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PubMed2004

Adaptively quadratic (AQua) image interpolation.

Image interpolation is a key aspect of digital image processing. This paper presents a novel interpolation method based on optimal recovery and adaptively determining the quadratic signal class from the local image behavior. The advantages of the new interpolation method are the ability to interpolate directly by any factor and to model properties of the data acquisition system into the algorithm itself. Through comparisons with other algorithms it is shown that the new interpolation is not only mathematically optimal with respect to the underlying image model, but visually it is very efficient at reducing jagged edges, a place where most other interpolation algorithms fail.

Algorithms↗
PubMed2005

Color demosaicking via directional linear minimum mean square-error estimation.

Digital cameras sample scenes using a color filter array of mosaic pattern (e.g., the Bayer pattern). The demosaicking of the color samples is critical to the image quality. This paper presents a new color demosaicking technique of optimal directional filtering of the green-red and green-blue difference signals. Under the assumption that the primary difference signals (PDS) between the green and red/blue channels are low pass, the missing green samples are adaptively estimated in both horizontal and vertical directions by the linear minimum mean square-error estimation (LMMSE) technique. These directional estimates are then optimally fused to further improve the green estimates. Finally, guided by the demosaicked full-resolution green channel, the other two color channels are reconstructed from the LMMSE filtered and fused PDS. The experimental results show that the presented color demosaicking technique outperforms the existing methods both in PSNR measure and visual perception.

Algorithms↗
PubMed2005

Statistical behavior of joint least-square estimation in the phase diversity context.

The images recorded by optical telescopes are often degraded by aberrations that induce phase variations in the pupil plane. Several wavefront sensing techniques have been proposed to estimate aberrated phases. One of them is phase diversity, for which the joint least-square approach introduced by Gonsalves et al. is a reference method to estimate phase coefficients from the recorded images. In this paper, we rely on the asymptotic theory of Toeplitz matrices to show that Gonsalves' technique provides a consistent phase estimator as the size of the images grows. No comparable result is yielded by the classical joint maximum likelihood interpretation (e.g., as found in the work by Paxman et al.). Finally, our theoretical analysis is illustrated through simulated problems.

Computer Simulation↗
PubMed2005

Is image steganography natural?

Steganography is the art of secret communication. Its purpose is to hide the presence of information, using, for example, images as covers. We experimentally investigate if stego-images, bearing a secret message, are statistically "natural." For this purpose, we use recent results on the statistics of natural images and investigate the effect of some popular steganography techniques. We found that these fundamental statistics of natural images are, in fact, generally altered by the hidden "nonnatural" information. Frequently, the change is consistently biased in a given direction. However, for the class of natural images considered, the change generally falls within the intrinsic variability of the statistics, and, thus, does not allow for reliable detection, unless knowledge of the data hiding process is taken into account. In the latter case, significant levels of detection are demonstrated.

Algorithms↗
PubMed2005

An information fidelity criterion for image quality assessment using natural scene statistics.

Measurement of visual quality is of fundamental importance to numerous image and video processing applications. The goal of quality assessment (QA) research is to design algorithms that can automatically assess the quality of images or videos in a perceptually consistent manner. Traditionally, image QA algorithms interpret image quality as fidelity or similarity with a "reference" or "perfecft" image in some perceptual space. Such "full-referenc" QA methods attempt to achieve consistency in quality prediction by modeling salient physiological and psychovisual features of the human visual system (HVS), or by arbitrary signal fidelity criteria. In this paper, we approach the problem of image QA by proposing a novel information fidelity criterion that is based on natural scene statistics. QA systems are invariably involved with judging the visual quality of images and videos that are meant for "human consumption." Researchers have developed sophisticated models to capture the statistics of natural signals, that is, pictures and videos of the visual environment. Using these statistical models in an information-theoretic setting, we derive a novel QA algorithm that provides clear advantages over the traditional approaches. In particular, it is parameterless and outperforms current methods in our testing. We validate the performance of our algorithm with an extensive subjective study involving 779 images. We also show that, although our approach distinctly departs from traditional HVS-based methods, it is functionally similar to them under certain conditions, yet it outperforms them due to improved modeling. The code and the data from the subjective study are available at.

Algorithms↗
PubMed2006

The fundamentals of average local variance--Part II: Sampling simple regular patterns with optical imagery.

In this investigation, the characteristics of the average local variance (ALV) function is investigated through the acquisition of images at different spatial resolutions of constructed scenes of regular patterns of black and white squares. It is shown that the ALV plot consistently peaks at a spatial resolution in which the pixels has a size corresponding to half the distance between scene objects, and that, under very specific conditions, it also peaks at a spatial resolution in which the pixel size corresponds to the whole distance between scene objects. It is argued that the peak at object distance when present is an expression of the Nyquist sample rate. The presence of this peak is, hence, shown to be a function of the matching between the phase of the scene pattern and the phase of the sample grid, i.e., the image. When these phases match, a clear and distinct peak is produced on the ALV plot. The fact that the peak at half the distance consistently occurs in the ALV plot is linked to the circumstance that the sampling interval (distance between pixels) and the extent of the sampling unit (size of pixels) are equal. Hence, at twice the Nyquist sampling rate, each fundamental period of the pattern is covered by four pixels; therefore, at least one pixel is always completely embedded within one pattern element, regardless of sample scene phase. If the objects in the scene are scattered with a distance larger than their extent, the peak will be related to the size by a factor larger than 1/2. This is suggested to be the explanation to the results presented by others that the ALV plot is related to scene-object size by a factor of 1/2-3/4.

Algorithms↗
PubMed2006

The fundamentals of average local variance--Part I: Detecting regular patterns.

The method of average local variance (ALV) computes the mean of the standard deviation values derived for a 3 x 3 moving window on a successively coarsened image to produce a function of ALV versus spatial resolution. In developing ALV, the authors used approximately a doubling of the pixel size at each coarsening of the image. They hypothesized that ALV is low when the pixel size is smaller than the size of scene objects because the pixels on the object will have similar response values. When the pixel and objects are of similar size, they will tend to vary in response and the ALV values will increase. As the size of pixels increase further, more objects will be contained in a single pixel and ALV will decrease. The authors showed that various cover types produced single peak ALV functions that inexplicitly peaked when the pixel size was 1/2 to 3/4 of the object size. This paper reports on work done to explore the characteristics of the various forms of the ALV function and to understand the location of the peaks that occur in this function. The work was conducted using synthetically generated image data. The investigation showed that the hypothesis originally proposed in is not adequate. A new hypothesis is proposed that the ALV function has peak locations that are related to the geometric size of pattern structures in the scene. These structures are not always the same as scene objects. Only in cases where the size of and separation between scene objects are equal does the ALV function detect the size of the objects. In situations where the distance between scene objects are larger than their size, the ALV function has a peak at the object separation, not at the object size. This work has also shown that multiple object structures of different sizes and distances in the image provide multiple peaks in the ALV function and that some of these structures are not implicitly recognized as such from our perspective. However, the magnitude of these peaks depends on the response mix in the structures, complicating their interpretation and analysis. The analysis of the ALV Function is, thus, more complex than that generally reported in the literature.

Algorithms↗
PubMed2006

Variational denoising of partly textured images by spatially varying constraints.

Denoising algorithms based on gradient dependent regularizers, such as nonlinear diffusion processes and total variation denoising, modify images towards piecewise constant functions. Although edge sharpness and location is well preserved, important information, encoded in image features like textures or certain details, is often compromised in the process of denoising. We propose a mechanism that better preserves fine scale features in such denoising processes. A basic pyramidal structure-texture decomposition of images is presented and analyzed. A first level of this pyramid is used to isolate the noise and the relevant texture components in order to compute spatially varying constraints based on local variance measures. A variational formulation with a spatially varying fidelity term controls the extent of denoising over image regions. Our results show visual improvement as well as an increase in the signal-to-noise ratio over scalar fidelity term processes. This type of processing can be used for a variety of tasks in partial differential equation-based image processing and computer vision, and is stable and meaningful from a mathematical viewpoint.

Algorithms↗
PubMed2006

Estimation of optimal PDE-based denoising in the SNR sense.

This paper is concerned with finding the best partial differential equation-based denoising process, out of a set of possible ones. We focus on either finding the proper weight of the fidelity term in the energy minimization formulation or on determining the optimal stopping time of a nonlinear diffusion process. A necessary condition for achieving maximal SNR is stated, based on the covariance of the noise and the residual part. We provide two practical alternatives for estimating this condition by observing that the filtering of the image and the noise can be approximated by a decoupling technique, with respect to the weight or time parameters. Our automatic algorithm obtains quite accurate results on a variety of synthetic and natural images, including piecewise smooth and textured ones. We assume that the statistics of the noise were previously estimated. No a priori knowledge regarding the characteristics of the clean image is required. A theoretical analysis is carried out, where several SNR performance bounds are established for the optimal strategy and for a widely used method, wherein the variance of the residual part equals the variance of the noise.

Algorithms↗
PubMed2006

A statistical evaluation of recent full reference image quality assessment algorithms.

Measurement of visual quality is of fundamental importance for numerous image and video processing applications, where the goal of quality assessment (QA) algorithms is to automatically assess the quality of images or videos in agreement with human quality judgments. Over the years, many researchers have taken different approaches to the problem and have contributed significant research in this area and claim to have made progress in their respective domains. It is important to evaluate the performance of these algorithms in a comparative setting and analyze the strengths and weaknesses of these methods. In this paper, we present results of an extensive subjective quality assessment study in which a total of 779 distorted images were evaluated by about two dozen human subjects. The "ground truth" image quality data obtained from about 25,000 individual human quality judgments is used to evaluate the performance of several prominent full-reference image quality assessment algorithms. To the best of our knowledge, apart from video quality studies conducted by the Video Quality Experts Group, the study presented in this paper is the largest subjective image quality study in the literature in terms of number of images, distortion types, and number of human judgments per image. Moreover, we have made the data from the study freely available to the research community. This would allow other researchers to easily report comparative results in the future.

Algorithms↗
PubMed2006

Mining statistically significant associations for exploratory analysis of human sleep data.

We introduce a specialized association rule mining technique that can extract patterns from complex sleep data comprising polysomnographic recordings, clinical summaries, and sleep questionnaire responses. The rules mined can describe associations among temporally annotated events and questionnaire or summary data; e.g., the likelihood that an occurrence of a rapid eye movement (REM) sleep stage during the second 100 sleep epochs of the night is associated with moderate caffeine intake. We use chi2 analysis to ensure statistical significance of the mined rules at the level P < 0.05. Our results, obtained by mining sleep-related data from 242 human subjects, reveal clinically interesting associations among the polysomnographic and summary variables. Our experience suggests that association mining may also be useful for selection of variables prior to using logistic regression.

Algorithms↗
PubMed2004

Propagation of errors from the sensitivity image in list mode reconstruction.

List mode image reconstruction is attracting renewed attention. It eliminates the storage of empty sinogram bins. However, a single back projection of all LORs is still necessary for the pre-calculation of a sensitivity image. Since the detection sensitivity is dependent on the object attenuation and detector efficiency, it must be computed for each study. Exact computation of the sensitivity image can be a daunting task for modern scanners with huge numbers of LORs. Thus, some fast approximate calculation may be desirable. In this paper, we analyze the error propagation from the sensitivity image into the reconstructed image. The theoretical analysis is based on the fixed point condition of the list mode reconstruction. The nonnegativity constraint is modeled using the Kuhn-Tucker condition. With certain assumptions and the first-order Taylor series approximation, we derive a closed form expression for the error in the reconstructed image as a function of the error in the sensitivity image. The result shows that the error response is frequency-dependent and provides a simple expression for determining the required accuracy of the sensitivity image calculation. Computer simulations show that the theoretical results are in good agreement with the measured results.

Algorithms↗
PubMed2006

Three-class ROC analysis--the equal error utility assumption and the optimality of three-class ROC surface using the ideal observer.

Previously, we have developed a decision model for three-class receiver operating characteristic (ROC) analysis based on decision theory. The proposed decision model maximizes the expected decision utility under the assumption that incorrect decisions have equal utilities under the same hypothesis (equal error utility assumption). This assumption reduced the dimensionality of the "general" three-class ROC analysis and provided a practical figure-of-merit to evaluate the three-class task performance. However, it also limits the generality of the resulting model because the equal error utility assumption will not apply for all clinical three-class decision tasks. The goal of this study was to investigate the optimality of the proposed three-class decision model with respect to several other decision criteria. In particular, besides the maximum expected utility (MEU) criterion used in the previous study, we investigated the maximum-correctness (MC) (or minimum-error), maximum likelihood (ML), and Nyman-Pearson (N-P) criteria. We found that by making assumptions for both MEU and N-P criteria, all decision criteria lead to the previously-proposed three-class decision model. As a result, this model maximizes the expected utility under the equal error utility assumption, maximizes the probability of making correct decisions, satisfies the N-P criterion in the sense that it maximizes the sensitivity of one class given the sensitivities of the other two classes, and the resulting ROC surface contains the maximum likelihood decision operating point. While the proposed three-class ROC analysis model is not optimal in the general sense due to the use of the equal error utility assumption, the range of criteria for which it is optimal increases its applicability for evaluating and comparing a range of diagnostic systems.

Algorithms↗
PubMed2004

Effects of classifier structures and training regimes on integrated segmentation and recognition of handwritten numeral strings.

In integrated segmentation and recognition of character strings, the underlying classifier is trained to be resistant to noncharacters. We evaluate the performance of state-of-the-art pattern classifiers of this kind. First, we build a baseline numeral string recognition system with simple but effective presegmentation. The classification scores of the candidate patterns generated by presegmentation are combined to evaluate the segmentation paths and the optimal path is found using the beam search strategy. Three neural classifiers, two discriminative density models, and two support vector classifiers are evaluated. Each classifier has some variations depending on the training strategy: maximum likelihood, discriminative learning both with and without noncharacter samples. The string recognition performances are evaluated on the numeral string images of the NIST Special Database 19 and the zipcode images of the CEDAR CDROM-1. The results show that noncharacter training is crucial for neural classifiers and support vector classifiers, whereas, for the discriminative density models, the regularization of parameters is important. The string recognition results compare favorably to the best ones reported in the literature though we totally ignored the geometric context. The best results were obtained using a support vector classifier, but the neural classifiers and discriminative density models show better trade-off between accuracy and computational overhead.

Algorithms↗
PubMed2004

Image distortion analysis using polynomial series expansion.

In this paper, we derive a technique for analysis of local distortions which affect data in real-world applications. In the paper, we focus on image data, specifically handwritten characters. Given a reference image and a distorted copy of it, the method is able to efficiently determine the rotations, translations, scaling, and any other distortions that have been applied. Because the method is robust, it is also able to estimate distortions for two unrelated images, thus determining the distortions that would be required to cause the two images to resemble each other. The approach is based on a polynomial series expansion using matrix powers of linear transformation matrices. The technique has applications in pattern recognition in the presence of distortions.

Algorithms↗
PubMed2004

Adaptation in statistical pattern recognition using tangent vectors.

We integrate the tangent method into a statistical framework for classification analytically and practically. The resulting consistent framework for adaptation allows us to efficiently estimate the tangent vectors representing the variability. The framework improves classification results on two real-world pattern recognition tasks from the domains handwritten character recognition and automatic speech recognition.

Algorithms↗
PubMed2004

Utilization of hierarchical, stochastic relationship modeling for Hangul character recognition.

In structural character recognition, a character is usually viewed as a set of strokes and the spatial relationships between them. Therefore, strokes and their relationships should be properly modeled for effective character representation. For this purpose, we propose a modeling scheme by which strokes as well as relationships are stochastically represented by utilizing the hierarchical characteristics of target characters. A character is defined by a multivariate random variable over the components and its probability distribution is learned from a training data set. To overcome difficulties of the learning due to the high order of the probability distribution (a problem of curse of dimensionality), the probability distribution is factorized and approximated by a set of lower-order probability distributions by applying the idea of relationship decomposition recursively to components and subcomponents. Based on the proposed method, a handwritten Hangul (Korean) character recognition system is developed. Recognition experiments conducted on a public database show the effectiveness of the proposed relationship modeling. The recognition accuracy increased by 5.5 percent in comparison to the most successful system ever reported.

Algorithms↗
PubMed2005

Offline geometric parameters for automatic signature verification using fixed-point arithmetic.

This paper presents a set of geometric signature features for offline automatic signature verification based on the description of the signature envelope and the interior stroke distribution in polar and Cartesian coordinates. The features have been calculated using 16 bits fixed-point arithmetic and tested with different classifiers, such as hidden Markov models, support vector machines, and Euclidean distance classifier. The experiments have shown promising results in the task of discriminating random and simple forgeries.

Algorithms↗