We describe a simple and efficient implementation of adaptive multiplexing control for high-order piezoelectric deformable mirrors. The relatively high capacitance of piezoelectric actuators allows the electrical charge to be stored in a disconnected actuator, retaining its displacement while the other actuators can be addressed. Adaptive multiplexing, consisting of selective addressing of only those actuators that need to change their elongation in the current cycle, improves the mirror performance and simplifies the driver electronics. In experiment, a 12-channel prototype of a deformable mirror with multiplexing control has been characterized. At appropriate update rates with a fixed set of control signals, the shape of the deformable mirror remains nearly constant. A surface displacement error does not exceed ~ /100 rms at a multiplexing frequency of 700 Hz with a full interactuator stroke of ~2 µm.

We present an all-fiber spectrum equalization filter that uses a Mach-Zehnder interferometer terminated with a loop. Compared with existing results, the proposed filter has a simpler and a more efficient all-fiber structure for equalizing Gaussian-like spectra with desired specifications.

A thermo-optically tunable fiber ring laser has been constructed. The laser is based on a polymer-spaced Fabry-Pérot (F-P) étalon with a cavity length of 470-µm and an ultra-low polarization-dependent loss (PDL) of <0.1 dB. A wavelength tuning range of ~1.4 nm and a high wavelength stability of ~0.02 nm have been demonstrated without involving any moving mechanical parts. Such a nonmechanical tunable fiber laser structure leads to a reduced device size and allows easy device packaging due to the ultra-low PDL of the wavelength tuning element.

A compact and low-cost detection electronics scheme for optical coherence imaging is demonstrated. The performance of the designed electronics is analyzed in comparison to a commercial lock-in amplifier of equal bandwidth. Images of a fresh-onion sample are presented for each detection configuration.

We describe how to use Markov chain Monte Carlo simulation (MCMC) to accurately estimate the outage probability of the optical communication system compensated by higher-order optical polarization mode dispersion (PMD) compensators. Markov chain fiber channel samples can drastically reduce the number of simulations required to estimate the outage probability of the compensated systems to 10–6 or less. Using MCMC, the efficiency of our proposed higher-order optical PMD compensator is proved further, and the accuracy of MCMC is affirmed.

We report and present an experimental investigation of spatially and thermally dependent self Q-switching effects generated in Nd:YVO4 cavity. The main application for the investigated effect is generation of an efficient Q-switched lasing in a Nd:YVO4 crystal that may be realized without the need for a saturable absorber module.

Large, high-bandwidth deformable mirrors (DMs) with thousands of actuators for adaptive optics are of high interest for existing large telescopes and indispensable for construction of efficient future extremely large telescopes. Different actuation and sensing principles are possible. We propose a novel concept using commercially available voice coil actuators attached to the back of the mirror with suction cups and using LVDT sensors on the actuators for local stabilization. Also, a new low-cost sensor for easy measurement of DM displacement or velocity has been developed. It has a sensitivity better than 20 nm and a bandwidth wider than 20 to 1000 Hz. Finally, studies are in progress of global, hierarchical mirror form controllers based on many parallel multiple-input, multiple-output regulators of low order.

The flux transfer efficiency of an optical array with spatial integration has been improved by adding a new element at the input surface. The optical characteristics of the input surfaces of the individual units do not affect the spatial integration property. We propose to fill this input surface with a nested optical array designed to transfer as much energy as possible to the plane of the synthetic image of the spatial integrator array. Several designs for the individual units of this array are discussed. The most promising design consists of a cylindrical axicon-diopter element. This element has been simulated, fabricated, and tested, showing the expected improvement in performance.

Time phase shift is an effective, reliable, and commonly used technique to measure the phase of fringe patterns. The major disadvantage of this technique is that it involves phase-shift devices, which introduce errors during the process of phase shift and require high compatibility of the photoelectrical performance of different detectors used in the experiment. More importantly, since at least three fringe patterns are needed to reconstruct the 3-D surface of the object, this technique is inappropriate for use under dynamic conditions. We propose and demonstrate a novel technique, i.e., grating projection tricolor fringe profilometry, for rapid determination of the profiles of objects. The technique, which is based on only one fringe pattern, obviates the need of phase-shift devices. Thus, errors resulting from the process of phase shift can be eliminated and rapid measurement can be achieved.

One of the more challenging applications of optical metrology is real-time dimensional control and surface inspection in industrial applications, where strong requirements of cost, setup, and applicability in adverse environments greatly limit the number of applicable technologies. This work shows an optic profilometer developed specifically for this purpose, the algorithms developed for efficient and accurate distance map calculation, and an example of its use in a harsh steelmaking environment. This device, based on conoscopic holography, is able to obtain a distance profile of a target in a single shot, works at long distance standoff (700 to 1200 mm), and still keeps good resolution (under 0.2 mm) with a very easy and reliable setup. The second part of the work focuses on a real example of this technology applied in an on-line inspection system in steel continuous casting funded by the European Coal and Steel Community, and which is currently working in the Aceralia LDA steelmaking factory in Asturias (Spain). The system is placed in the process line and performs on-line detection of surface defects over hot steel slabs (above 800°C in the inspection point) from a distance of 1200 mm. 100% of the production can be inspected without interfering with the process and without adding any delay.

A new method for measuring the radius of curvature (ROC) of an optical surface having a large radius is proposed. The method combines a Fizeau interferometer and a specially designed zoom lens to form a compact and convenient test setup, so that measurement of the curvatures for both concave and convex surfaces having a large ROC can be done in a simple and quick way. The design of the zoom lenses for this application, principle of the measurement, and calibration of the zoom lenses are discussed. By means of the proposed method, radii of 1.5 m to infinity, concave or convex surfaces, can be measured in compact setups efficiently. The accuracy of the measurements can reach up to 0.04% for a surface having a radius of 10 m.

Methods are described for attenuating solid glass and hollow retroreflectors, without introducing optical path length modifications, for electronic distance measurement. Construction of a prototype novel-design hollow retroreflector is described.

The near-field-intensity distributions of diffusion-cooled axisymmetric folded-combined CO2 lasers are investigated. Formulas representing the near-field distributions for some typical kinds of folded-combined CO2 lasers are suggested, and the near-field-intensity profiles are calculated numerically and simulated. For several centimeters from the output mirror along the direction of the symmetric axis, the intensity in the output beam is very high and its radius (or width) is very small (approximately double waist radius). The frequency differences between different cavities would induce fluctuations of the intensity distribution, but the fluctuations are not distinctive. The near-field beam can be used directly in some industrial material processing.

We develop a miniaturized optical signal pickup module, with a working wavelength of 650 nm, and an image numerical aperture (NA) of 0.6, comprised of several SiNX optical phase elements on stacked Si substrates, for use in optical storage systems. The optical module, which is optical-on-axis and transmissible in both visible and infrared ranges, is designed to include not only a light source, but also diffractive optical elements (DOEs), which can be made with micro-optoelectromechanical systems (MOEMS) technology. Its optical operation is simulated by ray tracing to optimize the spot size (~0.6 µm) focused on the disk by adjusting the tolerance of each element in the alignment. All the Si-based transmission optical elements are fabricated and stacked by self-alignment bonding to reduce the tolerance of the assembled system. We obtain a circular focused spot when the full-width at half maximum (FWHM) of the zero-order beam is 3.1 µm; the diffraction limited spot size on the optical disk is 0.7 µm.

We present a novel mode selective coupling technique for step index fiber. This technique utilizes phase matching for excitation of higher-order modes while suppressing the fundamental mode. Using this technique, a phase element is fabricated and tested to demonstrate the high coupling efficiency to the LP11 mode. In addition, we derive an analytical expression of the coupling efficiency of the LP11 using a single phase element.

Photo-written waveguides employing binary optical masks are investigated in an iron-doped lithium niobate crystal. Planar and Y-branch waveguides are experimentally demonstrated. The index variations along the propagation direction of the writing beam in the crystal are experimentally measured and theoretically analyzed. The influence of the diffraction from the optical masks, which imposes a limitation for the applications of the waveguide fabrication method, is numerically specified. Additionally, the asymmetry of the index distribution in the waveguide region, which is related to the transport process of the photoexcited charge carriers, is revealed and qualitatively explained.

The loss properties of multimode -branch waveguides are analyzed using coupled mode theory combined with two-dimensional Padé (1,1) approximation finite-difference beam propagation method. The radiation losses of zeroth-order mode propagating in single-mode and multimode turning channel waveguides are compared. Mode conversion in the symmetric five-layer waveguide for multimode -branch configuration is analyzed. Then the relations between radiation loss and the branching angle for single-mode and multimode -branch waveguides are obtained and explained. It is found that when there is not much coupling from zeroth-order mode to other higher-order modes in a multimode -branch waveguide, radiation loss of zeroth-order mode propagating in the waveguide is lower than that in a single mode one. For a multimode -branch waveguide, the radiation loss curve fluctuates as the result of mode coupling and influence of the turning points of the waveguide structure. By making use of the fluctuation of the radiation loss curve, optimizing the structural parameters such as branching angle and the width of waveguide and trying to eliminate the generation of the second-order mode at the turning points, a design of a multimode -branch waveguide with low loss and wide branching angle is obtained.

An optical soliton pulse can be effectively used as an information-carrying signal in a nonlinear optical fiber medium. We propose an analytical model for phase-sensitive switching by the use of two mutually orthogonal polarized Gaussian pulses. To realize it we consider a Gaussian pulse first propagating through an electro-optic modulator. The orthogonal components of the pulse are introduced into the optical fiber. By controlling the applied voltage across the modulator we can change the phase relation between the components. By this method, switching at a very long distance can be implemented in the optical fiber.

The length-dependent tuning of the fluorescence spectra of a dye doped polymer fiber is reported. The fiber is pumped sideways and the fluorescence is measured from one of the ends. The excitation of a finite length of dye doped fiber is done by a diode pumped solid state laser at a wavelength of 532 nm. The fluorescence emission is measured at various positions of the fiber starting from a position closer to the pumping region and then progressing toward the other end of the fiber. We observe that the optical loss coefficients for shorter and longer distances of propagation through the dye doped fiber are different. At longer distances of propagation, a decrease in optical loss coefficient is observed. The fluorescence peaks exhibit a redshift of 12 nm from 589 to 610 nm as the point of illumination progresses toward the detector end. This is attributed to the self-absorption and re-emission of the laser dye in the fiber.

Chirped return-to-zero differential phase-shift keying (CRZ-DPSK) modulation format under different channel spacings is investigated and compared with RZ-DPSK in 40×40-Gbit/s dense wavelength-division multiplexing transmission systems. An optimization operation over a wide range of parameters, such as span input power, precompensation percent, and chirp parameter (only for CRZ-DPSK), is performed in the simulation. Simulation results show that CRZ-DPSK demonstrates better performance in transmission distance, nonlinear, and dispersion tolerance with wider channel spacing of 100 GHz. When the channel spacing is reduced to 75 GHz, a slight degradation is observed for CRZ-DPSK and the performances of both formats are acceptable. But when it is reduced from 75 GHz to 50 GHz, a clear degradation of the CRZ-DPSK performance is measured, but RZ-DPSK demonstrates no significant degradation.

A novel approach based on microforce sensing for coarse alignment in active fiber pigtailing is proposed. It is shown that the microforce due to contact between a specially designed force sensor and a geometrical feature on the input surface of an optical device provides useful clues in guiding the fiber to rapidly locate the actual optical path of the optical device. The effectiveness of this approach was demonstrated on a photonic alignment system. These results suggest that microforce sensing can be an effective technique in augmenting conventional approaches for fast and accurate fiber pigtailing in photonic assembly.

A new shifted phase-encoded fringe-adjusted joint transform correlation (SPJTC) technique is proposed for class-associative color pattern recognition. In this technique, the joint color image containing the class member images and unknown input scene images is split into three fundamental color components—red, green, and blue—which are then processed through three different channels using the SPJTC technique to obtain individual joint power spectra (JPS). For correlation performance improvement, a new class-associative color fringe-adjusted filter (CCFAF) has been proposed. The combined JPSs obtained by fusing all of the individual joint power spectra are then multiplied by the CCFAF transfer function. The proposed scheme provides a single correlation peak per target with excellent correlation discrimination for both noise-free and noisy conditions. Simulation results are provided to verify the effectiveness of the proposed technique.

This paper describes a novel technique to perform fast phase demodulation in Michelson interferometers without any need for phase locking or heterodyning, thus enabling quantitative detection of vibrations in a noncontacting mode. The new scheme greatly simplifies the optical design of laser interferometers used for nondestructive evaluation of materials. It uses a matched moiré grating to transform the interference fringe pattern formed between the reference and signal beams into intensity modulation. It one divides the filter into four quadrants so that the gratings in each quadrant have been shifted to represent an equivalent phase difference of /2, the intensity signals collected behind the four quadrants effectively represent four simultaneous data points due to phase stepping, covering the full cycle. This means that a unique phase measurement can be obtained at any arbitrary phase position, and thus the interferometer may be left to operate in free-running mode. Since all the four signals originate from the same laser source, appropriate differential signal processing can be incorporated to remove intensity noise due to fluctuations in the laser source. In addition, we have studied the effect of angular misalignment between the grating filter and the interference fringe pattern. Our results show that such misalignments may be compensated through a back-substitution algorithm. This further enhances the practical benefits of our scheme in real situations.

Digital holographic particle image velocimetry is a promising technique for the measurement of the instantaneous flow velocity within a volume of a flow. It poses, however—problems of illumination and recording—the major problem of how to extract the information about the location of the particles within the flow and their displacement between two illuminations from the storage medium, i.e., the digital hologram. Various recording parameters, such as the recording distance, the particle size, the wavelength, the size of the CCD chip, the pixel size, and the particle concentration, will considerably affect the results of the reconstruction, and may even determine the success or failure of a measurement. This paper discusses the influence of these parameters and presents a formula for the critical recording distance. Numerical simulations indicate that when the recording distance is near to the critical value, the results of the reconstruction are much better than those obtained far away from it, especially for high particle concentration. An experiment has also been made to validate the analysis.

The Fresnel integral is the most often used numerical method for hologram reconstruction in digital holography. However, reconstructed images with this method always include different aberrations because of the neglect of the fourth- and higher-order phase terms in the calculation. The characteristics of these aberrations induced by a Fresnel integral are studied numerically and theoretically. It is found that the quality of the reconstructed image can be degraded seriously by these induced aberrations, especially for small recording distance, and the required experimental conditions of the Fresnel integral used to obtain aberration-neglectable reconstructed images are also studied with Marechal's criteria.

Dot-matrix holograms created by two-beam writers usually contain two-dimensional grating dots. Although the dot positions may be accurate, the fringe positions of the dots are randomly determined. The random fringe positions are good tools to identify a hologram. A grating position-deviation coefficient derived from the fringe position difference of two grating dots with the same pitch and the same orientation is defined and it is used as data to identify a dot-matrix hologram. Experiments have proved the proposed method practical and feasible. Because the fringe position difference between the two grating dots with the same pitch and the same orientation is difficult to reproduce, it is excellent for anticounterfeiting.

First-order weak-fluctuation Rytov theory predicts that the longitudinal (on-axis) component of the scintillation index of an uplink collimated beam will become significantly smaller as the size of the transmitter aperture increases up to around 100 cm. However, the results of recent computer simulations are at odds with this behavior, and we believe that this discrepancy is due to the fact that the conventional Rytov theory does not correctly account for the effects of beam wander on the scintillation index. We present a theoretical structure that accurately describes far-field irradiance fluctuations caused by uncorrected beam wander. This new theory is validated by demonstrating excellent agreement between the predicted scintillation index and computer code results for both tracked and untracked beams. For many applications of practical interest, such as free-space optical communications, a good understanding of the time-average Strehl ratio is also essential simulation results for this parameter are presented and shown to be in good agreement with the theory.

A portable lidar system has been developed for monitoring the evolution of the atmospheric boundary layer (ABL) using aerosols as the tracers of atmospheric motion. This lidar system utilizes state-of-the-art technology with a high repetition rate, low pulse energy laser, and photon-counting detection. The system is capable of continuous, autonomous data acquisition in both daytime and nighttime. During daytime, the aerosol profiles measured with the lidar are found to have sufficient signal strength to observe the structure of the ABL, which plays an important role in air pollution phenomena. The time series of the range-squared signal has been used for the interpretation of the ABL dynamics.

This paper considers the problem of detecting a subpixel target in a hyperspectral image with a uniform background. A uniform background region is defined as an area of a hyperspectral image composed of a single material except for possibly a target material. It is shown that in the uniform background case the likelihood ratio test (LRT), which is the optimal signal detection algorithm, can be evaluated. It is shown that the LRT derived in this paper is a special case of the constrained signal detector (CSD). Though no other detector outperforms the LRT, it is possible for other algorithms to equal its performance. It is shown in what special cases the orthogonal subspace projection (OSP) detector and the matched filter detector (MFD) perform the same as the CSD.

A novel method for fusion detection of small infrared targets based on support vector machines (SVM) in the wavelet domain is presented. Target detection task plays an important role in automatic target recognition (ATR) systems because overall ATR performance depends closely on detection results. SVM is a powerful methodology for solving problems in nonlinear classification, function estimation and density estimation. Least-squares support vector machines (LS-SVMs) are reformulations to standard SVMs. The proposed algorithm can be divided into four steps. First, each frame of the image sequence is decomposed by the discrete wavelet frame (DWF). Second, the components with low frequency are performed by regression based on LS-SVM. The one-order partial derivatives in row and column directions are derived. Therefore, feature images of the gradient strength can be obtained. Third, feature images of five consecutive frames are fused to accumulate the energy of target of interest and greatly reduce false alarms. Finally, the segmentation method based on contrast between target and background is utilized to extract the target. In terms of connectivity of moving targets, the majority of residual clutter and false alarms that survive are removed based on 3-D morphological dilation across three consecutive frames along the motion direction of the moving targets. Actual infrared image sequences in backgrounds of sea and sky are applied to validate the proposed approach. Experimental results demonstrate the robustness of the proposed method with high performance.

Pixels in both hybridized and monolithic complementary metal-oxide semiconductor (CMOS) detector arrays may couple capacitively to their neighboring pixels. This "interpixel capacitance" can significantly distort the characterization of conversion efficiency and modulation transfer function (MTF) in CMOS devices. These effects have been largely unaccounted for in measurements to date. In this work, the effects of this coupling are investigated. Compensation methods for these errors are described and applied to silicon P-I-N array measurements. The measurement of Poisson noise, traditionally done by finding the mean square difference in a pair of images, needs to be modified to include the mean square correlation of differences with neighboring pixels.

We propose a new deinterlacing algorithm with selective motion compensation. It has been reported that deinterlacing methods using motion compensation produce significantly improved results, although they tend to yield undesired results in fast moving areas. This is due to weak correlations between the previous and current frames. The proposed algorithm solves this problem by selectively applying motion-compensated deinterlacing. We first apply intrafield interpolation in the spatial domain, and then selectively apply motion compensations according to the type of motion vectors. Experimental results show that the proposed method produces noticeably improved performance compared to existing motion-compensated deinterlacing methods.

The fractal dimension is used in conjunction with a neural network to quantify effects of the chaotic behavior of radar clutter on the geometric aspects of target detection by synthetic aperture radar. To demonstrate the effectiveness of the proposed method, results are compared with those of the conventional constant-false-alarm-rate algorithm and the neural network technique. It is shown that the use of the fractal dimension substantially improves the detection performance based on some figures of merit, including detection rate, false-detection rate, and loss detection rate.

Previously, we introduced the idea of moment patterns in the Radon space and described normalization procedures to render the patterns invariant to translation, rotation, and amplitude and geometric scaling. We extend our work toward rendering the patterns invariant also to blurring, which is modeled as a convolution by a linear shift-invariant filter. This is achieved by considering blur-invariant functions of the central moments of the projections, and normalizing them to eliminate the effects of both amplitude and geometric scaling. Results of simulation are presented to demonstrate the invariance of the new moment-based functions in the Radon space to translation, rotation, amplitude and geometric scaling, and blur.

Fragile watermarking techniques are developed to ensure the credibility and integrity of images in open communication channels. Many related studies have proposed methods for accurately localizing tampered areas, but the ability to recover such areas has received less attention. Therefore, we propose a content-based fragile watermarking technique that can both accurately localize tampered areas and correct them in details, using embedded content-based watermarks. Our scheme provides a novel watermark structure. It adopts JPEG-compressed watermark prototypes and categorizes them into smooth, mid-textured, and textured areas. To resist forged-watermark attacks and promote self-recovery ability, the relationships among blocks are created by a toral automorphism with an asymmetric key structure. Furthermore, the watermark prototypes are disordered by a one-way hashing function and encrypted by a public-key encryption function to increase the security of watermarks. Finally, the watermarks are embedded to protect the integrity of images. Experiments show that the proposed scheme can correctly localize tampered areas and remedy them to the extent of JPEG-compression quality even when 50% of the image is cropped, and resist forged-watermark attacks.

X-ray fluorescence computed tomography (XFCT) allows for the reconstruction of the distribution of elements within a sample from measurements of fluorescence x rays produced by irradiation of the sample with monochromatic synchrotron radiation. XFCT is not a transmission tomography modality, but rather a stimulated emission tomography modality; thus correction for attenuation of the incident and fluorescence photons is essential if accurate images are to be obtained. This is challenging because the attenuation map is, in general, known only at the stimulating beam energy and not at the various fluorescence energies of interest. We make use of empirically fitted analytic expressions for x-ray attenuation coefficients to express the unknown attenuation maps as linear combinations of known quantities and the unknown elemental concentrations of interest. We then develop an iterative image reconstruction algorithm based on penalized-likelihood methods that have been developed for medical emission tomography. Studies with numerical phantoms indicate that the approach is able to produce qualitatively and quantitatively accurate reconstructed images even in the face of severe attenuation. We also apply the method to real synchrotron-acquired data and demonstrate a marked improvement in image quality relative to filtered backprojection reconstruction.

A modified code division multiple-access (MCDMA) technique is constructed by the spread-spectrum technique and a mix coder, and then it is used to configure a multiple-watermarking scheme for still images. Another type of multiple-watermarking scheme, non-code-division multiple-access watermarking (NCMW), is used to demonstrate that the MCDMA scheme is superior. In the embedding process, three watermark bits are modulated to the five-bit MCDMA code. Then the 15 MCDMA bits are concealed in the coefficients of a group that consists of four DCT blocks. Empirical results show that our proposed scheme can sustain attacks like JPEG lossy compression, rotation, resizing, cropping, painting, noising, and blurring. Compared with other multiple-watermarking schemes, our proposed method has two advantages: (1) The secret image has very high security owing to the use of MCDMA for digital communication. (2) The extracted watermarks have the same quality under all kinds of attacks, whereas other schemes yield different extracted-watermark quality.

The objective of region-of-interest (ROI) detection is to identify portions of an image that contain targets. It is an important procedure for reducing data volume without losing important target information. The proposed algorithm aims at generating accurate representations of the ROIs such that each ROI covers one complete target. In addition, computation of the proposed algorithm is reduced by making use of information such as image resolution and approximate size of the targets. For this purpose, a multiscale, hierarchical architecture is developed. Results of the ROI detection in low-quality aerial imagery are provided to illustrate the effectiveness of the proposed algorithm.

A new local feature extraction method is introduced. The directionality of local facial regions is regarded as essential information for discriminating faces in our approach, which is motivated by the directional selectivity of the Gabor wavelet transformation, which has been preferred to others for face recognition. The discriminative directional information is forced to be compacted in a few coefficients by applying principle-component analysis with the support of directional classification in the discrete cosine transform domain. The local features extracted by our method are better at discriminating face patterns than previous ones, as was verified by comparison of class-separability results. Also, in face recognition simulations using rigid and flexible face matching strategies based on locally extracted features, our proposed method showed outstanding performance.

A method of detecting target objects in still images despite any kind of geometrical distortion is demonstrated. Two existing techniques are combined, each one capable of creating invariance to various types of distortion of the target object. A maximum average correlation height (MACH) filter is used to create invariance to orientation and gives good tolerance to background clutter and noise. A log r- mapping is employed to give invariance to in-plane rotation and scale by transforming rotation and scale variations of the target object into vertical and horizontal shifts. The MACH filter is trained on the log r- map of the target for a range of orientations and applied sequentially over regions of interest in the input image. Areas producing a strong correlation response can then be used to determine the position, in-plane rotation, and scale of the target objects in the scene.

In visual tracking, the object's appearance may change over time due to illumination changes, pose variations, and partial or full occlusions. This variability makes tracking difficult. This paper proposes an adaptive appearance model for visual tracking. The model can adapt to changes in object appearance over time. The value of each pixel is modeled by a Gaussian mixture distribution. A novel update scheme based on the expectation maximization algorithm is developed to update the appearance model parameters. In designing the tracking algorithm, the observation model is based on the adaptive appearance model, and a particle filter is employed. Outlier pixels and occlusions are handled using a robust-statistics technique. Numerous experimental results demonstrate that the proposed algorithm can track objects well under illumination changes, large pose variations, and partial or full occlusions.

This paper presents an efficient skeletonization method based on generalized discrete local symmetries. A generalized discrete local symmetry is a local symmetry between a contour pixel and a contour segment on the opposite side of the underlying shape. The centerlines of the local symmetries of a shape form the skeleton of the shape. The proposed method is fast compared to two existing skeletonization methods. A speed-up factor of more than 50 can be achieved for high-resolution images. The method is also robust against noise and geometrical transformations, such as rotation and uniform scaling. The method is suitable for skeletonizing high-resolution images where it can be impractical to use other skeletonization techniques, such as thinning and distance transforms, because of the high computational complexity.

We consider integral transforms that can describe ideal imaging optical systems with annular impulse response. The integral transform, referred to as the annular Radon transform (ART), is considered as an average taken along all circles of fixed radius in the plane. The inversion formula for the ART is given. It is shown that for a function of two variables to be reconstructed uniquely, the averaging functions along all circles with at least two different radii need to be known. The ART can be optically realized using a spatial filtering system (SFS) with amplitude filter, its transmittance being proportional to the Bessel function of zero order. Also, an axicon transform (AT) is considered that can be optically realized using a SFS with axicon in the spatial-frequency plane. The inverse and direct ATs are shown to be of the same form (up to a constant). A numerical comparison of the AT and ART has been made when both were used for reconstruction of transformed and distorted images. The relation between the distortion variances of the output functions and the SFS reconstructed input function is derived.