amplitude only log radon transform for geometric invariant shape descriptor a shape descriptor combining the radon transform the amplitude extraction and the log mapping is proposed in this paper it is invariant to shape rotation scaling and translation invariance to translation is achieved by amplitude extraction on the radial coordinate rotation and scaling are log mapped into two dimensional translations and recovered with the phase only correlation function in addition all transformation parameters rotating angle scaling factor and position shift can be determined also the efficiency of the proposed descriptor compared to existing methods is shown experimentally on different kind of datasets highlightswe propose a new shape descriptor based on radon transformthis descriptor needs no normalizations it is invariant to geometric transformations rotation scale and translation and robust to noise the rotation angle the scaling factor and the position shift can be easily determined

exploring estimator bias variance tradeoffs using the uniform cr bound we introduce a plane which we call the delta sigma plane that is indexed by the norm of the estimator bias gradient and the variance of the estimator the norm of the bias gradient is related to the maximum variation in the estimator bias function over a neighborhood of parameter space using a uniform cramer rao cr bound on estimator variance a delta sigma tradeoff curve is specified that defines an unachievable region of the delta sigma plane for a specified statistical model in order to place an estimator on this plane for comparison with the delta sigma tradeoff curve the estimator variance bias gradient and bias gradient norm must be evaluated we present a simple and accurate method for experimentally determining the bias gradient norm based on applying a bootstrap estimator to a sample mean constructed from the gradient of the log likelihood we demonstrate the methods developed in this paper for linear gaussian and nonlinear poisson inverse problems

statistical analysis of maximum likelihood estimator images of human brain fdg pet studies the work presented evaluates the statistical characteristics of regional bias and expected error in reconstructions of real positron emission tomography pet data of human brain fluoro deoxiglucose fdg studies carried out by the maximum likelihood estimator mle method with a robust stopping rule and compares them with the results of filtered backprojection fbp reconstructions and with the method of sieves the task of evaluating radioisotope uptake in regions of interest rois is investigated an assessment of bias and variance in uptake measurements is carried out with simulated data then by using three different transition matrices with different degrees of accuracy and a components of variance model for statistical analysis it is shown that the characteristics obtained from real human fdg brain data are consistent with the results of the simulation studies

sparsity constrained contrast source inversion ultrasound imaging is used for detecting and characterizing breast lesions a state of the art imaging method is the contrast source inversion csi which solves the full wave nonlinear inverse problem however when the measurements are acquired in noisy environments csi can diverge from the correct solution after several iterations problems associated with noisy data were originally solved by including total variation tv regularization unfortunately for very noisy data tv regularization alone is not sufficient in this work compressed sensing ideas are used to regularize the inversion process by restricting the solution of the csi method to be sparse in a transformation domain the proposed method estimates the contrast source and contrast function by minimizing the mean squared error between the measured and modeled data an extra penalty term is added to measure sparsity in the transformation domain a second method that combines sparsity of the contrast source and minimal tv in the contrast function is also presented the proposed methods are tested on noise free and noisy synthetic data sets representing a scan of a cancerous breast numerical experiments show that for measurements contaminated with 1 noise the sparsity constrained csi improves the normalized mean squared error of the reconstructed speed of sound profiles up to 36 in comparison with traditional csi also for measurements contaminated with 5 noise the proposed methods improve the quality of the reconstruction up to 70 in comparison with the traditional csi method experimental results also show that the methods remain convergent to the correct speed of sound profile as the number of iterations increases

an algorithm for approximate calculation of the attainable sets of the nonlinear control systems with integral constraint on controls a b s t r a c t in this paper an algorithm for approximate calculation of the attainable sets of nonlinear control systems with integral constraint on controls is presented a numerical example of the computer application of this algorithm is also given

a method for registration of 3 d shapes the authors describe a general purpose representation independent method for the accurate and computationally efficient registration of 3 d shapes including free form curves and surfaces the method handles the full six degrees of freedom and is based on the iterative closest point icp algorithm which requires only a procedure to find the closest point on a geometric entity to a given point the icp algorithm always converges monotonically to the nearest local minimum of a mean square distance metric and the rate of convergence is rapid during the first few iterations therefore given an adequate set of initial rotations and translations for a particular class of objects with a certain level of shape complexity one can globally minimize the mean square distance metric over all six degrees of freedom by testing each initial registration one important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model prior to shape inspection experimental results show the capabilities of the registration algorithm on point sets curves and surfaces

practical tradeoffs between noise quantitation and number of iterations for maximum likelihood based reconstructions emission computerised tomography images reconstructed using a maximum likelihood expectation maximization ml based method with different reconstruction kernels and 1 200 iterations are compared to images reconstructed using filtered backprojection fbp ml based reconstructions using a single pixel sp kernel with or without a sieve filter show no quantitative advantage over fbp except in the background where a reduction of noise is possible if the number of iterations is kept small

registration of multiple range views using the reverse calibration technique abstract in this paper we propose a new registration algorithm the proposed algorithm consists of two steps the first step is to estimate the transformation parameters among multiple range views making use of the eigenvectors of the weighted covariance matrix of the 3 d coordinates of data points the weighting factors are carefully selected to take into account the projection effect caused by different viewpoints the next step is to register the views iteratively with the estimated transformation parameters as initial values to solve the correspondence problem the reverse calibration technique is used which is adapted to the space encoding range finder the object function defined by means of the reverse calibration technique is minimized iteratively experimental results show that the proposed algorithm is very fast and efficient

penalized weighted least squares image reconstruction for positron emission tomography presents an image reconstruction method for positron emission tomography pet based on a penalized weighted least squares pwls objective for pet measurements that are precorrected for accidental coincidences the author argues statistically that a least squares objective function is as appropriate if not more so than the popular poisson likelihood objective the author proposes a simple data based method for determining the weights that accounts for attenuation and detector efficiency a nonnegative successive over relaxation sor algorithm converges rapidly to the global minimum of the pwls objective quantitative simulation results demonstrate that the bias variance tradeoff of the pwls sor method is comparable to the maximum likelihood expectation maximization ml em method but with fewer iterations and is improved relative to the conventional filtered backprojection fbp method qualitative results suggest that the streak artifacts common to the fbp method are nearly eliminated by the pwls sor method and indicate that the proposed method for weighting the measurements is a significant factor in the improvement over fbp

a novel 3d vorticity based approach for automatic registration of low resolution range images this paper tackles the problem of feature matching and range image registration our approach is based on a novel set of discriminating three dimensional 3d local features named 3d vor vorticity in contrast to conventional local feature representation techniques which use the vector field i e surface normals to just construct their local reference frames the proposed feature representation exploits the vorticity of the vector field computed at each point of the local surface to capture the distinctive characteristics at each point of the underlying 3d surface the 3d vor descriptors of two range images are then matched using a fully automatic feature matching algorithm which identifies correspondences between the two range images correspondences are verified in a local validation step of the proposed algorithm and used for the pairwise registration of the range images quantitative results on low resolution kinect 3d data washington rgb d dataset show that our proposed automatic registration algorithm is accurate and computationally efficient the performance evaluation of the proposed descriptor was also carried out on the challenging low resolution washington rgb d kinect object dataset for the tasks of automatic range image registration reported experimental results show that the proposed local surface descriptor is robust to resolution noise and more accurate than state of the art techniques it achieves 90 registration accuracy compared to 50 69 2 and 52 for spin image 3d surf and sisi ld sift descriptors respectively highlightsa novel local surface descriptor 3d vor is proposed for surface representation the proposed 3d vor exploits the vector field s vorticity a novel pairwise registration algorithm is also proposed 3d vor is tested on low resolution dataset for range image registration 3d vor based registration achieves 90 accuracy on low resolution data and outperforms state of the art techniques

noise characterization of block iterative reconstruction algorithms i theory researchers have shown increasing interest in block iterative image reconstruction algorithms due to the computational and modeling advantages they provide although their convergence properties have been well documented little is known about how they behave in the presence of noise in this work the authors fully characterize the ensemble statistical properties of the rescaled block iterative expectation maximization rbi em reconstruction algorithm and the rescaled block iterative simultaneous multiplicative algebraic reconstruction technique rbi smart also included in the analysis are the special cases of rbi em maximum likelihood em ml em and ordered subset em os em and the special case of rbi smart smart a theoretical formulation strategy similar to that previously outlined for ml em is followed for the rbi methods the theoretical formulations in this paper rely on one approximation namely that the noise in the reconstructed image is small compared to the mean image in a second paper the approximation will be justified through monte carlo simulations covering a range of noise levels iteration points and subset orderings the ensemble statistical parameters could then be used to evaluate objective measures of image quality

maximum likelihood reconstruction for emission tomography previous models for emission tomography et do not distinguish the physics of et from that of transmission tomography we give a more accurate general mathematical model for et where an unknown emission density x y z generates and is to be reconstructed from the number of counts n d in each of d detector units d within the model we give an algorithm for determining an estimate of which maximizes the probability p n of observing the actual detector count data n over all possible densities let independent poisson variables n b with unknown means b b 1 b represent the number of unobserved emissions in each of b boxes pixels partitioning an object containing an emitter suppose each emission in box b is detected in detector unit d with probability p b d d 1 d with p b d a one step transition matrix assumed known we observe the total number n n d of emissions in each detector unit d and want to estimate the unknown b b 1 b for each the observed data n has probability or likelihood p n the em algorithm of mathematical statistics starts with an initial estimate 0 and gives the following simple iterative procedure for obtaining a new estimate new from an old estimate old to obtain k k 1 2 new b old b dd 1 n d p b d old b p b d b 1 b

a theoretical study of the contrast recovery and variance of map reconstructions from pet data the authors examine the spatial resolution and variance properties of pet images reconstructed using maximum a posteriori map or penalized likelihood methods resolution is characterized by the contrast recovery coefficient crc of the local impulse response simplified approximate expressions are derived for the local impulse response crcs and variances for each voxel using these results the authors propose a practical scheme for selecting spatially variant smoothing parameters to optimize lesion detectability through maximization of the local crc to noise ratio in the reconstructed image

precision and accuracy of regional radioactivity quantitation using the maximum likelihood em reconstruction algorithm the imaging characteristics of maximum likelihood ml reconstruction using the em algorithm for emission tomography have been extensively evaluated there has been less study of the precision and accuracy of ml estimates of regional radioactivity concentration the authors developed a realistic brain slice simulation by segmenting a normal subject s mri scan into gray matter white matter and csf and produced pet sinogram data with a model that included detector resolution and efficiencies attenuation scatter and randoms noisy realizations at different count levels were created and ml and filtered backprojection fbp reconstructions were performed the bias and variability of roi values were determined in addition the effects of ml pixel size image smoothing and region size reduction were assessed hit estimates at 3 000 iterations 0 6 sec per iteration on a parallel computer for 1 cm sup 2 gray matter rois showed negative biases of 6 spl plusmn 2 which can be reduced to 0 spl plusmn 3 by removing the outer 1 mm rim of each roi fbp applied to the full size rois had 15 spl plusmn 4 negative bias with 50 less noise than hit shrinking the fbp regions provided partial bias compensation with noise increases to levels similar to ml smoothing of ml images produced biases comparable to fbp with slightly less noise because of its heavy computational requirements the ml algorithm will be most useful for applications in which achieving minimum bias is important

using spin images for efficient object recognition in cluttered 3d scenes we present a 3d shape based object recognition system for simultaneous recognition of multiple objects in scenes containing clutter and occlusion recognition is based on matching surfaces by matching points using the spin image representation the spin image is a data level shape descriptor that is used to match surfaces represented as surface meshes we present a compression scheme for spin images that results in efficient multiple object recognition which we verify with results showing the simultaneous recognition of multiple objects from a library of 20 models furthermore we demonstrate the robust performance of recognition in the presence of clutter and occlusion through analysis of recognition trials on 100 scenes

affine transforms between image space and color space for invariant local descriptors accurate local region description is a keypoint in many applications and has been the topic of lots of recent papers starting from the very accurate sift most of the approaches exploit the local gradient information that suffers from several drawbacks first it is unstable in case of severe geometry distortions second it cannot be easily summarized in a compact way and third it is not designed to account vectorial color information in this paper we propose an alternative by designing compact descriptors that account both the colors present in the region and their spatial distribution each pixel being characterized by five coordinates two in the image space and three in the color space we try to evaluate affine transforms that allow to go from the spatial coordinates to the color coordinates and inversely obviously such kind of transform does not exist but we show that after applying it to the original coordinates the resulted positions are both discriminative and invariant to many acquisition conditions hence depending on the original space image or color and the destination space color or image we design different complementary descriptors their discriminative power and invariance properties are assessed and compared with the best color descriptors in the context of region matching and object classification

stopping rule for the mle algorithm based on statistical hypothesis testing it is known that when the maximum likelihood estimator mle algorithm passes a certain point it produces images that begin to deteriorate we propose a quantitative criterion with a simple probabilistic interpretation that allows the user to stop the algorithm just before this effect begins the mle algorithm searches for the image that has the maximum probability to generate the projection data the underlying assumption of the algorithm is a poisson distribution of the data therefore the best image according to the mle algorithm is the one that results in projection means which are as close to the data as possible it is shown that this goal conflicts with the assumption that the data are poisson distributed we test a statistical hypothesis whereby the projection data could have been generated by the image produced after each iteration the acceptance or rejection of the hypothesis is based on a parameter that decreases as the images improve and increases as they deteriorate we show that the best mle images which pass the test result in somewhat lower noise in regions of high activity than the filtered back projection results and much improved images in low activity regions the applicability of the proposed stopping rule to other iterative schemes is discussed

a fast reconstruction algorthm for stationary positron emission tomography based on a modified em algorithm an efficient iterative reconstruction method for positron emission tomography pet is presented the algorithm is basically an enhanced em expectation maximization algorithm with improved frequency response high frequency components of the ratio of measured to calculated projections are extracted and are taken into account for the iterative correction of image density in such a way that the correction is performed with a uniform efficiency over the image plane and with a flat frequency response as a result the convergence speed is not so sensitive to the image pattern or matrix size as the standard em algorithm and nonuniformity of the spatial resolution is significantly improved nonnegativity of the reconstructed image is preserved simulation studies have been made assuming two pet systems a scanning pet with ideal sampling and a stationary pet with sparse sampling in the latter a bank array of detectors is employed to improve the sampling in the object plane the new algorithm provides satisfactory images by two or three iterations starting from a flat image in either case the behavior of convergence is monitored by evaluating the root mean square of c b 1 where c b is the correction factor for pixel b in the em algorithm the value decreases rapidly and monotonically with iteration number although the theory is not accurate enough to assure the stability of convergence the algorithm is promising to achieve significant saving in computation compared to the standard em algorithm

feasible images and practical stopping rules for iterative algorithms in emission tomography the discussion of the causes of image deterioration in the maximum likelihood estimator mle method of tomographic image reconstruction initiated with the publication of a stopping rule for that iterative process e veklerov and j llacer 1987 is continued the concept of a feasible image is introduced which is a result of a reconstruction that if it were a radiation field could have generated the initial projection data by the poisson process that governs radioactive decay from the premise that the result of a reconstruction should be feasible the shape and characteristics of the region of feasibility in projection space are examined with a new rule reconstructions from real data can be tested for feasibility results of the tests and reconstructed images for the hoffman brain phantom are shown a comparative examination of the current methods of dealing with mle image deterioration is included

rapid transform based rotation invariant descriptor for texture classification under non ideal conditions rapid transform based descriptor is proposed for texture classification against rotation variations illumination variations as well as noise effect the proposed descriptor is based on the local circular neighborhood and the local feature vector is obtained by means of rapid transform the local feature vector is rotation invariant because of the cyclic shift invariance property of rapid transform combining several descriptors with different n r parameters the spatial multiscale is obtained feature selection approach is designed to improve the classification accuracy and reduce the computing cost the issue of noise is discussed and more robust descriptor based on rapid transform is introduced under noise condition texture classification experiments were carried out on the brodatz and outex databases and promising results are obtained from those experiments a rotation invariant descriptor is proposed for adapting non ideal conditions the proposed descriptor is based on rapid transform which is shift invariant feature selection approach is designed to improve the performance of the descriptor more robust descriptor is proposed under noise condition

keypoints based surface representation for 3d modeling and 3d object recognition the three dimensional 3d modeling and recognition of 3d objects have been traditionally performed using local features to represent the underlying 3d surface extraction of features requires cropping of several local surface patches around detected keypoints although an important step the extraction and representation of such local patches adds to the computational complexity of the algorithms this paper proposes a novel keypoints based surface representation ksr technique the proposed technique has the following two characteristics 1 it does not rely on the computation of features on a small surface patch cropped around a detected keypoint rather it exploits the geometrical relationship between the detected 3d keypoints for local surface representation 2 ksr is computationally efficient requiring only seconds to process 3d models with over 50 000 points with a matlab implementation experimental results on the uwa and stanford 3d models dataset suggest that it can accurately perform pairwise and multiview range image registration 3d modeling ksr was also tested for 3d object recognition with occluded scenes recognition results on the uwa dataset show that the proposed technique outperforms existing methods including 3d tensor vd lsd keypoint depth based feature spherical harmonics and spin image with a recognition rate of 95 9 the proposed approach also achieves a recognition rate of 93 5 on the challenging ca fascori dataset compared to 92 5 achieved by game theoretic the proposed method is computationally efficient compared to state of the art local feature methods highlightswe propose a novel technique called keypoint based surface representation ksr the proposed technique does not require local features around detected keypoints ksr exploits geometrical relationships between keypoints for surface representation ksr is tested on 3 popular datasets for 3d modeling and 3d object recognition ksr achieves superior 3d modeling and recognition results

interior point methodology for 3 d pet reconstruction interior point methods have been successfully applied to a wide variety of linear and nonlinear programming applications this paper presents a class of algorithms based on path following interior point methodology for performing regularized maximum likelihood ml reconstructions on three dimensional 3 d emission tomography data the algorithms solve a sequence of subproblems that converge to the regularized maximum likelihood solution from the interior of the feasible region the nonnegative orthant the authors propose two methods a primal method which updates only the primal image variables and a primal dual method which simultaneously updates the primal variables and the lagrange multipliers a parallel implementation permits the interior point methods to scale to very large reconstruction problems termination is based on well defined convergence measures namely the karush kuhn tucker first order necessary conditions for optimality the authors demonstrate the rapid convergence of the path following interior point methods using both data from a small animal scanner and monte carlo simulated data the proposed methods can readily be applied to solve the regularized weighted least squares reconstruction problem

accelerated iterative reconstruction for positron emission tomography based on the em algorithm for maximum likelihood estimation the em method that was originally developed for maximum likelihood estimation in the context of mathematical statistics may be applied to a stochastic model of positron emission tomography pet the result is an iterative algorithm for image reconstruction that is finding increasing use in pet due to its attractive theoretical and practical properties its major disadvantage is the large amount of computation that is often required due to the algorithm s slow rate of convergence this paper presents an accelerated form of the em algorithm for pet in which the changes to the image as calculated by the standard algorithm are multiplied at each iteration by an overrelaxation parameter the accelerated algorithm retains two of the important practical properties of the standard algorithm namely the selfnormalization and nonnegativity of the reconstructed images experimental results are presented using measured data obtained from a hexagonal detector system for pet the likelihood function and the norm of the data residual were monitored during the iterative process according to both of these measures the images reconstructed at iterations 7 and 11 of the accelerated algorithm are similar to those at iterations 15 and 30 of the standard algorithm for two different sets of data important theoretical properties remain to be investigated namely the convergence of the accelerated algorithm and its performance as a maximum likelihood estimator

a general class of preconditioners for statistical iterative reconstruction of emission computed tomography a major drawback of statistical iterative image reconstruction for emission computed tomography is its high computational cost the ill posed nature of tomography leads to slow convergence for standard gradient based iterative approaches such as the steepest descent or the conjugate gradient algorithm here new theory and methods for a class of preconditioners are developed for accelerating the convergence rate of iterative reconstruction to demonstrate the potential of this class of preconditioners a preconditioned conjugate gradient pcg iterative algorithm for weighted least squares reconstruction wls was formulated for emission tomography using simulated positron emission tomography pet data of the hoffman brain phantom it was shown that the convergence rate of the pcg can reduce the number of iterations of the standard conjugate gradient algorithm by a factor of 2 8 times depending on the convergence criterion