absolute moment block truncation coding and its application to color images a new quantization method that uses the criterion of preserving sample absolute moments is presented this is based on the same basic idea for block truncation coding of delp and mitchell but it is simpler in any practical implementation moreover output equations are those for a two level nonparametric minimum mean square error quantizer when the threshold is fixed to the sample mean the application of this method to single frame color images is developed a color image coding system that uses absolute moment block truncation coding of luminance and chroma information is presented resulting color images show reasonable performance with bit rates as low as 2 13 bits pixel

bispectrum estimation a parametric approach higher order spectra contain information about random processes that is not contained in the ordinary power spectrum such as the degree of nonlinearity and deviations from normality estimation of the bispectrum which is a third order spectrum has been applied in various fields to obtain information regarding quadratic phase coupling among harmonic components and non gaussianness of processes existing methods of bispectrum estimation are patterned after the conventional methods of power spectrum estimation which are known to possess certain limitations the paper proposes a parametric approach to bispectrum estimation based on a non gaussian white noise driven autoregressive ar model the ar parameter estimates are obtained by solving the third order recursion equations which may be toeplitz in form but not symmetric it is shown that the method provides bispectral estimates that are far superior to the conventional estimates in terms of bispectral fidelity and that in the case of detecting phase coupling among sinusoids the method provides significantly better resolution

the complex cepstrum of higher order cumulants and nonminimum phase system identification a computationally efficient identification procedure is proposed for a nongaussian white noise driven linear time invariant nonminimum phase system the method is based on the idea of computing the complex cepstrum of higher order cumulants of the system output in particular the differential cepstrum parameters of the nonminimum phase impulse response are estimated directly from higher order cumulants by least squares solution or two dimensional fft operations the method reconstructs the minimum phase and maximum phase impulse response components separately it is flexible enough to be applied on autoregressive ar moving average ma or arma system without a priori knowledge of the type of the system benchmark simulation examples demonstrate the effectiveness of the method even with short length data records

parameter estimation of exponentially damped sinusoids using higher order statistics a new approach for the estimation of the parameters of exponentially damped sinusoids is introduced based on third or fourth order statistics of the observation signal the method may be seen as an extension of the minimum norm principal eigenvectors method to higher order statistics domains the strong points and limitations of the method are discussed as well as sufficient conditions for the existence of the solution the utilization of the method in the case of finite length signals in the presence of additive gaussian noise white or colored is addressed monte carlo simulations demonstrate the effectiveness of the new method when the additive noise is colored gaussian with unknown autocorrelation sequence for different signal to noise ratios and a single data record the case of an ensemble of data records is studied when the exponentially damped sinusoids are assumed to have random phase

moment preserving quantization signal processing the general solution to the moment preserving mp quantizer problem is presented it is shown that the moment preserving quantizer is related to the gauss jacobi mechanical quadrature the output levels of the n level mp quantizer are the n zeros of an nth degree orthogonal polynomial associated with the input probability distribution function and the n 1 thresholds of the mp quantizer are related to the christoffel numbers through the chebyshev markov stieltjes separation theorem the statistical convergence of the mp quantizer is investigated mp quantizer tables are presented for the uniform gaussian and laplacian density functions the moment preserving quantizer is shown to be related to block truncation coding

color image compression based on block truncation coding using pattern fitting principle this paper describes a color image compression technique based on block truncation coding using pattern fitting btc pf high degree of correlation between the rgb planes of a color image is reduced by transforming them to o 1o 2o 3 planes each o i plane 1

k means type algorithms a generalized convergence theorem and characterization of local optimality the k means algorithm is a commonly used technique in cluster analysis in this paper several questions about the algorithm are addressed the clustering problem is first cast as a nonconvex mathematical program then a rigorous proof of the finite convergence of the k means type algorithm is given for any metric it is shown that under certain conditions the algorithm may fail to converge to a local minimum and that it converges under differentiability conditions to a kuhn tucker point finally a method for obtaining a local minimum solution is given

estimation of close sinusoids in colored noise and model discrimination this paper considers the estimation of the two close dominant frequencies in the signal when it is known a priori that the observation is a sum of two close sinusoids and an additive colored noise whose spectral density is unknown earlier attempts have assumed the additive noise to be independent next we develop decision rules for checking whether the observed signal has only one sinusoid or two close sinusoids all of the earlier studies assumed that there are two close sinusoids in the signal another model discrimination problem considered is the determination of the causal structure of the observed periodicity a rule is given to test whether the observation comes from a sinusoid plus additive noise possible colored or the observation comes from a stationary autoregressive model we also present a numerical study showing the efficacy of the robust estimation procedure for estimating the two frequencies and the decision rules for checking the number of dominant frequencies and the causal mechanism finally we compare the proposed method to well known methods used for two close sinusoids in white noise

toward a symbolic representation of intensity changes in images the symbolic representation of gray value variations is studied with emphasis on the gradient of the image function the goal is to relate the results of this analysis to the structure of the picture which is determined by the physics of the image generation process candidates for contour points are the maximal magnitudes of the gray value gradient for different scales in the direction of the gradient based on the output of such a bank of gradient filters a procedure is proposed to select automatically a suitable scale and with that the size of the right convolution kernel the application of poorly adapted filters which make the exact localization of gray value corners or t x and y junctions more difficult is thus avoided possible gaps at such junctions are discussed for images of real scenes and possibilities for the closure of some of these gaps are demonstrated when the extrema of the magnitudes of the gray value gradients are used

sensitivity analysis on the priority of the objective functions in lexicographic multiple objective linear programs this paper deals with a class of multiple objective linear programs molp called lexicographic multiple objective linear programs lmolp in this paper by providing an efficient algorithm which employs the preceding computations as well it is shown how we can solve the lmolp problem if the priority of the objective functions is changed in fact the proposed algorithm is a kind of sensitivity analysis on the priority of the objective functions in the lmolp problems

btc image coding using median filter roots in this paper we source encode the truncated block used in block truncation coding it is shown that the truncated block is well approximated by wide sense markoff statistics a signal having these characteristics has a high probability of belonging to the root signal set of median filters because the root signal space is much smaller than the binary space it takes fewer bits to specify the truncated block in the root signal space obtaining in this manner rate compression using two dimensional filtering we can reduce the standard btc rate of 1 63 bits pel to 1 31 bits pel using one dimensional filtering along with a trellis encoder rates close to 1 1 bits pel are obtained with this fixed length coding method

a preference structure on aspiration levels in a goal programming problem a fuzzy approach abstract a method is proposed for comparing different sets of aspiration levels assigned to goals in a goal programming problem this is based on the relative flexibilities that are realised under different sets of aspiration levels the relative flexibility depends upon the relative degree of choosing an objective in presence of other objectives a pair wise comparison method in the sense of shimura has been proposed for measuring the degree of choosing an objective in presence of other objectives this methodology affords to compare different sets of assigned aspiration levels and thereby choosing the best set as the one with least relative flexibility

exact maximum likelihood parameter estimation of superimposed exponential signals in noise a unified framework for the exact maximum likelihood estimation of the parameters of superimposed exponential signals in noise encompassing both the time series and the array problems is presented an exact expression for the ml criterion is derived in terms of the linear prediction polynomial of the signal and an iterative algorithm for the maximization of this criterion is presented the algorithm is equally applicable in the case of signal coherence in the array problem simulation shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques the algorithm is similar to those independently derived by kumaresan et al in addition to its practical value the present formulation is used to interpret previous methods such as prony s pisarenko s and modifications thereof

btc vq dct hybrid coding of digital images a hybrid btc vq dct block truncation coding vector quantization and discrete cosine transform image coding algorithm is presented the algorithm combines the simple computation and edge preservation properties of btc and the high fidelity and high compression ratio of adaptive dct with the high compression ratio and good subjective performance of vq and can be implemented with significantly lower coding delays than either vq or dct alone the bit map generated by btc is decomposed into a set of vectors which are vector quantized since the space of the btc bit map is much smaller than that of the original 8 b image a lookup table based vq encoder has been designed to fast encode the bit map adaptive dct coding using residual error feedback is implemented to encode the high mean and low mean subimages the overall computational complexity of btc vq dct coding is much less than either dct and vq while the fidelity performance is competitive the algorithm has strong edge preserving ability because of the implementation of btc as a precompress decimation the total compression ratio is about 10 1

vessel tree reconstruction in thoracic ct scans with application to nodule detection vessel tree reconstruction in volumetric data is a necessary prerequisite in various medical imaging applications specifically when considering the application of automated lung nodule detection in thoracic computed tomography ct scans vessel trees can be used to resolve local ambiguities based on global considerations and so improve the performance of nodule detection algorithms in this study a novel approach to vessel tree reconstruction and its application to nodule detection in thoracic ct scans was developed by using correlation based enhancement filters and a fuzzy shape representation of the data the proposed correlation based enhancement filters depend on first order partial derivatives and so are less sensitive to noise compared with hessian based filters additionally multiple sets of eigenvalues are used so that a distinction between nodules and vessel junctions becomes possible the proposed fuzzy shape representation is based on regulated morphological operations that are less sensitive to noise consequently the vessel tree reconstruction algorithm can accommodate vessel bifurcation and discontinuities a quantitative performance evaluation of the enhancement filters and of the vessel tree reconstruction algorithm was performed moreover the proposed vessel tree reconstruction algorithm reduced the number of false positives generated by an existing nodule detection algorithm by 38

btc image coding using vector quantization this paper describes source encoding of the outputs of a block truncation coder btc namely the overhead statistical information and the truncated block the statistical overhead and the truncated block exhibit properties which can be effectively used for their quantization as vectors vector quantization of these btc outputs results into reduction of the bit rate of the coder the bit rate reduces up to 1 5 bits pel if vector quantization is used on one of the outputs i e either the overhead information or the truncated block by vector quantizing both the btc outputs the bit rate can he reduced up to 1 0 bits pel without introducing many perceivable errors in the reconstructed output

piecewise linear approximation of vector valued images and curves via second order variational model variational models are known to work well for addressing image restoration regularization problems however most of the methods proposed in the literature are defined for scalar inputs and are used on multiband images such as rgb or multispectral imagery by the composition of a simple band wise processing this involves suboptimal results and may introduce artifacts only in a few cases variational models are extended to the case of vector valued inputs however the known implementations are restricted to the first order models while the second order models are never considered thus typical problems of the first order models such as the staircasing effect cannot be overtaken this paper considers a second order functional model to function approximation with free discontinuities given by blake zisserman bz and proposes an efficient minimization algorithm in the case of vector valued inputs in the bz model the hessian of the solution is penalized outside a set of finite length therefore the solution is forced to be piecewise linear moreover the model allows the formation of free discontinuities and free gradient discontinuities the proposed algorithm is applied to difficult color image restoration regularization problems and to piecewise linear approximation of curves in space

standardization of edge magnitude in color images edge detection is a useful task in low level image processing the efficiency of many image processing and computer vision tasks depends on the perfection of detecting meaningful edges to get a meaningful edge thresholding is almost inevitable in any edge detection algorithm many algorithms reported in the literature adopt ad hoc schemes for this purpose these algorithms require the threshold values to be supplied and tuned by the user there are many high level tasks in computer vision which are to be performed without human intervention thus there is a need to develop a scheme where a single set of threshold values would give acceptable results for many color images in this paper an attempt has been made to devise such an algorithm statistical variability of partial derivatives at each pixel is used to obtain standardized edge magnitude and is thresholded using two threshold values the advantage of standardization is evident from the results obtained

supervised enhancement filters application to fissure detection in chest ct scans in medical image processing many filters have been developed to enhance certain structures in 3 d data in this paper we propose to use pattern recognition techniques to design more optimal filters the essential difference with previous approaches is that we provide a system with examples of what it should enhance and suppress this training data is used to construct a classifier that determines the probability that a voxel in an unseen image belongs to the target structure s the output of a rich set of basis filters serves as input to the classifier in a feature selection process this set is reduced to a compact efficient subset we show that the output of the system can be reused to extract new features using the same filters that can be processed by a new classifier such a multistage approach further improves performance while the approach is generally applicable in this work the focus is on enhancing pulmonary fissures in 3 d computed tomography ct chest scans a supervised fissure enhancement filter is evaluated on two data sets one of scans with a normal clinical dose and one of ultra low dose scans results are compared with those of a recently proposed conventional fissure enhancement filter it is demonstrated that both methods are able to enhance fissures but the supervised approach shows better performance the areas under the receiver operating characteristic roc curve are 0 98 versus 0 90 for the normal dose data and 0 97 versus 0 87 for the ultra low dose data respectively

on the zeros of the linear prediction error filter for deterministic signals the zeros of a linear prediction error filter polynomial for a class of deterministic signals that are a sum of samples of m exponentially damped undamped sinusoids is studied it is assumed that n samples are available for processing and that they are uncorrupted by noise it is shown that the exponent parameters of the m signals can be determined from m zeros called signal zeros of an lth degree prediction error filter polynomial l m if l lies in between m and n m n m 2 in a special case the rest of the l m zeros of the filter polynomial switch are called extraneous zeros are shown to be approximately uniformly distributed with in the unit circle regardless of the type of exponentials in the signal if the prediction filter coefficients are chosen to have minimum euclidean length the results obtained provide insight into the estimation problem with noisy data

a differential geometric approach to automated segmentation of human airway tree airway diseases are frequently associated with morphological changes that may affect the physiology of the lungs accurate characterization of airways may be useful for quantitatively assessing prognosis and for monitoring therapeutic efficacy the information gained may also provide insight into the underlying mechanisms of various lung diseases we developed a computerized scheme to automatically segment the 3 d human airway tree depicted on computed tomography ct images the method takes advantage of both principal curvatures and principal directions in differentiating airways from other tissues in geometric space a puzzle game procedure is used to identify false negative regions and reduce false positive regions that do not meet the shape analysis criteria the negative impact of partial volume effects on small airway detection is partially alleviated by repeating the developed differential geometric analysis on lung anatomical structures modeled at multiple iso values thresholds in addition to having advantages such as full automation easy implementation and relative insensitivity to image noise and or artifacts this scheme has virtually no leakage issues and can be easily extended to the extraction or the segmentation of other tubular type structures e g vascular tree the performance of this scheme was assessed quantitatively using 75 chest ct examinations acquired on 45 subjects with different slice thicknesses and using 20 publicly available test cases that were originally designed for evaluating the performance of different airway tree segmentation algorithms

put absolute moment block truncation coding in perspective the purpose of this letter is to point out that the udpikar and raina 1987 modified block truncation coding btc has been misleading researchers as a different btc scheme in multiple publications for years in fact their algorithm is exactly identical to the second version of the lema and mitchell 1984 absolute moment block truncation coding ambtc mathematical proof is provided

junction detection for linear structures based on hessian correlation and shape information junctions have been demonstrated to be important features in many visual tasks such as image registration matching and segmentation as they can provide reliable local information this paper presents a method for detecting junctions in 2d images with linear structures as well as providing the number of branches and branch orientations the candidate junction points are selected through a new measurement which combines hessian information and correlation matrix then the locations of the junction centers are refined and the branches of the junctions are found using the intensity information of a stick shaped window at a number of orientations and the correlation value between the intensity of a local region and a gaussian shaped multi scale stick template the multi scale template is used here to detect the structures with various widths we present the results of our algorithm on images of different types and compare our algorithm with three other methods the results have shown that the proposed approach can detect junctions more accurately

estimating the parameters of exponentially damped sinusoids and pole zero modeling in noise we have presented techniques 1 6 based on linear prediction lp and singular value decomposition svd for accurate estimation of closely spaced frequencies of sinusoidal signals in noise in this note we extend these techniques to estimate the parameters of exponentially damped sinusoidal signals in noise the estimation procedure presented here makes use of backward prediction in addition to svd first the method is applied to data consisting of one and two exponentially damped sinusoids the choice of one and two signal components facilitates the comparison of estimation error in pole damping factors and pole frequencies to the appropriate cramer rao cr bounds and to traditional methods of linear prediction second our method is applied to an example due to steiglitz 8 in which the data consists of noisy values of the impulse response samples composed of many exponentially damped sinusoids of a linear system having both poles and zeros the poles of the system are accurately determined by our method and the zeros are obtained subsequently using shanks method

a novel block truncation coding of color images using a quaternion moment preserving principle block truncation coding btc is an efficient tool for image compression to compress color pixel blocks a novel color btc algorithm called quaternion moment block truncation coding qmbtc is presented analytical formulas for qmbtc whose computation time is on the order of pixel block size are derived by using quaternion arithmetic and the moment preserving principle the proposed color btc algorithm can adaptively truncate a pixel block into one or two output classes according to the distribution of the color values inside the blocks the experimental results show that the compression ratio is increased as compared with existing color btc algorithms and the picture quality of the reconstructed images is satisfactory in addition a post btc data compression scheme is proposed to further compress the subimage constructed by reproduction colors of truncated pixel blocks using a lookup table to display decoded data this postprocessing scheme can output images acceptable to human eyes

zero one programming with multiple criteria abstract the study of multiple criteria problems is not new but during the last seventeen years more and more study has been done in this area the study of 0 1 multiple criteria problems started much later than the study of continuous multiple criteria problems some of the earliest works on 0 1 problems with multiple criteria was first presented in 1973 quite a few solution methods have been developed since then especially during the last seven years in this paper most of these methods and some applications will be treated

efficient implementation of quaternion fourier transform convolution and correlation by 2 d complex fft the concepts of quaternion fourier transform qft quaternion convolution qcv and quaternion correlation which are based on quaternion algebra have been found to be useful for color image processing however the necessary computational algorithms and their complexity still need some attention we develop efficient algorithms for qft qcv and quaternion correlation the conventional complex two dimensional 2 d fourier transform ft is used to implement these quaternion operations very efficiently with these algorithms we only need two complex 2 d fts to implement a qft six complex 2 d fts to implement a one side qcv or a quaternion correlation and 12 complex 2 d fts to implement a two side qcv and the efficiency of these quaternion operations is much improved meanwhile we also discuss two additional topics the first one is about how to use qft and qcv for quaternion linear time invariant qlti system analysis this topic is important for quaternion filter design and color image processing besides we also develop the spectrum product qcv it is an improvement of the conventional form of qcv for any arbitrary input functions it always corresponds to the product operation in the frequency domain it is very useful for quaternion filter design

a novel approach for lung nodules segmentation in chest ct using level sets a new variational level set approach is proposed for lung nodule segmentation in lung ct scans a general lung nodule shape model is proposed using implicit spaces as a signed distance function the shape model is fused with the image intensity statistical information in a variational segmentation framework the nodule shape model is mapped to the image domain by a global transformation that includes inhomogeneous scales rotation and translation parameters a matching criteria between the shape model and the image implicit representations is employed to handle the alignment process transformation parameters evolve through gradient descent optimization to handle the shape alignment process and hence mark the boundaries of the nodule head the embedding process takes into consideration the image intensity as well as prior shape information a nonparametric density estimation approach is employed to handle the statistical intensity representation of the nodule and background regions the proposed technique does not depend on nodule type or location exhaustive experimental and validation results are demonstrated on 742 nodules obtained from four different ct lung databases illustrating the robustness of the approach

an algorithm for pole zero modeling and spectral analysis an explicit connection between fitting exponential models and pole zero models to observed data is made the fitting problem is formulated as a constrained nonlinear minimization problem this problem is then solved using a simplified iterative algorithm the algorithm is applied to simulated data and the performance of the algorithm is compared to previous results

high capacity data hiding for error diffused block truncation coding block truncation coding btc is an efficient compression technique with extremely low computational complexity however the blocking and false contour effects are two major deficiencies in btc which cause severe perceptual artifacts the former scheme error diffused btc edbtc can significantly improve the above issues through the visual low pass compensation on the bitmap which thus widens its possible application market yet the corresponding security issue may limit its value in this paper a method namely complementary hiding edbtc is developed to cope the above issue this paper is managed by firstly discussing when a single watermark is embedded and then multiple watermarks are employed to test the limitation of the proposed scheme herein an adaptive external bias factor is employed to control the watermark embedding and this factor also affects the image quality and robustness simultaneously experimental results demonstrate that the proposed method only requires an extremely small external bias factor to carry watermarks which enables a high capacity scenario without significantly damaging image quality

block truncation coding with entropy coding block truncation coding btc is a simple and fast image compression algorithm which achieves a constant bit rate of 2 0 bits per pixel the method is however suboptimal we propose a modification of btc in which the compression ratio is improved by coding the quantization data and the bit plane by arithmetic coding with an adaptive modelling scheme the results compare favorable with other btc variants the bit rate for test image lena is 1 53 bits per pixel with a mean square error of 16 51

a generalized block truncation coding algorithm for image compression block truncation coding is a recently developed approach to image compression whose design is specified by the appropriate moment preserving quantizer in this paper we show how the basic block truncation coding algorithm can be generalized to include a family of moment preserving quantizers with the potential for improved performance we then illustrate by way of example that such improvement is indeed possible from the standpoint of peak signal to noise ratio there is a subclass of this family of moment preserving quantizers for which practical difficulties in implementation exist however we show that frequently we can avoid this subclass and still obtain good performance

interpolative btc image coding with vector quantization the authors suggest two interpolative block truncation coding btc image coding schemes with vector quantization and median filters as the interpolator the first scheme is based on quincunx subsampling and the second one on every other row and every other column subsampling it is shown that the schemes yield a significant reduction in bit rate at only a small performance degradation and in general better channel error resisting capabilities as compared to the absolute moment btc the methods are further demonstrated to outperform the corresponding btc schemes with pure vector quantization at the same bit rate and require minimal computations for the interpolation

ilp approaches to the blockmodel problem blockmodelling is a method for identifying structural similarities or equivalences between elements which has applications in a variety of contexts including multiattribute performance assessment one criterion for forming blocks results in a difficult non linear integer programme we give several integer linear programming formulations of this problem and provide comparative computational results we show that methods of reducing symmetry proposed by sherali and smith are not effective in this case and propose an iterative approach in which the size of the problem is reduced

statistical analysis of effective singular values in matrix rank determination a major problem in using svd singular value decomposition as a tool in determining the effective rank of a perturbed matrix is that of distinguishing between significantly small and significantly large singular values to the end conference regions are derived for the perturbed singular values of matrices with noisy observation data the analysis is based on the theories of perturbations of singular values and statistical significance test threshold bounds for perturbation due to finite precision and i i d random models are evaluated in random models the threshold bounds depend on the dimension of the matrix the noisy variance and predefined statistical level of significance results applied to the problem of determining the effective order of a linear autoregressive system from the approximate rank of a sample autocorrelation matrix are considered various numerical examples illustrating the usefulness of these bounds and comparisons to other previously known approaches are given

a new method for linear feature and junction enhancement in 2d images based on morphological operation oriented anisotropic gaussian function and hessian information abstract feature enhancement is an important preprocessing step in many image processing tasks it is the process of adjusting image intensities so that the enhanced results are more suitable for analysis good enhancement results for linear structures such as vessels or neurites can be used as inputs for segmentation and other operations in this paper a novel linear feature enhancement filter an adaptive multi scale morpho gaussian filter which can enhance and smooth linear features is proposed based on morphological operation anisotropic gaussian function and hessian information this filter can enhance and smooth along the local orientation of the linear structures and the hessian measurement is used to further enhance the linear features we utilize the hessian matrix to calculate the orientation information for our directional morphological operation and the oriented anisotropic gaussian smoothing we also propose a novel method for junction enhancement which can solve the problem of junction suppression we decompose the junctions and enhance along each linear structure within a junction region we present the test results of our algorithm on images of different types and compare our method with three existing methods the experimental results show that the proposed approach can achieve better results

geometric methods for determining system poles from transient response the problem treated is that of identifying the poles of a finite order system by observing its transient decay after cessation of input for a limited time using possibly multiple observation points and experimental repetition various approaches are studied having the common characteristic that a homogeneous matrix equation must be solved several techniques that have been given scant attention in the literature are consolidated by a geometric treatment together with new results including an analytical treatment of the consequences of assuming an excessively high system order derivation of a statistically unbiased estimate for an intermediate parameter in the solution new theorems on error effects a recipe for effective use of the singular value decomposition and a new method for suppression of extraneous poles

an enhanced conversion scheme for lexicographic multiobjective integer programs abstract a number of approaches have been proposed and several implemented for the solution of lexicographic multiobjective programming problems these approaches may be divided into two classes the first encompasses the development of algorithms specifically designed to deal directly with the initial model while the second attempts to transform efficiently the lexicographic multiobjective model into an equivalent single objective programming problem this second approach would appear particularly attractive since it permits the use of conventional readily available mathematical programming software in this paper we address a particular form of the lexicographic multiobjective model specifically one in which all functions are linear and all variables integer it is then shown how a recently developed scheme for the transformation of this model may be substantially improved as a result lexicographic multiobjective integer linear programs may be easily converted into conventional linear integer programs wherein the magnitude of the objective function coefficients are minimized

color image processing by using binary quaternion moment preserving thresholding technique this paper presents a new moment preserving thresholding technique called the binary quaternion moment preserving bqmp thresholding for color image data based on representing color data by the quaternions the statistical parameters of color data can be expressed through the definition of quaternion moments analytical formulas of the bqmp thresholding can thus be determined by using the algebra of the quaternions the computation time for the bqmp thresholding is of order of the data size by using the bqmp thresholding quaternion moment based operators are designed for the application of color image processing such as color image compression multiclass clustering of color data and subpixel color edge detection the experimental results show that the proposed operator for color image compression can have output picture quality acceptable to human eyes in addition the proposed edge operator can detect the color edge at the subpixel level therefore the proposed bqmp thresholding can be used as a tool for color image processing

finding edges in noisy scenes edge detection in the presence of noise is a well known problem this paper examines an applications motivated approach for solving the problem using novel techniques and presents a method developed by the authors that performs well on a large class of targets roc curves are used to compare this method with other well known edge detection operators with favorable results a theoretical argument is presented that favors lmmse filtering over median filtering in extremely noisy scenes simulated results of the research are presented

the geometry of differential operators with application to image processing a family of second order nonlinear differential operators that are useful in building simple edge detectors is treated the authors provide a uniform definition for these operators and describe their internal geometry based on their geometric analysis they associate symbolic descriptors with the abstract edges defined by the operators one of them q is essentially the same operator that j f canny ibid vol pami 8 p 552 7 1986 used to define his two dimensional simple edge detector the authors give a parse tree for q which provides a complete analysis of its local geometry the analysis shows that q has a fondness for edges that lift to certain types of asymptotic curves these include select straight line segments lying on the surface inflections of mean curvature and paths with constant rate of ascent the methods are drawn largely from vector calculus and differential geometry the authors illustrate their theoretical work with results obtained when q was applied to image data that were interpolated with a b spline

color edge detection using vector order statistics a method is proposed whereby a color image is treated as a vector field and the edge information carried directly by the vectors is exploited a class of color edge detectors is defined as the minimum over the magnitudes of linear combinations of the sorted vector samples from this class a specific edge detector is obtained and its performance characteristics studied results of a quantitative evaluation and comparison to other color edge detectors using pratt s 1991 figure of merit and an artificially generated test image are presented edge detection results obtained for real color images demonstrate the efficiency of the detector

optimal binary vector quantization via enumeration of covering codes binary vector quantization bvq refers to block coding of binary vectors under a fidelity measure covering codes were studied as a means of lattice bvq but a further source coding problem hidden in the equivalence of covering codes has seemingly eluded attention given a d dimensional hypercube code space equivalent covering codes of the same covering radius but of different codewords have different expected bvq distortions for a general probability mass function thus one can minimize within the code equivalence the expected distortion over all different covering codes this leads a two stage optimization scheme for bvq design first we use an optimal covering code to minimize the maximum per vector distortion at a given rate then under the minmax constraint we minimize the expected quantization distortion this minmax constrained bvq method mcbvq controls both the maximum and average distortions and hence improves subjective quality of compressed binary images mcbvq also avoids poor local minima that may trap the generalized lloyd method the 7 4 hamming code and 8 4 extended hamming code are found to be particularly suitable for mcbvq on binary images an efficient and simple algorithm is introduced to enumerate all distinct 7 4 hamming 8 4 extended hamming codes and compute the corresponding expected distortions in optimal mcbvq design furthermore mcbvq using linear covering codes has a compact codebook and a fast syndrome encoding algorithm

single bit map block truncation coding of color images using a hopfield neural network abstract this paper describes a new single bit map block truncation coding sbbtc scheme that works with a hopfield neural network hnn for the coding of color images an incoming color block is encoded using three block truncation coding btc encoders with a common bit map for each of the three primary color planes an hnn is used to generate a good single bit map in the sbbtc by clustering the color vectors in the block into two classes the considering block is then encoded by the generated bit map and the two reconstruction colors each associated to one of the two classes in comparison with other existing methods the proposed color btc gives the best mean square error mse performance at the same bit rate

a variational method for geometric regularization of vascular segmentation in medical images in this paper a level set based geometric regularization method is proposed which has the ability to estimate the local orientation of the evolving front and utilize it as shape induced information for anisotropic propagation we show that preserving anisotropic fronts can improve elongations of the extracted structures while minimizing the risk of leakage to that end for an evolving front using its shape offset level set representation a novel energy functional is defined it is shown that constrained optimization of this functional results in an anisotropic expansion flow which is useful for vessel segmentation we have validated our method using synthetic data sets 2 d retinal angiogram images and magnetic resonance angiography volumetric data sets a comparison has been made with two state of the art vessel segmentation methods quantitative results as well as qualitative comparisons of segmentations indicate that our regularization method is a promising tool to improve the efficiency of both techniques

arma bispectrum approach to nonminimum phase system identification an identification procedure is proposed for a nongaussian white noise driven linear time invariant nonminimum phase fir finite impulse response system the method is based on parametric modeling of the third moments of the output sequence and uses causal and anticausal autoregressive moving average arma models the magnitude and phase response of the system are expressed in terms of the ar parameters of the arma models in particular the ar part of the causal arma model captures the minimum phase component of the system and the ar part of the anticausal arma captures the maximum phase component both sets of parameters are obtained by solving overdetermined linear systems of equations a model order selection criterion based on third order moments is proposed the arma bispectrum approach is compared to more conventional approaches for magnitude and phase reconstruction it is demonstrated that the proposed identification procedure exhibits improved modeling performance the method does not require knowledge of the non gaussian noise distribution

a method of block truncation coding for color image compression a basic color block truncation coding cbtc algorithm for color image compression is described a modification of the algorithm that reduces truncation errors is also described the block statistics related to cbtc methods are investigated some experimental results are given for a 256 256 pixel color image with 24 b pixel

generalized multichannel image filtering structures recent works in multispectral image processing advocate the employment of vector approaches for this class of signals vector processing operators that involve the minimization of a suitable error criterion have been proposed and shown appropriate for this task in this framework two main classes of vector processing filters have been reported in the literature astola et al 1990 introduce the well known class of vector median filters vmf which are derived as maximum likelihood ml estimates from exponential distributions trahanias et al see ibid vol 2 no 4 p 528 34 1993 and vol 5 no 6 p 868 80 1996 study the processing of color image data using directional information considering the class of vector directional filters vdf we introduce a new filter structure the directional distance filters ddf which combine both vdf and vmf in a novel way we show that ddf are robust signal estimators under various noise distributions they have the property of chromaticity preservation and finally compare favorably to other multichannel image processing filters

image field categorization and edge corner detection from gradient covariance edges corners and vertices in an image correspond to 1d one dimensional and 2d discontinuities in the intensity surface of the underlying scene ridges and peaks correspond to 1d and 2d extrema in it all of them can be characterized by the distribution of gradients particularly by the dimensionality of it the approach to image field categorization here is to construct a covariance matrix of the gradient vector in each small window and apply the canonical correlation analysis to it schwarz s inequality on the matrix determinant and the related differential equation is the key to this analysis we obtain two operators p sub eg and q sub eg to categorize the image field into a unidirectionally varying region univar an omidirectionally varying region omnivar and a nonvarying region we investigate the conditions under which their absolute maximum response i e p sub eg 1 and q sub eg 1 occurs in the small window and show that they are respectively the desired 1d and 2d discontinuities extrema and omnivar is in many cases a 1d pattern in polar coordinates this leads to an algorithm to obtain further classification and accurate localization of them into edges ridges peaks corners and vertices through detailed analysis in the informative varying axis of them we examined and compared the performance of the operators and the localization algorithm on various types of images and various noise levels the results indicate that the proposed method is superior with respect to stability localization and resolution

hypercomplex fourier transforms of color images fourier transforms are a fundamental tool in signal and image processing yet until recently there was no definition of a fourier transform applicable to color images in a holistic manner in this paper hypercomplex numbers specifically quaternions are used to define a fourier transform applicable to color images the properties of the transform are developed and it is shown that the transform may be computed using two standard complex fast fourier transforms the resulting spectrum is explained in terms of familiar phase and modulus concepts and a new concept of hypercomplex axis a method for visualizing the spectrum using color graphics is also presented finally a convolution operational formula in the spectral domain is discussed

applications of vector fields to image processing we use rotational and curvature properties of vector fields to identify critical features of an image using vector analysis and dif ferential geometry we establish the properties needed and then use these properties in three ways first our results make it theoretically possible to identify extremal edges of an intensity function f x y of two variables by considering the gradient vector field v f there is also enough information in f to find regions of high curvature i e high curvature of the level paths of f for color images we use the vector field v i q in application the image is partitioned into a grid of squares on the boundary of each square v v is sampled and these unit vectors are used as the tangents of a curve the rotation number or topological degree and the average curvature f are computed for each square analysis of these numbers yields infor mation on edges and curvature experimental results from both simu lated and real data are described

segmentation of vessel like patterns using mathematical morphology and curvature evaluation this paper presents an algorithm based on mathematical morphology and curvature evaluation for the detection of vessel like patterns in a noisy environment such patterns are very common in medical images vessel detection is interesting for the computation of parameters related to blood flow its tree like geometry makes it a usable feature for registration between images that can be of a different nature in order to define vessel like patterns segmentation is performed with respect to a precise model we define a vessel as a bright pattern piece wise connected and locally linear mathematical morphology is very well adapted to this description however other patterns fit such a morphological description in order to differentiate vessels from analogous background patterns a cross curvature evaluation is performed they are separated out as they have a specific gaussian like profile whose curvature varies smoothly along the vessel the detection algorithm that derives directly from this modeling is based on four steps 1 noise reduction 2 linear pattern with gaussian like profile improvement 3 cross curvature evaluation 4 linear filtering we present its theoretical background and illustrate it on real images of various natures then evaluate its robustness and its accuracy with respect to noise

image coding using vector quantization a review a review of vector quantization techniques used for encoding digital images is presented first the concept of vector quantization is introduced then its application to digital images is explained spatial predictive transform hybrid binary and subband vector quantizers are reviewed the emphasis is on the usefulness of the vector quantization when it is combined with conventional image coding techniques or when it is used in different domains

directional processing of color images theory and experimental results the processing of color image data using directional information is studied the class of vector directional filters vdf which was introduced by the authors in a previous work is further considered the analogy of vdf to the spherical median is shown and their relation to the spatial median is examined moreover their statistical and deterministic properties are studied which demonstrate their appropriateness in image processing vdf result in optimal estimates of the image vectors in the directional sense this is very important in the case of color images where the vectors direction signifies the chromaticity of a given color issues regarding the practical implementation of vdf are also considered in addition efficient filtering schemes based on vdf are proposed which include adaptive and or double window structures experimental and comparative results in image filtering show very good performance measures when the error is measured in the l a b space l a b is known as a space where equal color differences result in equal distances and therefore it is very close to the human perception of colors moreover an indication of the chromaticity error is obtained by measuring the error on the maxwell triangle the results demonstrate that vdf are very accurate chromaticity estimators

equivalent weights for lexicographic multi objective programs characterizations and computations abstract a recent paper 19 demonstrated the existence of a set of equivalent weights for which the optimal solution set of a preemptive priority multi objective program is precisely equal to the set of optimal solutions to the resulting nonpreemptive program with the objective function given as a linear weighting of the multiple objectives this paper addresses two further issues firstly for some important special cases or applications it is demonstrated that not only is the computation of a set of equivalent weights feasible but it is also highly desirable two algorithms are presented to compute a set of equivalent weights one method is a direct specialization of the approach adopted in 19 whereas the second approach is an alternative technique the latter method is shown to yield weights of uniformly smaller values than the former method while being of the same computational complexity and is hence preferable secondly as opposed to constructing one vector of equivalent weights a characterization is provided for the entire set of equivalent weights

improved direction estimation for di zenzo s multichannel image gradient operator gradient estimation is one of the most important tasks in image video processing for multichannel images a classical and widely used gradient method is di zenzo s gradient operator which is based on the measure of squared local contrast variation of multichannel images however up to now the indetermination of di zenzo s gradient direction has not been well solved which results in errors occurring in most of the subsequent studies in which di zenzo s vector gradient is used in this paper this problem is solved thoroughly furthermore the ranges of the values that the gradient angle should take in various cases are also analyzed as an application in color image processing a color version of canny edge detector is implemented by introducing the new gradient estimator to the traditional grayscale image canny operator the experimental results indicate that the improved di zenzo s gradient operator is currently one of the best color gradient estimators and outperforms other state of the art color image gradient methods the improved multichannel gradient operator not only provides accurate gradient estimation but also is efficient and easy to implement

consistent gradient operators we propose optimal gradient operators based on a newly derived consistency criterion this criterion is based on an orthogonal decomposition of the difference between a continuous gradient and discrete gradients into the intrinsic smoothing effect and the self inconsistency involved in the operator we show that consistency assures the exactness of gradient direction of a locally 1d pattern in spite of its orientation spectral composition and sub pixel translation stressing that inconsistency reduction is of primary importance we derive an iterative algorithm which leads to accurate gradient operators of arbitrary size we compute the optimum 3 spl times 3 4 spl times 4 and 5 spl times 5 operators compare them with conventional operators and examine the performance for one synthetic and several real images the results indicate that the proposed operators are superior with respect to accuracy bandwidth and isotropy

commutative reduced biquaternions and their fourier transform for signal and image processing applications digital signal and image processing using reduced biquaternions rbs are introduced in this paper rbs are an extension of the complex numbers following the doubling procedure two useful representations of rbs e sub 1 e sub 2 form and matrix representation are discussed in this paper besides we propose a new representation of rbs the polar form to calculate the multiplication and conjugation of rbs easily furthermore we define a unique and suitable rb norm and its conjugate these definitions are similar and compatible with the complex numbers the efficient algorithms of the discrete reduced biquaternion fourier transform drbft convolution drbcv correlation drbcr and phase only correlation are discussed in this paper in addition linear time invariant and symmetric multichannel complex systems can be easily analyzed by rbs for color image processing we define a simplified rb polar form to represent the color image this representation is useful to process color images in the brightness hue saturation color space many different types of color template matching and color sensitive edge detection brightness hue saturation and chromaticity matched edges can be performed simultaneously by rbs

a computational geometry approach to automated pulmonary fissure segmentation in ct examinations identification of pulmonary fissures which form the boundaries between the lobes in the lungs may be useful during clinical interpretation of computed tomography ct examinations to assess the early presence and characterization of manifestation of several lung diseases motivated by the unique nature of the surface shape of pulmonary fissures in 3 d space we developed a new automated scheme using computational geometry methods to detect and segment fissures depicted on ct images after a geometric modeling of the lung volume using the marching cubes algorithm laplacian smoothing is applied iteratively to enhance pulmonary fissures by depressing nonfissure structures while smoothing the surfaces of lung fissures next an extended gaussian image based procedure is used to locate the fissures in a statistical manner that approximates the fissures using a set of plane ldquopatchesrdquo this approach has several advantages such as independence of anatomic knowledge of the lung structure except the surface shape of fissures limited sensitivity to other lung structures and ease of implementation the scheme performance was evaluated by two experienced thoracic radiologists using a set of 100 images slices randomly selected from 10 screening ct examinations in this preliminary evaluation 98 7 and 94 9 of scheme segmented fissure voxels are within 2 mm of the fissures marked independently by two radiologists in the testing image dataset using the scheme detected fissures as reference 89 4 and 90 1 of manually marked fissure points have distance les2 mm to the reference suggesting a possible under segmentation of the scheme the case based root mean square rms distances ldquoerrorsrdquo between our scheme and the radiologist ranged from 1 48plusmn0 92 to 2 04plusmn3 88 mm the discrepancy of fissure detection results between the automated scheme and either radiologist is smaller in this dataset than the interreader variability

multiobjective mathematical programming via the multiplex model and algorithm abstract the increased interest in the existence and consideration of multiple objectives has made itself evident in the significant growth in the development and implementation of multiobjective mathematical programming unfortunately it is our opinion that this field is now characterized by such a diversity of philosophies models approaches and terminology that any unifying theme is obscured in fact rather than stressing the substantial degree of inherent commonality between multiobjective models and methods most presentations seem to focus on their real or imagined differences we believe that such treatment can be counterproductive and thus propose herein what we hope is a more unified treatment of multiobjective mathematical programming via the use of the multiphase simplex or multiplex model and algorithm while none of the components and concepts of the multiplex method are in themselves new we do believe that the specific arrangement of these ideas in the form presented does serve to clarify the close relationships between the models and simplex based algorithms for most forms of multiobjective mathematical programming and in turn their relationship to conventional single objective programming

block truncation coding using pattern fitting block truncation coding btc divides an image into blocks having given size and then encodes each block by two representative gray levels and a bit pattern in this work a modified scheme of btc is proposed where the computed representative gray levels are the bias and the contrast in each block secondly instead of determining bit pattern for each block an optimum bit pattern is selected from a pattern book thus the index of the optimum pattern is used to encode in lieu of the explicit pattern thirdly if the contrast is low the block is assumed to be smooth and bit pattern is not required to reconstruct the block this leads to significant reduction in bit rate bpp finally the contrast component and the predictive residual of the bias component are entropy coded to achieve further reduction in bpp performance of the proposed scheme is measured in terms of peak signal to noise ratio and bpp and is compared with other recently reported methods

quaternion music for vector sensor array processing this paper considers the problem of direction of arrival doa and polarization parameters estimation in the case of multiple polarized sources impinging on a vector sensor array the quaternion model is used and a data covariance model is proposed using quaternion formalism a comparison between long vector orthogonality and quaternion vector orthogonality is also performed and its implications for signal subspace estimation are discussed consequently a music like algorithm is presented allowing estimation of wave s doas and polarization parameters the algorithm is tested in numerical simulations and performance analysis is conducted when compared with other music like algorithms for vector sensor array the newly proposed algorithm results in a reduction by half of memory requirements for representation of data covariance model and reduces the computational effort for equivalent performance this paper also illustrates a compact and elegant way of dealing with multicomponent complex valued data

edge junction and corner detection using color distributions for over 30 years 1970 2000 researchers in computer vision have been proposing new methods for performing low level vision tasks such as detecting edges and corners one key element shared by most methods is that they represent local image neighborhoods as constant in color or intensity with deviations modeled as noise due to computational considerations that encourage the use of small neighborhoods where this assumption holds these methods remain popular the research presented models a neighborhood as a distribution of colors the goal is to show that the increase in accuracy of this representation translates into higher quality results for low level vision tasks on difficult natural images especially as neighborhood size increases we emphasize large neighborhoods because small ones often do not contain enough information we emphasize color because it subsumes gray scale as an image range and because it is the dominant form of human perception we discuss distributions in the context of detecting edges corners and junctions and we show results for each

a novel active contour model for medical images via the hessian matrix and eigenvalues abstract this paper presents a new level set formulation for active contour models acm we propose the idea of integrating the eigenvalue information of hessian matrix into the level set function by this new level set function the principal curvature information of images is used to enhance the ability of segmenting boundary regions the advantages of our model are as follows firstly the interior and exterior object boundaries can be segmented with the initial contour being anywhere in the input image secondly this method can work with heterogeneous images thirdly the proposed model can produce smooth and right boundaries of objects having vital importance in medical operations extensive experiments demonstrate that the proposed model can obtain better segmentation results

color quantization and processing by fibonacci lattices color quantization is sampling of three dimensional 3 d color spaces such as rgb or lab which results in a discrete subset of colors known as a color codebook or palette it is extensively used for display transfer and storage of natural images in internet based applications computer graphics and animation we propose a sampling scheme which provides a uniform quantization of the lab space the idea is based on several results from number theory and phyllotaxy the sampling algorithm is very much systematic and allows easy design of universal image independent color codebooks for a given set of parameters the codebook structure allows fast quantization and ordered dither of color images the display quality of images quantized by the proposed color codebooks is comparable with that of image dependent quantizers most importantly the quantized images are more amenable to the type of processing used for grayscale ones methods for processing grayscale images cannot be simply extended to color images because they rely on the fact that each gray level is described by a single number and the fact that a relation of full order can be easily established on the set of those numbers color spaces such as rgb or lab are on the other hand 3 d the proposed color quantization i e color space sampling and numbering of sampled points makes methods for processing grayscale images extendible to color images we illustrate possible processing of color images by first introducing the basic average and difference operations and then implementing edge detection and compression of color quantized images