 degrees at a time is developed. Furthermore, the effectiveness of the technique is demonstrated by using this system. Index Terms--3-D display, autostereoscopic, focused light array, multiple-views.