Tip/tilt estimation from defocused images

In astronomical imaging, the errors in the wave-front slope are a significant cause of aberrations in the detected image. We investigate how the slope can be estimated optimally using an intensity measurement of the propagated wave front. We show that the optimal location for detection of wave-front tilt is the focal plane, and we quantify the error in using defocused images, such as would be obtained from a curvature sensor, for estimating the wave-front tilt. The effect of using broadband light is also quantified.     

Equilibrated patch recovery error estimates: simple and accurate upper bounds of the error

This paper introduces a new recovery‐type error estimator ensuring local equilibrium and yielding a guaranteed upper bound of the error. The upper bound property requires the recovered solution to be both statically equilibrated and continuous. The equilibrium is obtained locally (patch‐by‐patch) and the continuity is enforced by a postprocessing based on the partition of the unity concept. This postprocess is expected to preserve the features of the locally equilibrated stress field. Nevertheless, the postprocess phase modifies the equilibrium, which is no longer exactly fulfilled. A new methodology is introduced that yields upper bound estimates by taking into account this lack of equilibrium. This requires computing the ??₂ norm of the error or relating it with the energy norm. The guaranteed upper bounds are obtained by using a pessimistic bound of the error ??₂ norm, derived from an eigenvalue problem. Nevertheless, these bounds are not sharp. An additional strategy based on a more accurate assessment of the error ??₂ norm is introduced, providing sharp estimates, which are practical upper bounds as it is demonstrated in the numerical tests. Copyright © 2006 John Wiley & Sons, Ltd.     

Digital restoration of defocused images in the wavelet domain

Many cameras nowadays are equipped with an autofocus mechanism that attempts to take pictures at the best possible focus. However, there are situations in which the pictures are still out of focus, such as when the photographer has mistakenly focused at a wrong position or when the focusing region consists of objects of different depths and therefore confuses the autofocus system. With a digital camera, we can attempt to use digital image-restoration techniques to bring the pictures back into focus. We design an algorithm that restores the image by digitally enhancing the corresponding frequency bands. We employ the restoration in the wavelet domain so that this restoration scheme can be compliant with JPEG 2000, which is positioned to succeed JPEG as the next image-compression standard and has the potential to be widely adopted by the digital photography industry owing to its many advanced features.     

Wave-front sensing from defocused images by use of wave-front slopes

We describe a novel technique for deriving wave-front aberrations from two defocused intensity measurements. The intensity defines a probability density function, and the method is based on the evolution of the cumulative density function of the intensity with light propagation. In one dimension, the problem is easily solved with a histogram specification procedure, with a linear relationship between the wave-front slope and the difference in the abscissas of the histograms. In two dimensions, the method requires use of a Radon transform. Simulation results demonstrate that good reconstructions can be attained down to 100 photons in each detector. In addition, the method is insensitive to scintillation at the aperture.     

Correlation postprocessing-based method for the detection of defocused images

We present a method to detect patterns in defocused scenes by means of a joint transform correlator. We describe analytically the correlation plane, and we also introduce an original procedure to recognize the target by postprocessing the correlation plane. The performance of the methodology when the defocused images are corrupted by additive noise is also considered.     

Discrete cosine transform domain restoration of defocused images

In discrete-cosine-transform-based (DCT-based) compressions such as JPEG it is a common practice to use the same quantization matrix for both encoding and decoding. However, this need not be the case, and the flexibility of designing different matrices for encoding and decoding allows us to perform image restoration in the DCT domain. This is especially useful when we have severe limitations on the computational power, for instance, with in-camera image manipulation for programmable digital cameras. We provide an algorithm that compensates partially for a defocus error in image acquisition, and experimental results show that the restored image is closer to the in-focus image than is the defocused image.     

Nanometric depth resolution from multi-focal images in microscopy

We describe a method for tracking the position of small features in three dimensions from images recorded on a standard microscope with an inexpensive attachment between the microscope and the camera. The depth-measurement accuracy of this method is tested experimentally on a wide-field, inverted microscope and is shown to give approximately 8 nm depth resolution, over a specimen depth of approximately 6 µm, when using a 12-bit charge-coupled device (CCD) camera and very bright but unresolved particles. To assess low-flux limitations a theoretical model is used to derive an analytical expression for the minimum variance bound. The approximations used in the analytical treatment are tested using numerical simulations. It is concluded that approximately 14 nm depth resolution is achievable with flux levels available when tracking fluorescent sources in three dimensions in live-cell biology and that the method is suitable for three-dimensional photo-activated localization microscopy resolution. Sub-nanometre resolution could be achieved with photon-counting techniques at high flux levels.     

合成孔径成像中掩埋目标的深度误差分析

在掩埋目标三维成像过程中,沉积层底质的不同与掩埋深度的变化,会使成像结果中目标深度与真实深度出现偏差。针对这一问题,可以利用下视的面阵合成孔径三维成像算法,通过构建水下分层模型与声速剖面模型,对掩埋点目标进行三维成像仿真。通过改变沉积层底质与掩埋深度,从理论分析与仿真结果研究深度误差的变化。研究表明,深度误差随沉积层声速和掩埋深度的增加而不断变大。     

Quantitative analysis of sinoatrial node using Doppler tissue images

A method has been developed to quantitatively analyze sinoatrial nodes (SAN) using Doppler tissue images (DTI). Doppler tissue images of SAN are acquired using an intracardiac catheter via the superior vena cava in an in vivo experiment. A sequence of DTI images of a SAN is obtained, and a complete cycle of the SAN excitation is observed. The tissue acceleration of the SAN is extracted and quantitatively analyzed. The estimated time-acceleration curve of the SAN exhibits remarkable similarity to the electrocardiogram curve. This is the first report on such finding. The experimental results show that the tissue movement of the SAN correlates with electrical cardiac activities and closely associates with the different phases of the cardiac cycle. This method has great potential in characterizing the local cardiac activities through the study of the conduct pathway.     

Recovering lower bounds of the error by postprocessing implicit residual a posteriori error estimates

Classical residual type error estimators approximate the error flux around the elements and yield upper bounds of the exact (or reference) error. Lower bounds of the error are also needed in goal oriented adaptivity and for bounds on functional outputs. This work introduces a simple and cheap strategy to recover a lower bound estimate from standard upper bound estimates. This lower bound may also be used to assess the effectivity of the former estimate and to improve it. Copyright © 2003 John Wiley & Sons, Ltd.     

New error bounds for M-testing and estimation of source location with subdiffractive error

I present new lower and upper bounds on the minimum probability of error (MPE) in Bayesian multihypothesis testing that follow from an exact integral of a version of the statistical entropy of the posterior distribution, or equivocation. I also show that these bounds are exponentially tight and thus achievable in the asymptotic limit of many conditionally independent and identically distributed measurements. I then relate the minimum mean-squared error (MMSE) and the MPE by means of certain elementary error probability integrals. In the second half of the paper, I compare the MPE and MMSE for the problem of locating a single point source with subdiffractive uncertainty. The source-strength threshold needed to achieve a desired degree of source localization seems to be far more modest than the well established threshold for the different optical super-resolution problem of disambiguating two point sources with subdiffractive separation.     

Quantitative image analysis of broadband CARS hyperspectral images of polymer blends

We demonstrate that broadband coherent anti-Stokes Raman scattering (CARS) microscopy can be very useful for fast acquisition of quantitative chemical images of multilayer polymer blends. This is challenging because the raw CARS signal results from the coherent interference of resonant Raman and nonresonant background and its intensity is not linearly proportional to the concentration of molecules of interest. Here we have developed a sequence of data-processing steps to retrieve background-free and noise-reduced Raman spectra over the whole frequency range including both the fingerprint and C-H regions. Using a classical least-squares approach, we are able to decompose a Raman hyperspectral image of a tertiary polymer blend into quantitative chemical images of individual components. We use this method to acquire 3-D sectioned quantitative chemical images of a multilayer polymer blend of polystyrene, styrene-ethylene/propylene copolymer, and polypropylene that have overlapping spectral peaks.     

颅像重合检验中的形变与误差

本文从几何光学的锥体投影原理出发,全面阐述颅像重合检验过程中的若干主要问题,对形变及误差进行了数理分析。并得出,除对颅骨进行的法医学(如DNA识别)、人类学及相貌学检验外,颅像重合检验不宜作为法律审判的依据。     

New splitting algorithms for geometric transformations of digital images and their error analysis

For digital images and patterns under the nonlinear geometric transformation, T: (ξ, η) → (x, y), this study develops the splitting algorithms (i.e., the pixel‐division algorithms) that divide a 2D pixel into N × N subpixels, where N is a positive integer chosen as N = 2 ^k(k ≥ 0) in practical computations. When the true intensity values of pixels are known, this method makes it easy to compute the true intensity errors. As true intensity values are often unknown, the proposed approaches can compute the sequential intensity errors based on the differences between the two approximate intensity values at N and N/2. This article proposes the new splitting–shooting method, new splitting integrating method, and their combination. These methods approximate results show that the true errors of pixel intensity are O(H), where H is the pixel size. Note that the algorithms in this article do not produce any sequential errors as N ≥ N₀, where N₀ (≥2) is an integer independent of N and H. This is a distinctive feature compared to our previous papers on this subject. The other distinct feature of this article is that the true error bound O(H) is well suited to images with all kinds of discontinuous intensity, including scattered pixels. © 2011 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 21, 323–335, 2011     

Bispectral analysis and recovery of images distorted by a moving water surface

We propose a new algorithm to recover a geometrically correct image of an object or scene from a set of images distorted by the wave motion of a water surface. Under mild conditions where the wavy surface normals weakly satisfy a Gaussian distribution, we demonstrate that the geometric distortion can be removed and a corrected image can be recovered. Our method is based on higher-order spectra analysis-in particular, the bispectrum, similar to its use in astronomical speckle imaging. In adapting this technique to imaging through or over a moving water surface, special care must be taken, and specifically tailored techniques are discussed in this paper. Our algorithm has been tested under two different scenarios: the refraction of light through a water surface (the underwater case) and the reflection of light from a water surface (the reflection case). Results in both cases have been encouraging.     

调制度测量轮廓术高度信息获取新算法

理论分析表明,在正弦光栅成像面前后调制度分布是一种高斯分布,据此提出一种基于高斯曲线拟合的调制度测量轮廓术高度信息获取新算法：高斯曲线拟合法。该算法对调制度分布序列中极值位置附近的部分数据点利用高斯函数进行拟合,从获得的拟合曲线求出调制度极大值的真实位置,该位置对应的扫描距离即为对应点的高度信息。对同一测量数据利用三种高度算法分别计算高度,测量精度为：极值算法0．78mm、重心算法0．37mm和高斯曲线拟合算法0．22mm,表明高斯曲线拟合法可以获得更高的测量精度。     

Algorithm for training the minimum error one-class classifier of images

We propose a training algorithm for one-class classifiers in order to minimize the classification error. The aim is to choose the optimal value of the slack parameter, which controls the selectiveness of a classifier. The one-class classifier based on the coordinated clusters representation of images is trained and then used for the classification of texture images. As the slack parameter C varies through a range of values, for each C, the misclassification rate is computed using only the training samples. The value of C that yields the minimum misclassification rate, estimated over the training set, is taken as the optimal value, C(opt). Finally, the optimized classifier is tested on the extended database of images. Experimental results demonstrate the validity of the proposed method. In our experiments, classification efficiency approaches, or is equal to, 100%, after the optimal training of the classifier.     

Derivatives and their error bounds in second order problems by finite element

A previous paper by the authors presented a finite element technique for computing accurate and bounded solutions at arbitrary points in second order mixed boundary value problems. The technique is extended herein to the computation of accurate and bounded derivatives at arbitrary interior points. Numerical results are presented to illustrate both the strengths and limitations to the method.     

Quantitative depth profile analysis of micrometer-thick multilayered thin coatings using step-scan FT-IR photoacoustic spectroscopy

This paper demonstrates the results of the comparison of step-scan FT-IR photoacoustic spectroscopy with other established spectroscopic and microscopic techniques in the quantitative depth profile determination of micrometer- and submicrometer-thick multilayered thin coatings. The power of the phase rotation and phase spectrum analytical methods to clearly distinguish the infrared signature of submicrometer-thick coatings is demonstrated. The thickness determined by the step-scan FT-IR photoacoustic method is in very reasonable agreement with optical microtomy/microscopy measurements performed at-line during the coating process. The former technique described in detailed here offers substantial benefits in terms of measurement time and operator dependency, while not sacrificing the accuracy of the measurement. The problem of saturation and its effect on "real-life" samples is also discussed.