the image foresting transform theory algorithms and applications the image foresting transform ift is a graph based approach to the design of image processing operators based on connectivity it naturally leads to correct and efficient implementations and to a better understanding of how different operators relate to each other we give here a precise definition of the ift and a procedure to compute it a generalization of dijkstra s algorithm with a proof of correctness we also discuss implementation issues and illustrate the use of the ift in a few applications

parallel monte carlo simulations using a residence weight algorithm a parallel monte carlo mc algorithm the residence weight algorithm is proposed this algorithm is an extension to continuous ensembles of the residence time algorithm the proposed algorithm consists of generating several trial mc moves in parallel selecting one of them using appropriate relative probabilities and correcting the non boltzmannian sampling procedure by means of appropriate configuration weights the corresponding parallel boltzmannian scheme is based on a configurational bias monte carlo scheme and will also be considered the efficiency of both parallel algorithms has been compared in a case study the slow relaxation dynamics in a model silicate for a small number of trial moves generated in parallel we observe that the residence weight algorithm performs less efficiently than its corresponding configurational bias scheme by a factor of about 2 however when the number of parallel trial moves increases and becomes larger than ten we observe that the residence weight algorithm and the corresponding configurational bias scheme perform with equivalent efficiencies

optimal surface segmentation in volumetric images a graph theoretic approach efficient segmentation of globally optimal surfaces representing object boundaries in volumetric data sets is important and challenging in many medical image analysis applications we have developed an optimal surface detection method capable of simultaneously detecting multiple interacting surfaces in which the optimality is controlled by the cost functions designed for individual surfaces and by several geometric constraints defining the surface smoothness and interrelations the method solves the surface segmentation problem by transforming it into computing a minimum s hbox t cut in a derived arc weighted directed graph the proposed algorithm has a low order polynomial time complexity and is computationally efficient it has been extensively validated on more than 300 computer synthetic volumetric images 72 ct scanned data sets of different sized plexiglas tubes and tens of medical images spanning various imaging modalities in all cases the approach yielded highly accurate results our approach can be readily extended to higher dimensional image segmentation

the piecewise smooth mumford shah functional on an arbitrary graph the mumford shah functional has had a major impact on a variety of image analysis problems including image segmentation and filtering and despite being introduced over two decades ago it is still in widespread use present day optimization of the mumford shah functional is predominated by active contour methods until recently these formulations necessitated optimization of the contour by evolving via gradient descent which is known for its overdependence on initialization and the tendency to produce undesirable local minima in order to reduce these problems we reformulate the corresponding mumford shah functional on an arbitrary graph and apply the techniques of combinatorial optimization to produce a fast low energy solution in contrast to traditional optimization methods use of these combinatorial techniques necessitates consideration of the reconstructed image outside of its usual boundary requiring additionally the inclusion of regularization for generating these values the energy of the solution provided by this graph formulation is compared with the energy of the solution computed via traditional gradient descent based narrow band level set methods this comparison demonstrates that our graph formulation and optimization produces lower energy solutions than the traditional gradient descent based contour evolution methods in significantly less time finally we demonstrate the usefulness of the graph formulation to apply the mumford shah functional to new applications such as point clustering and filtering of nonuniformly sampled images

constructing smoothing functions in smoothed particle hydrodynamics with applications this paper presents a general approach to construct analytical smoothing functions for the meshfree lagrangian and particle method of smoothed particle hydrodynamics the approach uses integral form of function representation and applies taylor series expansion to the sph function and derivative approximations the constructing conditions are derived systematically which not only interpret the consistency condition of the method but also describe the compact supportness requirement of the smoothing function examples of sph smoothing function are constructed including some existing ones with this approach a new quartic smoothing function with some advantages is constructed and is applied to the one dimensional shock problem and a one dimensional tnt detonation problem the good agreement between the sph results and those from other sources shows the effectiveness of the approach and the newly constructed smoothing function in numerical simulations

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

improving the accuracy of risk prediction from particle based breakthrough curves reconstructed with kernel density estimators an edited version of this paper was published by agu copyright 2015 american geophysical union

local optimization based segmentation of spatially recurring multi region objects with part configuration constraints incorporating prior knowledge into image segmentation algorithms has proven useful for obtaining more accurate and plausible results two important constraints containment and exclusion of regions have gained attention in recent years mainly due to their descriptive power in this paper we augment the level set framework with the ability to handle these two intuitive geometric relationships containment and exclusion along with a distance constraint between boundaries of multi region objects level set s important property of automatically handling topological changes of evolving contours surfaces enables us to segment spatially recurring objects e g multiple instances of multi region cells in a large microscopy image while satisfying the two aforementioned constraints in addition the level set approach gives us a very simple and natural way to compute the distance between contours surfaces and impose constraints on it the downside however is a local optimization framework in which the final segmentation solution depends on the initialization in fact here we sacrifice the optimizability local instead of global solution in exchange for lower space complexity less memory usage and faster runtime especially for large microscopic images as well as no grid artifacts nevertheless the result from validating our method on several biomedical applications showed the utility and advantages of this augmented level set framework even with rough initialization that is distant from the desired boundaries we also compared our framework with its counterpart methods in the discrete domain and reported the pros and cons of each of these methods in terms of metrication error and efficiency in memory usage and runtime

beyond the flow decomposition barrier we introduce a new approach to the maximum flow problem this approach is based on assigning arc lengths based on the residual flow value and the residual arc capacities our approach leads to an o min n 2 3 m 1 2 m log n 2 m log u time bound for a network with n vertices m arcs and integral arc capacities in the range 1 u this is a fundamental improvement over the previous time bounds we also improve bounds for the gomory hu tree problem the parametric flow problem and the approximate s t cut problem

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

logismos b layered optimal graph image segmentation of multiple objects and surfaces for the brain automated reconstruction of the cortical surface is one of the most challenging problems in the analysis of human brain magnetic resonance imaging mri a desirable segmentation must be both spatially and topologically accurate as well as robust and computationally efficient we propose a novel algorithm logismos b based on probabilistic tissue classification generalized gradient vector flows and the logismos graph segmentation framework quantitative results on mri datasets from both healthy subjects and multiple sclerosis patients using a total of 16 thinspace 800 manually placed landmarks illustrate the excellent performance of our algorithm with respect to spatial accuracy remarkably the average signed error was only 0 084 mm for the white matter and 0 008 mm for the gray matter even in the presence of multiple sclerosis lesions statistical comparison shows that logismos b produces a significantly more accurate cortical reconstruction than freesurfer the current state of the art approach p ll 0 001 furthermore logismos b enjoys a run time that is less than a third of that of freesurfer which is both substantial considering the latter takes 10 h subject on average and a statistically significant speedup

efficient multiple range random walk algorithm to calculate the density of states we present a new monte carlo algorithm that produces results of high accuracy with reduced simulational effort independent random walks are performed concurrently or serially in different restricted ranges of energy and the resultant density of states is modified continuously to produce locally flat histograms this method permits us to directly access the free energy and entropy is independent of temperature and is efficient for the study of both 1st order and 2nd order phase transitions it should also be useful for the study of complex systems with a rough energy landscape

guided replication of random chain a new monte carlo method the authors introduce a new monte carlo method to study random chains the method uses i a link by link growth procedure of the chain ii a chain replication procedure based on boltzmann weights they apply it to various cases in two and three dimensions pure self avoiding walk repulsion between nearest neighbour links and attraction between the chain extremities etc when the competition or frustration between the different interaction terms increases the chain may get trapped in local minima to overcome this problem they introduce a guiding field or potential phi i r step ii is now performed in the presence of this guiding field which makes the chain population temporarily non boltzmannian however when the chain is completed the final population obeys again the boltzmann law they study simple cases where phi i r may be chosen on physical grounds

oriented image foresting transform segmentation by seed competition seed based methods for region based image segmentation are known to provide satisfactory results for several applications being usually easy to extend to multidimensional images however while boundary based methods like live wire can easily incorporate a preferred boundary orientation region based methods are usually conceived for undirected graphs and do not resolve well between boundaries with opposite orientations this motivated researchers to investigate extensions for some region based frameworks seeking to better solve oriented transitions in this same spirit we discuss how to incorporate this orientation information in a region based approach called ift segmentation by seed competition by exploring digraphs we give direct proof for the optimality of the proposed extensions in terms of energy functions associated with the cuts to stress these theoretical results we also present an experimental evaluation that shows the obtained gains in accuracy for some 2d and 3d data sets of medical images

pruned enriched rosenbluth method simulations of θ polymers of chain length up to 1 000 000 we present an algorithm for simulating flexible chain polymers it combines the rosenbluth rosenbluth method with recursive enrichment although it can be applied also in more general situations it is most efficient for three dimensional theta polymers on the simple cubic lattice there it allows high statistics simulations of chains of length up to n 10 sup 6 for storage reasons this is feasable only for polymers in a finite volume for free theta polymers in infinite volume we present very high statistics runs with n 10000 these simulations fully agree with previous simulations made by hegger and grassberger j chem phys bold 102 6681 1995 with a similar but less efficient algorithm showing that logarithmic corrections to mean field behavior are much stronger than predicted by field theory but the finite volume simulations show that the density inside a collapsed globule scales with the distance from the theta point as predicted by mean field theory in contrast to claims in the work mentioned above in addition to the simple cubic lattice we also studied two versions of the bond fluctuation model but with much shorter chains finally we show that our method can be applied also to off lattice models and illustrate this with simulations of amore model studied in detail by freire ital et al macromolecules bold 19 452 1986 and later work copyright ital 1997 ital the american physical society less

efficient graph based image segmentation this paper addresses the problem of segmenting an image into regions we define a predicate for measuring the evidence for a boundary between two regions using a graph based representation of the image we then develop an efficient segmentation algorithm based on this predicate and show that although this algorithm makes greedy decisions it produces segmentations that satisfy global properties we apply the algorithm to image segmentation using two different kinds of local neighborhoods in constructing the graph and illustrate the results with both real and synthetic images the algorithm runs in time nearly linear in the number of graph edges and is also fast in practice an important characteristic of the method is its ability to preserve detail in low variability image regions while ignoring detail in high variability regions

automated 3 d extraction of inner and outer surfaces of cerebral cortex from mri automatic computer processing of large multidimensional images such as those produced by magnetic resonance imaging mri is greatly aided by deformable models which are used to extract identify and quantify specific neuroanatomic structures a general method of deforming polyhedra is presented here with two novel features first explicit prevention of self intersecting surface geometries is provided unlike conventional deformable models which use regularization constraints to discourage but not necessarily prevent such behavior second deformation of multiple surfaces with intersurface proximity constraints allows each surface to help guide other surfaces into place using model based constraints such as expected thickness of an anatomic surface these two features are used advantageously to identify automatically the total surface of the outer and inner boundaries of cerebral cortical gray matter from normal human mr images accurately locating the depths of the sulci even where noise and partial volume artifacts in the image obscure the visibility of sulci the extracted surfaces are enforced to be simple two dimensional manifolds having the topology of a sphere even though the data may have topological holes this automatic 3 d cortex segmentation technique has been applied to 150 normal subjects simultaneously extracting both the gray white and gray cerebrospinal fluid interface from each individual the collection of surfaces has been used to create a spatial map of the mean and standard deviation for the location and the thickness of cortical gray matter three alternative criteria for defining cortical thickness at each cortical location were developed and compared these results are shown to corroborate published postmortem and in vivo measurements of cortical thickness

b spline signal processing ii efficiency design and applications for pt i see ibid vol 41 no 2 p 821 33 1993 a class of recursive filtering algorithms for the efficient implementation of b spline interpolation and approximation techniques is described in terms of simplicity of realization and reduction of computational complexity these algorithms compare favorably with conventional matrix approaches a filtering interpretation low pass filter followed by an exact polynomial spline interpolator of smoothing spline and least squares approximation methods is proposed these techniques are applied to the design of digital filters for cubic spline signal processing an efficient implementation of a smoothing spline edge detector is proposed it is also shown how to construct a cubic spline image pyramid that minimizes the loss of information in passage from one resolution level to the next in terms of common measures of fidelity this data structure appears to be superior to the gaussian laplacian pyramid

implementation of the three dimensional turning bands random field generator numerical techniques to generate replicates of spatially correlated random fields are often used to synthesize sets of highly variable physical quantities in stochastic models of naturally heterogeneous systems within the realm of hydrologic research for example such tools are widely used to develop hypothetical rainfall distributions hydraulic conductivity fields fracture set properties and other surface or subsurface flow parameters the turning bands method is one such algorithm which generates two and three dimensional fields by combining values found from a series of one dimensional simulations along lines radiating outward from a coordinate origin previous work with two dimensional algorithms indicates that radial lines evenly spaced about the unit circle lead to enhanced convergence properties the same can be said for the three dimensional models but it is more difficult to choose an arbitrary number of evenly spaced lines about the unit sphere the current investigation shows that the use of larger numbers of randomly oriented lines 100 can enhance the performance of the three dimensional algorithm this improved performance is needed to effectively simulate problems characterized by full three dimensionality and or anisotropy in either monte carlo or single realization applications use of a large number of lines will also reduce the presence of a distortion effect manifested as linelike patterns in the field increased computational costs can be reduced by employing a fast fourier transform technique to generate the line processes

motion compensated mega voltage cone beam ct using the deformation derived directly from 2d projection images this paper presents a novel method for respiratory motion compensated reconstruction for cone beam computed tomography cbct the reconstruction is based on a time sequence of motion vector fields which is generated by a dynamic geometrical object shape model the dynamic model is extracted from the 2d projection images of the cbct the process of the motion extraction is converted into an optimal 3d multiple interrelated surface detection problem which can be solved by computing a maximum flow in a 4d directed graph the method was tested on 12 mega voltage mv cbct scans from three patients two sets of motion artifact free 3d volumes full exhale fe and full inhale fi phases were reconstructed for each daily scan the reconstruction was compared with three other motion compensated approaches based on quantification accuracy of motion and size contrast to noise ratio cnr was also quantified for image quality the proposed approach has the best overall performance with a relative tumor volume quantification error of 3 39 3 64 and 8 57 8 31 for fe and fi phases respectively the cnr near the tumor area is 3 85 0 42 fe and 3 58 3 33 fi these results show the clinical feasibility to use the proposed method to reconstruct motion artifact free mvcbct volumes

equilibrium free energies from nonequilibrium measurements using maximum likelihood methods we present a maximum likelihood argument for the bennett acceptance ratio method and derive a simple formula for the variance of free energy estimates generated using this method this derivation of the acceptance ratio method using a form of logistic regression a common statistical technique allows us to shed additional light on the underlying physical and statistical properties of the method for example we demonstrate that the acceptance ratio method yields the lowest variance for any estimator of the free energy which is unbiased in the limit of large numbers of measurements

optimal graph search based segmentation of airway tree double surfaces across bifurcations identification of both the luminal and the wall areas of the bronchial tree structure from volumetric x ray computed tomography ct data sets is of critical importance in distinguishing important phenotypes within numerous major lung diseases including chronic obstructive pulmonary diseases copd and asthma however accurate assessment of the inner and outer airway wall surfaces of a complete 3 d tree structure is difficult due to their complex nature particularly around the branch areas in this paper we extend a graph search based technique logismos to simultaneously identify multiple inter related surfaces of branching airway trees we first perform a presegmentation of the input 3 d image to obtain basic information about the tree topology the presegmented image is resampled along judiciously determined paths to produce a set of vectors of voxels called voxel columns the resampling process utilizes medial axes to ensure that voxel columns of appropriate lengths and directions are used to capture the object surfaces without interference a geometric graph is constructed whose edges connect voxels in the resampled voxel columns and enforce validity of the smoothness and separation constraints on the sought surfaces cost functions with directional information are employed to distinguish inner and outer walls the assessment of wall thickness measurement on a ct scanned double wall physical phantom patterned after an in vivo imaged human airway tree achieved highly accurate results on the entire 3 d tree the observed mean signed error of wall thickness ranged from 0 09 0 24 mm to 0 07 0 23 mm in bifurcating nonbifurcating areas the mean unsigned errors were 0 16 0 12 mm to 0 20 0 11 mm when the airway wall surface was partitioned into meaningful subregions the airway wall thickness accuracy was the same in most tested bifurcation nonbifurcation and carina noncarina regions p ns once validated on phantoms our method was applied to human in vivo volumetric ct data to demonstrate relationships of airway wall thickness as a function of luminal dimension and airway tree generation wall thickness differences between the bifurcation nonbifurcation regions were statistically significant p 0 05 for tree generations 6 7 8 and 9 in carina noncarina regions the wall thickness was statistically different in generations 1 4 5 6 7 and 8

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

fast geodesic active contours we use an unconditionally stable numerical scheme to implement a fast version of the geodesic active contour model the proposed scheme is useful for object segmentation in images like tracking moving objects in a sequence of images the method is based on the weickert romeney viergever additive operator splitting aos scheme it is applied at small regions motivated by the adalsteinsson sethian level set narrow band approach and uses sethian s 1996 fast marching method for re initialization experimental results demonstrate the power of the new method for tracking in color movies

monte carlo simulation of 3d self avoiding walks presents simulation results for 3d self avoiding walks of moderate length n or 2000 using a recently introduced recursive sampling method it is shown that this method is indeed maximally efficient for determining the connectivity constant mu combining the data with previous results from exact enumerations and from simulations of very long walks using the pivot algorithm the author obtains very precise estimates of mu and of the critical exponents gamma and nu he also points out significant deviations from uniformity in a very popular random number generator which was considered safe until now

active appearance models we describe a new method of matching statistical models of appearance to images a set of model parameters control modes of shape and gray level variation learned from a training set we construct an efficient iterative matching algorithm by learning the relationship between perturbations in the model parameters and the induced image errors

path sampling with stochastic dynamics some new algorithms we propose here some new sampling algorithms for path sampling in the case when stochastic dynamics are used in particular we present a new proposal function for equilibrium sampling of paths with a monte carlo dynamics the so called brownian tube proposal this proposal is based on the continuity of the dynamics with respect to the random forcing and generalizes all previous approaches when stochastic dynamics are used the efficiency of this proposal is demonstrated using some measure of decorrelation in path space we also discuss a switching strategy that allows to transform ensemble of paths at a finite rate while remaining at equilibrium in contrast with the usual jarzynski like switching this switching is very interesting to sample constrained paths starting from unconstrained paths or to perform simulated annealing in a rigorous way

an optimal graph theoretic approach to data clustering theory and its application to image segmentation a novel graph theoretic approach for data clustering is presented and its application to the image segmentation problem is demonstrated the data to be clustered are represented by an undirected adjacency graph g with arc capacities assigned to reflect the similarity between the linked vertices clustering is achieved by removing arcs of g to form mutually exclusive subgraphs such that the largest inter subgraph maximum flow is minimized for graphs of moderate size approximately 2000 vertices the optimal solution is obtained through partitioning a flow and cut equivalent tree of g which can be efficiently constructed using the gomory hu algorithm 1961 however for larger graphs this approach is impractical new theorems for subgraph condensation are derived and are then used to develop a fast algorithm which hierarchically constructs and partitions a partially equivalent tree of much reduced size this algorithm results in an optimal solution equivalent to that obtained by partitioning the complete equivalent tree and is able to handle very large graphs with several hundred thousand vertices the new clustering algorithm is applied to the image segmentation problem the segmentation is achieved by effectively searching for closed contours of edge elements equivalent to minimum cuts in g which consist mostly of strong edges while rejecting contours containing isolated strong edges this method is able to accurately locate region boundaries and at the same time guarantees the formation of closed edge contours

a topology preserving level set method for geometric deformable models active contour and surface models also known as deformable models are powerful image segmentation techniques geometric deformable models implemented using level set methods have advantages over parametric models due to their intrinsic behavior parameterization independence and ease of implementation however a long claimed advantage of geometric deformable models the ability to automatically handle topology changes turns out to be a liability in applications where the object to be segmented has a known topology that must be preserved we present a new class of geometric deformable models designed using a novel topology preserving level set method which achieves topology preservation by applying the simple point concept from digital topology these new models maintain the other advantages of standard geometric deformable models including subpixel accuracy and production of nonintersecting curves or surfaces moreover since the topology preserving constraint is enforced efficiently through local computations the resulting algorithm incurs only nominal computational overhead over standard geometric deformable models several experiments on simulated and real data are provided to demonstrate the performance of this new deformable model algorithm

image segmentation with ratio cut this paper proposes a new cost function cut ratio for segmenting images using graph based methods the cut ratio is defined as the ratio of the corresponding sums of two different weights of edges along the cut boundary and models the mean affinity between the segments separated by the boundary per unit boundary length this new cost function allows the image perimeter to be segmented guarantees that the segments produced by bipartitioning are connected and does not introduce a size shape smoothness or boundary length bias the latter allows it to produce segmentations where boundaries are aligned with image edges furthermore the cut ratio cost function allows efficient iterated region based segmentation as well as pixel based segmentation these properties may be useful for some image segmentation applications while the problem of finding a minimum ratio cut in an arbitrary graph is np hard one can find a minimum ratio cut in the connected planar graphs that arise during image segmentation in polynomial time while the cut ratio alone is not sufficient as a baseline method for image segmentation it forms a good basis for an extended method of image segmentation when combined with a small number of standard techniques we present an implemented algorithm for finding a minimum ratio cut prove its correctness discuss its application to image segmentation and present the results of segmenting a number of medical and natural images using our techniques

on the formation of multiple local peaks in breakthrough curves the analysis of breakthrough curves btcs is of interest in hydrogeology as a way to parameterize and explain processes related to anomalous transport classical btcs assume the presence of a single peak in the curve where the location and size of the peak and the slope of the receding limb has been of particular interest as more information is incorporated into btcs for example with high frequency data collection supercomputing efforts it is likely that classical definitions of btc shapes will no longer be adequate descriptors for contaminant transport problems we contend that individual btcs may display multiple local peaks depending on the hydrogeologic conditions and the solute travel distance in such cases classical definitions should be reconsidered in this work the presence of local peaks in btcs is quantified from high resolution numerical simulations in synthetic fields with a particle tracking technique and a kernel density estimator to avoid either overly jagged or smoothed curves that could mask the results individual btcs from three dimensional heterogeneous hydraulic conductivity fields with varying combinations of statistical anisotropy heterogeneity models and local dispersivity are assessed as a function of travel distance the number of local peaks their corresponding slopes and a transport connectivity index are shown to strongly depend on statistical anisotropy and travel distance results show that the choice of heterogeneity model also affects the frequency of local peaks but the slope is less sensitive to model selection we also discuss how solute shearing and rerouting can be determined from local peak quantification

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

optimal multiple surface segmentation with shape and context priors segmentation of multiple surfaces in medical images is a challenging problem further complicated by the frequent presence of weak boundary evidence large object deformations and mutual influence between adjacent objects this paper reports a novel approach to multi object segmentation that incorporates both shape and context prior knowledge in a 3 d graph theoretic framework to help overcome the stated challenges we employ an arc based graph representation to incorporate a wide spectrum of prior information through pair wise energy terms in particular a shape prior term is used to penalize local shape changes and a context prior term is used to penalize local surface distance changes from a model of the expected shape and surface distances respectively the globally optimal solution for multiple surfaces is obtained by computing a maximum flow in a low order polynomial time the proposed method was validated on intraretinal layer segmentation of optical coherence tomography images and demonstrated statistically significant improvement of segmentation accuracy compared to our earlier graph search method that was not utilizing shape and context priors the mean unsigned surface positioning errors obtained by the conventional graph search approach 6 30 1 58 m was improved to 5 14 0 99 m when employing our new method with shape and context priors

b spline signal processing i theory the use of continuous b spline representations for signal processing applications such as interpolation differentiation filtering noise reduction and data compressions is considered the b spline coefficients are obtained through a linear transformation which unlike other commonly used transforms is space invariant and can be implemented efficiently by linear filtering the same property also applies for the indirect b spline transform as well as for the evaluation of approximating representations using smoothing or least squares splines the filters associated with these operations are fully characterized by explicitly evaluating their transfer functions for b splines of any order applications to differentiation filtering smoothing and least squares approximation are examined the extension of such operators for higher dimensional signals such as digital images is considered

cortex segmentation a fast variational geometric approach an automatic cortical gray matter segmentation from a three dimensional 3 d brain images magnetic resonance mr or computed tomography is a well known problem in medical image processing in this paper we first formulate it as a geometric variational problem for propagation of two coupled bounding surfaces an efficient numerical scheme is then used to implement the geodesic active surface model experimental results of cortex segmentation on real 3 d mr data are provided

globally optimal regions and boundaries as minimum ratio weight cycles we describe a new form of energy functional for the modeling and identification of regions in images the energy is defined on the space of boundaries in the image domain and can incorporate very general combinations of modeling information both from the boundary intensity gradients etc and from the interior of the region texture homogeneity etc we describe two polynomial time digraph algorithms for finding the global minima of this energy one of the algorithms is completely general minimizing the functional for any choice of modeling information it runs in a few seconds on a 256 spl times 256 image the other algorithm applies to a subclass of functionals but has the advantage of being extremely parallelizable neither algorithm requires initialization

exact solution to median surface problem using 3d graph search and application to parameter space exploration in this paper we propose the generalized median surface problem and present an exact solution by applying a 3d graph search algorithm to our knowledge this is a novel class of median computation problem which has not been considered before in the literature in addition to the theoretic interest in median surface computation we also demonstrate its practical value by means of the task of parameter space exploration without ground truth which is an effective means of dealing with the difficult parameter selection problem for image segmentation we present a concrete application for artery boundary detection in sonography ultrasound imaging it will be shown that the median computation can not only avoid the parameter training but also potentially achieve results comparable with trained parameters the median based approach can thus be a good alternate particularly in situations with no ground truth available highlightsthis paper proposes the median surface problem an optimal graph search algorithm is applied to solve the problem efficiently experimental work is conducted to demonstrate its usability it can potentially be used for segmentation parameter exploration

automatic liver segmentation based on shape constraints and deformable graph cut in ct images liver segmentation is still a challenging task in medical image processing area due to the complexity of the liver s anatomy low contrast with adjacent organs and presence of pathologies this investigation was used to develop and validate an automated method to segment livers in ct images the proposed framework consists of three steps 1 preprocessing 2 initialization and 3 segmentation in the first step a statistical shape model is constructed based on the principal component analysis and the input image is smoothed using curvature anisotropic diffusion filtering in the second step the mean shape model is moved using thresholding and euclidean distance transformation to obtain a coarse position in a test image and then the initial mesh is locally and iteratively deformed to the coarse boundary which is constrained to stay close to a subspace of shapes describing the anatomical variability finally in order to accurately detect the liver surface deformable graph cut was proposed which effectively integrates the properties and inter relationship of the input images and initialized surface the proposed method was evaluated on 50 ct scan images which are publicly available in two databases sliver07 and 3dircadb the experimental results showed that the proposed method was effective and accurate for detection of the liver surface

computation of a chemical potential using a residence weight algorithm the test particle insertion method and its generalization to biased insertion schemes allows the computation of chemical potentials in fluids even though these techniques can be implemented in dense systems the convergence of the estimated value for the chemical potential must be carefully checked and additional simulations are actually required we propose to compute the chemical potential using a residence weight algorithm with this algorithm it is shown that for a given amount of computer time the degree of convergence towards the exact chemical potential correlates with the mean rate for accepting the trial particle insertions or deletions the residence weight algorithm thus offers a reliable built in tool for diagnosing the numerical convergence

do we really need a large number of particles to simulate bimolecular reactive transport with random walk methods a kernel density estimation approach random walk particle tracking methods are a computationally efficient family of methods to solve reactive transport problems while the number of particles in most realistic applications is in the order of 10 6 10 9 the number of reactive molecules even in diluted systems might be in the order of fractions of the avogadro number thus each particle actually represents a group of potentially reactive molecules the use of a low number of particles may result not only in loss of accuracy but also may lead to an improper reproduction of the mixing process limited by diffusion recent works have used this effect as a proxy to model incomplete mixing in porous media in this work we propose using a kernel density estimation kde of the concentrations that allows getting the expected results for a well mixed solution with a limited number of particles the idea consists of treating each particle as a sample drawn from the pool of molecules that it represents this way the actual location of a tracked particle is seen as a sample drawn from the density function of the location of molecules represented by that given particle rigorously represented by a kernel density function the probability of reaction can be obtained by combining the kernels associated to two potentially reactive particles we demonstrate that the observed deviation in the reaction vs time curves in numerical experiments reported in the literature could be attributed to the statistical method used to reconstruct concentrations fixed particle support from discrete particle distributions and not to the occurrence of true incomplete mixing we further explore the evolution of the kernel size with time linking it to the diffusion process our results show that kdes are powerful tools to improve computational efficiency and robustness in reactive transport simulations and indicates that incomplete mixing in diluted systems should be modeled based on alternative mechanistic models and not on a limited number of particles

graph cuts and efficient n d image segmentation combinatorial graph cut algorithms have been successfully applied to a wide range of problems in vision and graphics this paper focusses on possibly the simplest application of graph cuts segmentation of objects in image data despite its simplicity this application epitomizes the best features of combinatorial graph cuts methods in vision global optima practical efficiency numerical robustness ability to fuse a wide range of visual cues and constraints unrestricted topological properties of segments and applicability to n d problems graph cuts based approaches to object extraction have also been shown to have interesting connections with earlier segmentation methods such as snakes geodesic active contours and level sets the segmentation energies optimized by graph cuts combine boundary regularization with region based properties in the same fashion as mumford shah style functionals we present motivation and detailed technical description of the basic combinatorial optimization framework for image segmentation via s t graph cuts after the general concept of using binary graph cut algorithms for object segmentation was first proposed and tested in boykov and jolly 2001 this idea was widely studied in computer vision and graphics communities we provide links to a large number of known extensions based on iterative parameter re estimation and learning multi scale or hierarchical approaches narrow bands and other techniques for demanding photo video and medical applications

3 d carotid multi region mri segmentation by globally optimal evolution of coupled surfaces in this paper we propose a novel global optimization based 3 d multi region segmentation algorithm for t1 weighted black blood carotid magnetic resonance mr images the proposed algorithm partitions a 3 d carotid mr image into three regions wall lumen and background the algorithm performs such partitioning by simultaneously evolving two coupled 3 d surfaces of carotid artery adventitia boundary ab and lumen intima boundary lib while preserving their anatomical inter surface consistency such that the lib is always located within the ab in particular we show that the proposed algorithm results in a fully time implicit scheme that propagates the two linearly ordered surfaces of the ab and lib to their globally optimal positions during each discrete time frame by convex relaxation in this regard we introduce the continuous max flow model and prove its duality equivalence to the convex relaxed optimization problem with respect to each evolution step we then propose a fully parallelized continuous max flow based algorithm which can be readily implemented on a gpu to achieve high computational efficiency extensive experiments with four users using 12 3t mr and 26 1 5t mr images demonstrate that the proposed algorithm yields high accuracy and low operator variability in computing vessel wall volume in addition we show the algorithm outperforms previous methods in terms of high computational efficiency and robustness with fewer user interactions

automatic renal cortex segmentation using implicit shape registration and novel multiple surfaces graph search in this paper we present an automatic renal cortex segmentation approach using the implicit shape registration and novel multiple surfaces graph search the proposed approach is based on a hierarchy system first the whole kidney is roughly initialized using an implicit shape registration method with the shapes embedded in the space of euclidean distance functions second the outer and inner surfaces of renal cortex are extracted utilizing multiple surfaces graph searching which is extended to allow for varying sampling distances and physical constraints to better separate the renal cortex and renal column third a renal cortex refining procedure is applied to detect and reduce incorrect segmentation pixels around the renal pelvis further improving the segmentation accuracy the method was evaluated on 17 clinical computed tomography scans using the leave one out strategy with five metrics dice similarity coefficient dsc volumetric overlap error oe signed relative volume difference svd average symmetric surface distance davg and average symmetric rms surface distance drms the experimental results of dsc oe svd davg and drms were 90 50 1 19 4 38 3 93 2 37 1 72 0 14 mm 0 09 mm and 0 80 mm 0 64 mm respectively the results showed the feasibility efficiency and robustness of the proposed method

rare events and the convergence of exponentially averaged work values equilibrium free energy differences are given by exponential averages of nonequilibrium work values such averages however often converge poorly as they are dominated by rare realizations i show that there is a simple and intuitively appealing description of these rare but dominant realizations this description is expressed as a duality between forward and reverse processes and provides both heuristic insights and quantitative estimates regarding the number of realizations needed for convergence of the exponential average analogous results apply to the equilibrium perturbation method of estimating free energy differences the pedagogical example of a piston and gas r c lua and a y grosberg j phys chem b 109 6805 2005 is used to illustrate the general discussion

free energy reconstruction from steered dynamics without post processing various methods achieving importance sampling in ensembles of nonequilibrium trajectories enable one to estimate free energy differences and by maximum likelihood post processing to reconstruct free energy landscapes here based on bayes theorem we propose a more direct method in which a posterior likelihood function is used both to construct the steered dynamics and to infer the contribution to equilibrium of all the sampled states the method is implemented with two steering schedules first using non autonomous steering we calculate the migration barrier of the vacancy in email protected second using an autonomous scheduling related to metadynamics and equivalent to temperature accelerated molecular dynamics we accurately reconstruct the two dimensional free energy landscape of the 38 atom lennard jones cluster as a function of an orientational bond order parameter and energy down to the solid solid structural transition temperature of the cluster and without maximum likelihood post processing

a new approach to the maximum flow problem all previously known efficient maximum flow algorithms work by finding augmenting paths either one path at a time as in the original ford and fulkerson algorithm or all shortest length augmenting paths at once using the layered network approach of dinic an alternative method based on the preflow concept of karzanov is introduced a preflow is like a flow except that the total amount flowing into a vertex is allowed to exceed the total amount flowing out the method maintains a preflow in the original network and pushes local flow excess toward the sink along what are estimated to be shortest paths the algorithm and its analysis are simple and intuitive yet the algorithm runs as fast as any other known method on dense graphs achieving an o n 3 time bound on an n vertex graph by incorporating the dynamic tree data structure of sleator and tarjan we obtain a version of the algorithm running in o nm log n 2 m time on an n vertex m edge graph this is as fast as any known method for any graph density and faster on graphs of moderate density the algorithm also admits efficient distributed and parallel implementations a parallel implementation running in o n 2 log n time using n processors and o m space is obtained this time bound matches that of the shiloach vishkin algorithm which also uses n processors but requires o n 2 space

first order based cumulative distribution function for solute concentration in heterogeneous aquifers theoretical analysis and implications for human health risk assessment quantifying the uncertainty of solute concentration in heterogeneous aquifers is an important step in both human health and ecological risk analysis the need for a probabilistic representation of transport is justified by the incomplete characterization of the subsurface we derive the one point concentration cumulative distribution function cdf while taking into account the spatial statistical structure of the hydraulic conductivity space dimensionality the injection source size the peclet number and the sampling volume at the monitoring location the cdf is application oriented and derived at first order in the log conductivity variance we illustrate how several key parameters control the shape of the concentration cdf the cdf shape is important since it reflects both uncertainty and the dilution state of the plume the transition from a bimodal to a unimodal cdf is examined and results are further supported by analyzing the concentration coefficient of variation results indicate the significance of the statistical anisotropy ratio i e the ratio between the hydraulic conductivity correlation scales in determining the cdf shape the importance of the sampling volume in the tails of the concentration cdf and a comparison between the proposed model with the cdf approach i e beta distribution are also shown finally we illustrate how the framework could be used in applications by evaluating the human health risk cdf our results are formally valid for low to moderate heterogeneous aquifers and source sizes small as compared to the hydraulic conductivity correlation length the proposed approach can serve as a benchmark tool for other methods

graph based airway tree reconstruction from chest ct scans evaluation of different features on five cohorts we present a graph based framework for airway tree reconstruction from computerized tomography ct scans and evaluate the performance of different feature categories and their combinations on five lung cohorts the approach consists of two main processing steps first potential airway branch and connection candidates are identified and represented by a graph structure with weighted nodes and edges respectively second an optimization algorithm is utilized for generating an airway detection result by selecting a subset of airway branches and connections based on graph weights derived from image features the performance of the algorithm with different feature categories and their combinations was assessed on a set of 50 lung ct scans from five different cohorts including normal and diseased lungs results show trade offs between feature categories combinations in terms of correctly true positive and incorrectly false positive identified airways also the performance of features in dependence of lung cohort was analyzed across all cohorts a good trade off with high true positive rate tpr and low false positive rate fpr was achieved by a combination of gray value local shape and structural features this combination enabled extracting 91 80 of reference airways tpr in combination with a low fpr of 1 00 in addition this variant was evaluated on the public exact 09 test set and a comparison with other airway detection approaches is provided one of the main advantages of the presented method is that it is robust against local disturbances artifacts or other ambiguities that are frequently occurring in lung ct scans

minimal surfaces extend shortest path segmentation methods to 3d shortest paths have been used to segment object boundaries with both continuous and discrete image models although these techniques are well defined in 2d the character of the path as an object boundary is not preserved in 3d an object boundary in three dimensions is a 2d surface however many different extensions of the shortest path techniques to 3d have been previously proposed in which the 3d object is segmented via a collection of shortest paths rather than a minimal surface leading to a solution which bears an uncertain relationship to the true minimal surface specifically there is no guarantee that a minimal path between points on two closed contours will lie on the minimal surface joining these contours we observe that an elegant solution to the computation of a minimal surface on a cellular complex e g a 3d lattice was given by sullivan sullivan showed that the discrete minimal surface connecting one or more closed contours may be found efficiently by solving a minimum cost circulation network flow mcnf problem in this work we detail why a minimal surface properly extends a shortest path in the context of a boundary to three dimensions present sullivan s solution to this minimal surface problem via an mcnf calculation and demonstrate the use of these minimal surfaces on the segmentation of image data

modeling low reynolds number incompressible flows using sph the method of smoothed particle hydrodynamics sph is extended to model incompressible flows of low reynolds number for such flows modification of the standard sph formalism is required to minimize errors associated with the use of a quasi incompressible equation of state treatment of viscosity state equation kernel interpolation and boundary conditions are described simulations using the method show close agreement with series solutions for couette and poiseuille flows furthermore comparison with finite element solutions for flow past a regular lattice of cylinders shows close agreement for the velocity and pressure fields the sph results exhibit small pressure fluctuations near curved boundaries further improvements to the boundary conditions may be possible which will reduce these errors a similar method to that used here may permit the simulation of other flows at low reynolds numbers using sph further development will be needed for cases involving free surfaces or substantially different equations of state

three dimensional segmentation of fluid associated abnormalities in retinal oct probability constrained graph search graph cut an automated method is reported for segmenting 3 d fluid associated abnormalities in the retina so called symptomatic exudate associated derangements sead from 3 d oct retinal images of subjects suffering from exudative age related macular degeneration in the first stage of a two stage approach retinal layers are segmented candidate sead regions identified and the retinal oct image is flattened using a candidate sead aware approach in the second stage a probability constrained combined graph search graph cut method refines the candidate seads by integrating the candidate volumes into the graph cut cost function as probability constraints the proposed method was evaluated on 15 spectral domain oct images from 15 subjects undergoing intravitreal anti vegf injection treatment leave one out evaluation resulted in a true positive volume fraction tpvf false positive volume fraction fpvf and relative volume difference ratio rvdr of 86 5 1 7 and 12 8 respectively the new graph cut graph search method significantly outperformed both the traditional graph cut and traditional graph search approaches p 0 01 p 0 04 and has the potential to improve clinical management of patients with choroidal neovascularization due to exudative age related macular degeneration