a fast globally optimal algorithm for template matching using low resolution pruning template matching has many applications in signal processing image processing pattern recognition and video compression this paper proposes a fast coarse to fine template matching algorithm for finding the exact best match i e the match that may be found by a full search this is obtained by pruning the number of candidates in the full search using the results of a coarse search experimental results show that speed ups of a couple of orders of magnitude can easily be achieved using this method for typical low noise cases of two dimensional 2 d template matching

tomographic reconstruction of three dimensional volumes using the distorted born iterative method although real imaging problems involve objects that have variations in three dimensions a majority of work examining inverse scattering methods for ultrasonic tomography considers 2 d imaging problems therefore the study of 3 d inverse scattering methods is necessary for future applications of ultrasonic tomography in this work 3 d reconstructions using different arrays of rectangular elements focused on elevation were studied when reconstructing spherical imaging targets by producing a series of 2 d image slices using the 2 d distorted born iterative method dbim the effects of focal number f speed of sound contrast deltac and scatterer size were considered for comparison the 3 d wave equation was also inverted using point like transducers to produce fully 3 d dbim image reconstructions in 2 d slicing blurring in the vertical direction was highly correlated with the transmit receive elevation point spread function of the transducers for low deltac the eventual appearance of overshoot artifacts in the vertical direction were observed with increasing deltac these diffraction related artifacts were less severe for smaller focal number values and larger spherical target sizes when using 3 d dbim the overshoot artifacts were not observed and spatial resolution was improved however results indicate that array configuration in 3 d reconstructions is important for good image reconstruction practical arrays were designed and assessed for image reconstruction using 3 d dbim

a modified gradient method for two dimensional problems in tomography abstract a method for reconstructing the complex index of refraction of a bounded two dimensional inhomogeneous object of known geometric configuration from measured scattered field data is presented this work is an extension of recent results on the direct scattering problem wherein the governing domain integral equation was solved iteratively by a successive over relaxation technique the relaxation parameter was chosen to minimize the residual error at each step convergence of this process was established for indices of refraction much larger than required for convergence of the born approximation for the inverse problem the same technique is applied except in this case both the index of refraction and the field are unknown iterative solutions for both unknowns are postulated with two relaxation parameters at each step they are determined by simultaneously minimizing the residual errors in satisfying the domain integral equation and matching the measured data this procedure retains the nonlinear relation between the two unknowns numerical results are presented for a number of representative two dimensional objects the algorithm is shown to be effective in cases where the iterative solution of the direct problem is rapidly convergent

representing images using nonorthogonal haar like bases the efficient and compact representation of images is a fundamental problem in computer vision in this paper we propose methods that use haar like binary box functions to represent a single image or a set of images a desirable property of these box functions is that their inner product operation with an image can be computed very efficiently we propose two closely related novel subspace methods to model images the nonorthogonal binary subspace nbs method and the binary principal component analysis b pca algorithm nbs is spanned directly by binary box functions and can be used for image representation fast template matching and many other vision applications b pca is a structure subspace that inherits the merits of both nbs fast computation and pca modeling data structure information b pca base vectors are obtained by a novel pca guided nbs method we also show that b pca base vectors are nearly orthogonal to each other as a result in the nonorthogonal vector decomposition process the computationally intensive pseudoinverse projection operator can be approximated by the direct dot product without causing significant distance distortion experiments on real image data sets show a promising performance in image matching reconstruction and recognition tasks with significant speed improvement

real time pattern matching using projection kernels a novel approach to pattern matching is presented in which time complexity is reduced by two orders of magnitude compared to traditional approaches the suggested approach uses an efficient projection scheme which bounds the distance between a pattern and an image window using very few operations on average the projection framework is combined with a rejection scheme which allows rapid rejection of image windows that are distant from the pattern experiments show that the approach is effective even under very noisy conditions the approach described here can also be used in classification schemes where the projection values serve as input features that are informative and fast to extract

contrast source inversion methods in elastodynamics in this paper a nonlinear inversion method is presented for determining the mass density of an elastic inclusion from the knowledge of how the inclusion scatters known incident elastic waves the algorithm employed is an extension of the multiplicative regularized contrast source inversion method mr csi to elasticity this method involves alternate determination of the mass density contrast and the contrast sources the product of the contrast and the fields in each iterative step the simple updating schemes of the method allow the introduction of an extra regularization term to the cost functional as a multiplicative constraint this so called mr csi method mr csi has been proven to be very effective for the acoustic and electromagnetic inverse scattering problems numerical examples demonstrate that the mr csi method shows excellent edge preserving properties by robustly handling noisy data very well even for more complicated elastodynamic problems

speeding up the bilateral filter a joint acceleration way computational complexity of the brute force implementation of the bilateral filter bf depends on its filter kernel size to achieve the constant time bf whose complexity is irrelevant to the kernel size many techniques have been proposed such as 2d box filtering dimension promotion and shiftability property although each of the above techniques suffers from accuracy and efficiency problems previous algorithm designers were used to take only one of them to assemble fast implementations due to the hardness of combining them together hence no joint exploitation of these techniques has been proposed to construct a new cutting edge implementation that solves these problems jointly employing five techniques kernel truncation best n term approximation as well as previous 2d box filtering dimension promotion and shiftability property we propose a unified framework to transform bf with arbitrary spatial and range kernels into a set of 3d box filters that can be computed in linear time to the best of our knowledge our algorithm is the first method that can integrate all these acceleration techniques and therefore can draw upon one another s strong point to overcome deficiencies the strength of our method has been corroborated by several carefully designed experiments in particular the filtering accuracy is significantly improved without sacrificing the efficiency at running time

template matching based object recognition with unknown geometric parameters we examine the problem of locating an object in an image when size and rotation are unknown previous work has shown that with known geometric parameters an image restoration method can be useful by estimating a delta function at the object location when the geometric parameters are unknown this method becomes impractical because the likelihood surface to be minimized across size and rotation has numerous local minima and areas of zero gradient we propose a new approach where a smooth approximation of the template is used to minimize a well behaved likelihood surface a coarse to fine approximation of the original template using a diffusion like equation is used to create a library of templates using this library we can successively perform minimizations which are locally well behaved as detail is added to the template the likelihood surface gains local minima but previous estimates place us within a well behaved bowl around the global minimum leading to an accurate estimate numerical experiments are shown which verify the value of this approach for a wide range of values of the geometric parameters

full search equivalent pattern matching with incremental dissimilarity approximations this paper proposes a novel method for fast pattern matching based on dissimilarity functions derived from the lp norm such as the sum of squared differences ssd and the sum of absolute differences sad the proposed method is full search equivalent i e it yields the same results as the full search fs algorithm in order to pursue computational savings the method deploys a succession of increasingly tighter lower bounds of the adopted lp norm based dissimilarity function such bounding functions allow for establishing a hierarchy of pruning conditions aimed at skipping rapidly those candidates that cannot satisfy the matching criterion the paper includes an experimental comparison between the proposed method and other full search equivalent approaches known in literature which proves the remarkable computational efficiency of our proposal

an acoustic inverse scattering problem for spheres with radially inhomogeneous compressibility an inverse acoustic scattering problem the main aim of which is to reconstruct the one dimensional variation of the acoustical parameters of a spherical object is investigated the problem is first formulated conventionally through a coupled system of integral equations and then this system is reduced to one dimensional form by using the orthogonality properties of spherical harmonics the inverse problem is solved in an iterative fashion via classical newton algorithm some numerical simulations are carried out to test the feasibility of the method as well as to see the effects of some parameters on the solution it is shown that the method is very effective for the profiles having smooth variations provided that an appropriate initial guess is chosen however some of the classical disadvantages of the newton type algorithms are also observed in numerical experiments which may limit the applicability of the method to a certain extent

fast template matching based on normalized cross correlation with adaptive multilevel winner update in this paper we propose a fast pattern matching algorithm based on the normalized cross correlation ncc criterion by combining adaptive multilevel partition with the winner update scheme to achieve very efficient search this winner update scheme is applied in conjunction with an upper bound for the cross correlation derived from cauchy schwarz inequality to apply the winner update scheme in an efficient way we partition the summation of cross correlation into different levels with the partition order determined by the gradient energies of the partitioned regions in the template thus this winner update scheme in conjunction with the upper bound for ncc can be employed to skip unnecessary calculation experimental results show the proposed algorithm is very efficient for image matching under different lighting conditions

a performance evaluation of local descriptors in this paper we compare the performance of descriptors computed for local interest regions as for example extracted by the harris affine detector mikolajczyk k and schmid c 2004 many different descriptors have been proposed in the literature it is unclear which descriptors are more appropriate and how their performance depends on the interest region detector the descriptors should be distinctive and at the same time robust to changes in viewing conditions as well as to errors of the detector our evaluation uses as criterion recall with respect to precision and is carried out for different image transformations we compare shape context belongie s et al april 2002 steerable filters freeman w and adelson e setp 1991 pca sift ke y and sukthankar r 2004 differential invariants koenderink j and van doorn a 1987 spin images lazebnik s et al 2003 sift lowe d g 1999 complex filters schaffalitzky f and zisserman a 2002 moment invariants van gool l et al 1996 and cross correlation for different types of interest regions we also propose an extension of the sift descriptor and show that it outperforms the original method furthermore we observe that the ranking of the descriptors is mostly independent of the interest region detector and that the sift based descriptors perform best moments and steerable filters show the best performance among the low dimensional descriptors

fast full search equivalent template matching by enhanced bounded correlation we propose a novel algorithm referred to as enhanced bounded correlation ebc that significantly reduces the number of computations required to carry out template matching based on normalized cross correlation ncc and yields exactly the same result as the full search algorithm the algorithm relies on the concept of bounding the matching function finding an efficiently computable upper bound of the ncc rapidly prunes those candidates that cannot provide a better ncc score with respect to the current best match in this framework we apply a succession of increasingly tighter upper bounding functions based on cauchy schwarz inequality moreover by including an online parameter prediction step into ebc we obtain a parameter free algorithm that in most cases affords computational advantages very similar to those attainable by optimal offline parameter tuning experimental results show that the proposed algorithm can significantly accelerate a full search equivalent template matching process and outperforms state of the art methods

variable density acoustic tomography the theory and algorithms of diffraction tomography are generalized to the case of acoustic objects whose density and compressibility vary as a function of position a generalized projection slice theorem is presented for objects of this class and filtered backpropagation algorithms are derived that allow separate reconstructions of the objects density and compressibility using measurements of the transmitted acoustic field performed at two distinct frequencies computer simulations are presented testing the algorithms in the noise free case

fast orthogonal haar transform patternmatching via image square sum although using image strip sum an orthogonal haar transform oht pattern matching algorithm may have good performance it requires three subtractions to calculate each haar projection value on the sliding windows by establishing a solid mathematical foundation for oht this paper based on the concept of image square sum proposes a novel fast orthogonal haar transform foht pattern matching algorithm from which a haar projection value can be obtained by only one subtraction thus higher speed ups can be achieved while producing the same results with the full search pattern matching a large number of experiments show that the speed ups of foht are very competitive with oht in most cases of matching one single pattern and generally higher than oht in all cases of matching multiple patterns exceeding other high level full search equivalent algorithms

a forward model and conjugate gradient inversion technique for low frequency ultrasonic imaging emerging methods of hyperthermia cancer treatment require noninvasive temperature monitoring and ultrasonic techniques show promise in this regard various tomographic algorithms are available that reconstruct sound speed or contrast profiles which can be related to temperature distribution the requirement of a high enough frequency for adequate spatial resolution and a low enough frequency for adequate tissue penetration is a difficult compromise in this study the feasibility of using low frequency ultrasound for imaging and temperature monitoring was investigated the transient probing wave field had a bandwidth spanning the frequency range 2 5 320 5 khz the results from a forward model which computed the propagation and scattering of low frequency acoustic pressure and velocity wave fields were used to compare three imaging methods formulated within the born approximation representing two main types of reconstruction the first uses fourier techniques to reconstruct sound speed profiles from projection or radon data based on optical ray theory seen as an asymptotical limit for comparison the second uses backpropagation and conjugate gradient inversion methods based on acoustical wave theory the results show that the accuracy in localization was 2 5 mm or better when using low frequencies and the conjugate gradient inversion scheme which could be used for temperature monitoring

video block motion estimation based on gray code kernels motion in modern video coders is estimated using a block matching algorithm that calculates the distance and direction of motion on a block by block basis in this paper a novel fast block based motion estimation algorithm is proposed this algorithm uses an efficient projection framework that bounds the distance between a template block and candidate blocks fast projection is performed using a family of highly efficient filter kernels the gray code kernels requiring only 2 operations per pixel per kernel the projection framework is combined with a rejection scheme which allows rapid rejection of candidate blocks that are distant from the template block the tradeoff between computational complexity and quality of results can be easily controlled in the proposed algorithm thus it enables adaptivity to image content to further improve the results experiments show that the proposed adaptive algorithm outperforms other popular fast motion estimation algorithms

robust real time pattern matching using bayesian sequential hypothesis testing this paper describes a method for robust real time pattern matching we first introduce a family of image distance measures the image hamming distance family members of this family are robust to occlusion small geometrical transforms light changes and nonrigid deformations we then present a novel bayesian framework for sequential hypothesis testing on finite populations based on this framework we design an optimal rejection acceptance sampling algorithm this algorithm quickly determines whether two images are similar with respect to a member of the image hamming distance family we also present a fast framework that designs a near optimal sampling algorithm extensive experimental results show that the sequential sampling algorithm s performance is excellent implemented on a pentium iv 3 ghz processor the detection of a pattern with 2 197 pixels in 640times480 pixel frames where in each frame the pattern rotated and was highly occluded proceeds at only 0 022 seconds per frame

iterative forward and inverse algorithms based on domain integral equations for three dimensional electric and magnetic objects an iterative approach to full vector three dimensional inverse scattering problems where the unknown objects can have conductivity permittivity and permeability different from the known background medium is discussed since this problem involves a large number of unknowns it has to be solved effectively and efficiently so that the results can be obtained in timely manner the forward modeling is based on a domain integral equation approach formulated in terms of the electric and magnetic contrast sources normalized with the characteristic impedance of the background medium our numerical tests indicate that this formulation is prerequisite in order to arrive at a forward solution within an acceptable number of iterations and hence it is also of significant importance in the optimization process of the inverse problem the inverse scattering problem is attacked using the multiplicative regularized contrast source inversion method as known in the literature the complexity of this inverse method is approximately equal to the complexity of two equivalent forward algorithms of the conjugate gradient type furthermore this inverse method has been armed with a weighted l2 norm regularizer which has been included as a multiplicative constraint some representative numerical testings will be presented to illustrate the ability of the our numerical algorithms

iterated impact dynamics of n beads on a ring when n beads slide along a frictionless hoop their collision sequence gives rise to a dynamical system that can be studied via matrix products it is of general interest to understand the distribution of velocities and the corresponding eigenvalue spectrum that a given collision sequence can produce we formulate the problem for general n and state some basic theorems regarding the eigenvalues of the collision matrices and their products the case of three beads of masses m1 m2 m3 is studied in detail we exploit the fact that each collision sequence can be viewed as a billiard trajectory in a right triangle with non standard reflection rules existence of families of periodic orbits are proven and orbits that densely fill the triangle are computed eigenvalue distributions and position and velocity histograms are computed as a function of the restitution coefficient both periodic and dense collision sequences are discussed and a series of conjectures based on computational evidence are formulated comparisons are made between the eigenvalue distributions and autocorrelation matrices associated with dense trajectories generated from a chaotic collision sequence and spectra from matrix sequences generated from random orderings and we describe how the three bead system could be used as the basis for a random number generating algorithm that is computationally efficient

image denoising by sparse 3 d transform domain collaborative filtering we propose a novel image denoising strategy based on an enhanced sparse representation in transform domain the enhancement of the sparsity is achieved by grouping similar 2d image fragments e g blocks into 3d data arrays which we call groups collaborative altering is a special procedure developed to deal with these 3d groups we realize it using the three successive steps 3d transformation of a group shrinkage of the transform spectrum and inverse 3d transformation the result is a 3d estimate that consists of the jointly filtered grouped image blocks by attenuating the noise the collaborative filtering reveals even the finest details shared by grouped blocks and at the same time it preserves the essential unique features of each individual block the filtered blocks are then returned to their original positions because these blocks are overlapping for each pixel we obtain many different estimates which need to be combined aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy a significant improvement is obtained by a specially developed collaborative wiener filtering an algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail an extension to color image denoising is also developed the experimental results demonstrate that this computationally scalable algorithm achieves state of the art denoising performance in terms of both peak signal to noise ratio and subjective visual quality

fast algorithm for walsh hadamard transform on sliding windows this paper proposes a fast algorithm for walsh hadamard transform on sliding windows which can be used to implement pattern matching most efficiently the computational requirement of the proposed algorithm is about 1 5 additions per projection vector per sample which is the lowest among existing fast algorithms for walsh hadamard transform on sliding windows

a full vectorial contrast source inversion scheme for three dimensional acoustic imaging of both compressibility and density profiles imaging the two acoustic medium parameters density and compressibility requires the use of both the acoustic pressure and velocity wave fields described via integral equations imaging is based on solving for the unknown medium parameters using known measured scattered wave fields and it is difficult to solve this ill posed inverse problem directly using a conjugate gradient inversion scheme here a contrast source inversion method is used in which the contrast sources defined via the product of changes in compressibility and density with the pressure and velocity wave fields respectively are computed iteratively after each update of the contrast sources an update of the medium parameters is obtained total variation as multiplicative regularization is used to minimize blurring in the reconstructed contrasts the method successfully reconstructed three dimensional contrast profiles based on changes in both density and compressibility using synthetic data both with and without 50 white noise the results were compared with imaging based only on the pressure wave field where speed of sound profiles were solely based on changes in compressibility it was found that the results improved significantly by using the full vectorial method when changes in speed of sound depended on changes in both compressibility and density

the gray code filter kernels in this paper we introduce a family of filter kernels the gray code kernels gck and demonstrate their use in image analysis filtering an image with a sequence of gray code kernels is highly efficient and requires only two operations per pixel for each filter kernel independent of the size or dimension of the kernel we show that the family of kernels is large and includes the walsh hadamard kernels among others the gck can be used to approximate any desired kernel and as such forms a complete representation the efficiency of computation using a sequence of gck filters can be exploited for various real time applications such as pattern detection feature extraction texture analysis texture synthesis and more