False normal Lung Clearance Index in infants with cystic fibrosis due to software algorithms.

BACKGROUND: Lung clearance index (LCI), a marker of ventilation inhomogeneity, is elevated early in children with cystic fibrosis (CF). However, in infants with CF, LCI values are found to be normal, although structural lung abnormalities are often detectable. We hypothesized that this discrepancy is due to inadequate algorithms of the available software package. AIM: Our aim was to challenge the validity of these software algorithms. METHODS: We compared multiple breath washout (MBW) results of current software algorithms (automatic modus) to refined algorithms (manual modus) in 17 asymptomatic infants with CF, and 24 matched healthy term-born infants. The main difference between these two analysis methods lies in the calculation of the molar mass differences that the system uses to define the completion of the measurement. RESULTS: In infants with CF the refined manual modus revealed clearly elevated LCI above 9 in 8 out of 35 measurements (23%), all showing LCI values below 8.3 using the automatic modus (paired t-test comparing the means, P < 0.001). Healthy infants showed normal LCI values using both analysis methods (n = 47, paired t-test, P = 0.79). The most relevant reason for false normal LCI values in infants with CF using the automatic modus was the incorrect recognition of the end-of-test too early during the washout. CONCLUSION: We recommend the use of the manual modus for the analysis of MBW outcomes in infants in order to obtain more accurate results. This will allow appropriate use of infant lung function results for clinical and scientific purposes. Pediatr Pulmonol. 2015; 50:970-977. © 2015 Wiley Periodicals, Inc.

Error models in hydrogeology applications

Notre consommation en eau souterraine, en particulier comme eau potable ou pour l'irrigation, a considérablement augmenté au cours des années. De nombreux problèmes font alors leur apparition, allant de la prospection de nouvelles ressources à la remédiation des aquifères pollués. Indépendamment du problème hydrogéologique considéré, le principal défi reste la caractérisation des propriétés du sous-sol. Une approche stochastique est alors nécessaire afin de représenter cette incertitude en considérant de multiples scénarios géologiques et en générant un grand nombre de réalisations géostatistiques. Nous rencontrons alors la principale limitation de ces approches qui est le coût de calcul dû à la simulation des processus d'écoulements complexes pour chacune de ces réalisations. Dans la première partie de la thèse, ce problème est investigué dans le contexte de propagation de l'incertitude, oú un ensemble de réalisations est identifié comme représentant les propriétés du sous-sol. Afin de propager cette incertitude à la quantité d'intérêt tout en limitant le coût de calcul, les méthodes actuelles font appel à des modèles d'écoulement approximés. Cela permet l'identification d'un sous-ensemble de réalisations représentant la variabilité de l'ensemble initial. Le modèle complexe d'écoulement est alors évalué uniquement pour ce sousensemble, et, sur la base de ces réponses complexes, l'inférence est faite. Notre objectif est d'améliorer la performance de cette approche en utilisant toute l'information à disposition. Pour cela, le sous-ensemble de réponses approximées et exactes est utilisé afin de construire un modèle d'erreur, qui sert ensuite à corriger le reste des réponses approximées et prédire la réponse du modèle complexe. Cette méthode permet de maximiser l'utilisation de l'information à disposition sans augmentation perceptible du temps de calcul. La propagation de l'incertitude est alors plus précise et plus robuste. La stratégie explorée dans le premier chapitre consiste à apprendre d'un sous-ensemble de réalisations la relation entre les modèles d'écoulement approximé et complexe. Dans la seconde partie de la thèse, cette méthodologie est formalisée mathématiquement en introduisant un modèle de régression entre les réponses fonctionnelles. Comme ce problème est mal posé, il est nécessaire d'en réduire la dimensionnalité. Dans cette optique, l'innovation du travail présenté provient de l'utilisation de l'analyse en composantes principales fonctionnelles (ACPF), qui non seulement effectue la réduction de dimensionnalités tout en maximisant l'information retenue, mais permet aussi de diagnostiquer la qualité du modèle d'erreur dans cet espace fonctionnel. La méthodologie proposée est appliquée à un problème de pollution par une phase liquide nonaqueuse et les résultats obtenus montrent que le modèle d'erreur permet une forte réduction du temps de calcul tout en estimant correctement l'incertitude. De plus, pour chaque réponse approximée, une prédiction de la réponse complexe est fournie par le modèle d'erreur. Le concept de modèle d'erreur fonctionnel est donc pertinent pour la propagation de l'incertitude, mais aussi pour les problèmes d'inférence bayésienne. Les méthodes de Monte Carlo par chaîne de Markov (MCMC) sont les algorithmes les plus communément utilisés afin de générer des réalisations géostatistiques en accord avec les observations. Cependant, ces méthodes souffrent d'un taux d'acceptation très bas pour les problèmes de grande dimensionnalité, résultant en un grand nombre de simulations d'écoulement gaspillées. Une approche en deux temps, le "MCMC en deux étapes", a été introduite afin d'éviter les simulations du modèle complexe inutiles par une évaluation préliminaire de la réalisation. Dans la troisième partie de la thèse, le modèle d'écoulement approximé couplé à un modèle d'erreur sert d'évaluation préliminaire pour le "MCMC en deux étapes". Nous démontrons une augmentation du taux d'acceptation par un facteur de 1.5 à 3 en comparaison avec une implémentation classique de MCMC. Une question reste sans réponse : comment choisir la taille de l'ensemble d'entrainement et comment identifier les réalisations permettant d'optimiser la construction du modèle d'erreur. Cela requiert une stratégie itérative afin que, à chaque nouvelle simulation d'écoulement, le modèle d'erreur soit amélioré en incorporant les nouvelles informations. Ceci est développé dans la quatrième partie de la thèse, oú cette méthodologie est appliquée à un problème d'intrusion saline dans un aquifère côtier. -- Our consumption of groundwater, in particular as drinking water and for irrigation, has considerably increased over the years and groundwater is becoming an increasingly scarce and endangered resource. Nofadays, we are facing many problems ranging from water prospection to sustainable management and remediation of polluted aquifers. Independently of the hydrogeological problem, the main challenge remains dealing with the incomplete knofledge of the underground properties. Stochastic approaches have been developed to represent this uncertainty by considering multiple geological scenarios and generating a large number of realizations. The main limitation of this approach is the computational cost associated with performing complex of simulations in each realization. In the first part of the thesis, we explore this issue in the context of uncertainty propagation, where an ensemble of geostatistical realizations is identified as representative of the subsurface uncertainty. To propagate this lack of knofledge to the quantity of interest (e.g., the concentration of pollutant in extracted water), it is necessary to evaluate the of response of each realization. Due to computational constraints, state-of-the-art methods make use of approximate of simulation, to identify a subset of realizations that represents the variability of the ensemble. The complex and computationally heavy of model is then run for this subset based on which inference is made. Our objective is to increase the performance of this approach by using all of the available information and not solely the subset of exact responses. Two error models are proposed to correct the approximate responses follofing a machine learning approach. For the subset identified by a classical approach (here the distance kernel method) both the approximate and the exact responses are knofn. This information is used to construct an error model and correct the ensemble of approximate responses to predict the "expected" responses of the exact model. The proposed methodology makes use of all the available information without perceptible additional computational costs and leads to an increase in accuracy and robustness of the uncertainty propagation. The strategy explored in the first chapter consists in learning from a subset of realizations the relationship between proxy and exact curves. In the second part of this thesis, the strategy is formalized in a rigorous mathematical framework by defining a regression model between functions. As this problem is ill-posed, it is necessary to reduce its dimensionality. The novelty of the work comes from the use of functional principal component analysis (FPCA), which not only performs the dimensionality reduction while maximizing the retained information, but also allofs a diagnostic of the quality of the error model in the functional space. The proposed methodology is applied to a pollution problem by a non-aqueous phase-liquid. The error model allofs a strong reduction of the computational cost while providing a good estimate of the uncertainty. The individual correction of the proxy response by the error model leads to an excellent prediction of the exact response, opening the door to many applications. The concept of functional error model is useful not only in the context of uncertainty propagation, but also, and maybe even more so, to perform Bayesian inference. Monte Carlo Markov Chain (MCMC) algorithms are the most common choice to ensure that the generated realizations are sampled in accordance with the observations. Hofever, this approach suffers from lof acceptance rate in high dimensional problems, resulting in a large number of wasted of simulations. This led to the introduction of two-stage MCMC, where the computational cost is decreased by avoiding unnecessary simulation of the exact of thanks to a preliminary evaluation of the proposal. In the third part of the thesis, a proxy is coupled to an error model to provide an approximate response for the two-stage MCMC set-up. We demonstrate an increase in acceptance rate by a factor three with respect to one-stage MCMC results. An open question remains: hof do we choose the size of the learning set and identify the realizations to optimize the construction of the error model. This requires devising an iterative strategy to construct the error model, such that, as new of simulations are performed, the error model is iteratively improved by incorporating the new information. This is discussed in the fourth part of the thesis, in which we apply this methodology to a problem of saline intrusion in a coastal aquifer.

Iterative reconstruction in CT : using mathematical model observers to determine low dose images' trustworthiness

La tomodensitométrie (TDM) est une technique d'imagerie pour laquelle l'intérêt n'a cessé de croitre depuis son apparition au début des années 70. De nos jours, l'utilisation de cette technique est devenue incontournable, grâce entre autres à sa capacité à produire des images diagnostiques de haute qualité. Toutefois, et en dépit d'un bénéfice indiscutable sur la prise en charge des patients, l'augmentation importante du nombre d'examens TDM pratiqués soulève des questions sur l'effet potentiellement dangereux des rayonnements ionisants sur la population. Parmi ces effets néfastes, l'induction de cancers liés à l'exposition aux rayonnements ionisants reste l'un des risques majeurs. Afin que le rapport bénéfice-risques reste favorable au patient il est donc nécessaire de s'assurer que la dose délivrée permette de formuler le bon diagnostic tout en évitant d'avoir recours à des images dont la qualité est inutilement élevée. Ce processus d'optimisation, qui est une préoccupation importante pour les patients adultes, doit même devenir une priorité lorsque l'on examine des enfants ou des adolescents, en particulier lors d'études de suivi requérant plusieurs examens tout au long de leur vie. Enfants et jeunes adultes sont en effet beaucoup plus sensibles aux radiations du fait de leur métabolisme plus rapide que celui des adultes. De plus, les probabilités des évènements auxquels ils s'exposent sont également plus grandes du fait de leur plus longue espérance de vie. L'introduction des algorithmes de reconstruction itératifs, conçus pour réduire l'exposition des patients, est certainement l'une des plus grandes avancées en TDM, mais elle s'accompagne de certaines difficultés en ce qui concerne l'évaluation de la qualité des images produites. Le but de ce travail est de mettre en place une stratégie pour investiguer le potentiel des algorithmes itératifs vis-à-vis de la réduction de dose sans pour autant compromettre la qualité du diagnostic. La difficulté de cette tâche réside principalement dans le fait de disposer d'une méthode visant à évaluer la qualité d'image de façon pertinente d'un point de vue clinique. La première étape a consisté à caractériser la qualité d'image lors d'examen musculo-squelettique. Ce travail a été réalisé en étroite collaboration avec des radiologues pour s'assurer un choix pertinent de critères de qualité d'image. Une attention particulière a été portée au bruit et à la résolution des images reconstruites à l'aide d'algorithmes itératifs. L'analyse de ces paramètres a permis aux radiologues d'adapter leurs protocoles grâce à une possible estimation de la perte de qualité d'image liée à la réduction de dose. Notre travail nous a également permis d'investiguer la diminution de la détectabilité à bas contraste associée à une diminution de la dose ; difficulté majeure lorsque l'on pratique un examen dans la région abdominale. Sachant que des alternatives à la façon standard de caractériser la qualité d'image (métriques de l'espace Fourier) devaient être utilisées, nous nous sommes appuyés sur l'utilisation de modèles d'observateurs mathématiques. Nos paramètres expérimentaux ont ensuite permis de déterminer le type de modèle à utiliser. Les modèles idéaux ont été utilisés pour caractériser la qualité d'image lorsque des paramètres purement physiques concernant la détectabilité du signal devaient être estimés alors que les modèles anthropomorphes ont été utilisés dans des contextes cliniques où les résultats devaient être comparés à ceux d'observateurs humain, tirant profit des propriétés de ce type de modèles. Cette étude a confirmé que l'utilisation de modèles d'observateurs permettait d'évaluer la qualité d'image en utilisant une approche basée sur la tâche à effectuer, permettant ainsi d'établir un lien entre les physiciens médicaux et les radiologues. Nous avons également montré que les reconstructions itératives ont le potentiel de réduire la dose sans altérer la qualité du diagnostic. Parmi les différentes reconstructions itératives, celles de type « model-based » sont celles qui offrent le plus grand potentiel d'optimisation, puisque les images produites grâce à cette modalité conduisent à un diagnostic exact même lors d'acquisitions à très basse dose. Ce travail a également permis de clarifier le rôle du physicien médical en TDM: Les métriques standards restent utiles pour évaluer la conformité d'un appareil aux requis légaux, mais l'utilisation de modèles d'observateurs est inévitable pour optimiser les protocoles d'imagerie. -- Computed tomography (CT) is an imaging technique in which interest has been quickly growing since it began to be used in the 1970s. Today, it has become an extensively used modality because of its ability to produce accurate diagnostic images. However, even if a direct benefit to patient healthcare is attributed to CT, the dramatic increase in the number of CT examinations performed has raised concerns about the potential negative effects of ionising radiation on the population. Among those negative effects, one of the major risks remaining is the development of cancers associated with exposure to diagnostic X-ray procedures. In order to ensure that the benefits-risk ratio still remains in favour of the patient, it is necessary to make sure that the delivered dose leads to the proper diagnosis without producing unnecessarily high-quality images. This optimisation scheme is already an important concern for adult patients, but it must become an even greater priority when examinations are performed on children or young adults, in particular with follow-up studies which require several CT procedures over the patient's life. Indeed, children and young adults are more sensitive to radiation due to their faster metabolism. In addition, harmful consequences have a higher probability to occur because of a younger patient's longer life expectancy. The recent introduction of iterative reconstruction algorithms, which were designed to substantially reduce dose, is certainly a major achievement in CT evolution, but it has also created difficulties in the quality assessment of the images produced using those algorithms. The goal of the present work was to propose a strategy to investigate the potential of iterative reconstructions to reduce dose without compromising the ability to answer the diagnostic questions. The major difficulty entails disposing a clinically relevant way to estimate image quality. To ensure the choice of pertinent image quality criteria this work was continuously performed in close collaboration with radiologists. The work began by tackling the way to characterise image quality when dealing with musculo-skeletal examinations. We focused, in particular, on image noise and spatial resolution behaviours when iterative image reconstruction was used. The analyses of the physical parameters allowed radiologists to adapt their image acquisition and reconstruction protocols while knowing what loss of image quality to expect. This work also dealt with the loss of low-contrast detectability associated with dose reduction, something which is a major concern when dealing with patient dose reduction in abdominal investigations. Knowing that alternative ways had to be used to assess image quality rather than classical Fourier-space metrics, we focused on the use of mathematical model observers. Our experimental parameters determined the type of model to use. Ideal model observers were applied to characterise image quality when purely objective results about the signal detectability were researched, whereas anthropomorphic model observers were used in a more clinical context, when the results had to be compared with the eye of a radiologist thus taking advantage of their incorporation of human visual system elements. This work confirmed that the use of model observers makes it possible to assess image quality using a task-based approach, which, in turn, establishes a bridge between medical physicists and radiologists. It also demonstrated that statistical iterative reconstructions have the potential to reduce the delivered dose without impairing the quality of the diagnosis. Among the different types of iterative reconstructions, model-based ones offer the greatest potential, since images produced using this modality can still lead to an accurate diagnosis even when acquired at very low dose. This work has clarified the role of medical physicists when dealing with CT imaging. The use of the standard metrics used in the field of CT imaging remains quite important when dealing with the assessment of unit compliance to legal requirements, but the use of a model observer is the way to go when dealing with the optimisation of the imaging protocols.

Accounting for adsorption and desorption in Lattice Boltzmann simulations

We report a Lattice-Boltzmann scheme that accounts for adsorption and desorption in the calculation of mesoscale dynamical properties of tracers in media of arbitrary complexity. Lattice Boltzmann simulations made it possible to solve numerically the coupled Navier-Stokes equations of fluid dynamics and Nernst-Planck equations of electrokinetics in complex, heterogeneous media. With the moment propagation scheme, it became possible to extract the effective diffusion and dispersion coefficients of tracers, or solutes, of any charge, e.g., in porous media. Nevertheless, the dynamical properties of tracers depend on the tracer-surface affinity, which is not purely electrostatic and also includes a species-specific contribution. In order to capture this important feature, we introduce specific adsorption and desorption processes in a lattice Boltzmann scheme through a modified moment propagation algorithm, in which tracers may adsorb and desorb from surfaces through kinetic reaction rates. The method is validated on exact results for pure diffusion and diffusion-advection in Poiseuille flows in a simple geometry. We finally illustrate the importance of taking such processes into account in the time-dependent diffusion coefficient in a more complex porous medium.

Design and evaluation of learning algorithms for dynamic resource management in virtual networks

Network virtualisation is considerably gaining attentionas a solution to ossification of the Internet. However, thesuccess of network virtualisation will depend in part on how efficientlythe virtual networks utilise substrate network resources.In this paper, we propose a machine learning-based approachto virtual network resource management. We propose to modelthe substrate network as a decentralised system and introducea learning algorithm in each substrate node and substrate link,providing self-organization capabilities. We propose a multiagentlearning algorithm that carries out the substrate network resourcemanagement in a coordinated and decentralised way. The taskof these agents is to use evaluative feedback to learn an optimalpolicy so as to dynamically allocate network resources to virtualnodes and links. The agents ensure that while the virtual networkshave the resources they need at any given time, only the requiredresources are reserved for this purpose. Simulations show thatour dynamic approach significantly improves the virtual networkacceptance ratio and the maximum number of accepted virtualnetwork requests at any time while ensuring that virtual networkquality of service requirements such as packet drop rate andvirtual link delay are not affected.

Defining housing market areas using commuting and migration algorithms. Catalonia (Spain) as an applied case study

In the literature on housing market areas, different approaches can be found to defining them, for example, using travel-to-work areas and, more recently, making use of migration data. Here we propose a simple exercise to shed light on which approach performs better. Using regional data from Catalonia, Spain, we have computed housing market areas with both commuting data and migration data. In order to decide which procedure shows superior performance, we have looked at uniformity of prices within areas. The main finding is that commuting algorithms present more homogeneous areas in terms of housing prices.

MCMC Analysis Of Classical Time Series Algorithms

Identification of order of an Autoregressive Moving Average Model (ARMA) by the usual graphical method is subjective. Hence, there is a need of developing a technique to identify the order without employing the graphical investigation of series autocorrelations. To avoid subjectivity, this thesis focuses on determining the order of the Autoregressive Moving Average Model using Reversible Jump Markov Chain Monte Carlo (RJMCMC). The RJMCMC selects the model from a set of the models suggested by better fitting, standard deviation errors and the frequency of accepted data. Together with deep analysis of the classical Box-Jenkins modeling methodology the integration with MCMC algorithms has been focused through parameter estimation and model fitting of ARMA models. This helps to verify how well the MCMC algorithms can treat the ARMA models, by comparing the results with graphical method. It has been seen that the MCMC produced better results than the classical time series approach.

Algorithmic Solutions for Combinatorial Problems in Resource Management of Manufacturing Environments

This thesis studies the use of heuristic algorithms in a number of combinatorial problems that occur in various resource constrained environments. Such problems occur, for example, in manufacturing, where a restricted number of resources (tools, machines, feeder slots) are needed to perform some operations. Many of these problems turn out to be computationally intractable, and heuristic algorithms are used to provide efficient, yet sub-optimal solutions. The main goal of the present study is to build upon existing methods to create new heuristics that provide improved solutions for some of these problems. All of these problems occur in practice, and one of the motivations of our study was the request for improvements from industrial sources. We approach three different resource constrained problems. The first is the tool switching and loading problem, and occurs especially in the assembly of printed circuit boards. This problem has to be solved when an efficient, yet small primary storage is used to access resources (tools) from a less efficient (but unlimited) secondary storage area. We study various forms of the problem and provide improved heuristics for its solution. Second, the nozzle assignment problem is concerned with selecting a suitable set of vacuum nozzles for the arms of a robotic assembly machine. It turns out that this is a specialized formulation of the MINMAX resource allocation formulation of the apportionment problem and it can be solved efficiently and optimally. We construct an exact algorithm specialized for the nozzle selection and provide a proof of its optimality. Third, the problem of feeder assignment and component tape construction occurs when electronic components are inserted and certain component types cause tape movement delays that can significantly impact the efficiency of printed circuit board assembly. Here, careful selection of component slots in the feeder improves the tape movement speed. We provide a formal proof that this problem is of the same complexity as the turnpike problem (a well studied geometric optimization problem), and provide a heuristic algorithm for this problem.

Efficiency of distinct data mining algorithms for classifying stress level in piglets from their vocalization

Among the challenges of pig farming in today's competitive market, there is factor of the product traceability that ensures, among many points, animal welfare. Vocalization is a valuable tool to identify situations of stress in pigs, and it can be used in welfare records for traceability. The objective of this work was to identify stress in piglets using vocalization, calling this stress on three levels: no stress, moderate stress, and acute stress. An experiment was conducted on a commercial farm in the municipality of Holambra, São Paulo State , where vocalizations of twenty piglets were recorded during the castration procedure, and separated into two groups: without anesthesia and local anesthesia with lidocaine base. For the recording of acoustic signals, a unidirectional microphone was connected to a digital recorder, in which signals were digitized at a frequency of 44,100 Hz. For evaluation of sound signals, Praat® software was used, and different data mining algorithms were applied using Weka® software. The selection of attributes improved model accuracy, and the best attribute selection was used by applying Wrapper method, while the best classification algorithms were the k-NN and Naive Bayes. According to the results, it was possible to classify the level of stress in pigs through their vocalization.

Multidata inverse problems and Bayesian solution methods in astronomy

Statistical analyses of measurements that can be described by statistical models are of essence in astronomy and in scientific inquiry in general. The sensitivity of such analyses, modelling approaches, and the consequent predictions, is sometimes highly dependent on the exact techniques applied, and improvements therein can result in significantly better understanding of the observed system of interest. Particularly, optimising the sensitivity of statistical techniques in detecting the faint signatures of low-mass planets orbiting the nearby stars is, together with improvements in instrumentation, essential in estimating the properties of the population of such planets, and in the race to detect Earth-analogs, i.e. planets that could support liquid water and, perhaps, life on their surfaces. We review the developments in Bayesian statistical techniques applicable to detections planets orbiting nearby stars and astronomical data analysis problems in general. We also discuss these techniques and demonstrate their usefulness by using various examples and detailed descriptions of the respective mathematics involved. We demonstrate the practical aspects of Bayesian statistical techniques by describing several algorithms and numerical techniques, as well as theoretical constructions, in the estimation of model parameters and in hypothesis testing. We also apply these algorithms to Doppler measurements of nearby stars to show how they can be used in practice to obtain as much information from the noisy data as possible. Bayesian statistical techniques are powerful tools in analysing and interpreting noisy data and should be preferred in practice whenever computational limitations are not too restrictive.

Scalable algorithms for height field illumination

Global illumination algorithms are at the center of realistic image synthesis and account for non-trivial light transport and occlusion within scenes, such as indirect illumination, ambient occlusion, and environment lighting. Their computationally most difficult part is determining light source visibility at each visible scene point. Height fields, on the other hand, constitute an important special case of geometry and are mainly used to describe certain types of objects such as terrains and to map detailed geometry onto object surfaces. The geometry of an entire scene can also be approximated by treating the distance values of its camera projection as a screen-space height field. In order to shadow height fields from environment lights a horizon map is usually used to occlude incident light. We reduce the per-receiver time complexity of generating the horizon map on N N height fields from O(N) of the previous work to O(1) by using an algorithm that incrementally traverses the height field and reuses the information already gathered along the path of traversal. We also propose an accurate method to integrate the incident light within the limits given by the horizon map. Indirect illumination in height fields requires information about which other points are visible to each height field point. We present an algorithm to determine this intervisibility in a time complexity that matches the space complexity of the produced visibility information, which is in contrast to previous methods which scale in the height field size. As a result the amount of computation is reduced by two orders of magnitude in common use cases. Screen-space ambient obscurance methods approximate ambient obscurance from the depth bu er geometry and have been widely adopted by contemporary real-time applications. They work by sampling the screen-space geometry around each receiver point but have been previously limited to near- field effects because sampling a large radius quickly exceeds the render time budget. We present an algorithm that reduces the quadratic per-pixel complexity of previous methods to a linear complexity by line sweeping over the depth bu er and maintaining an internal representation of the processed geometry from which occluders can be efficiently queried. Another algorithm is presented to determine ambient obscurance from the entire depth bu er at each screen pixel. The algorithm scans the depth bu er in a quick pre-pass and locates important features in it, which are then used to evaluate the ambient obscurance integral accurately. We also propose an evaluation of the integral such that results within a few percent of the ray traced screen-space reference are obtained at real-time render times.