[pt] Predição de porosidade em reservatórios de óleo e gás representa em uma tarefa crucial e desafiadora na indústria de petróleo. Neste trabalho é proposto um novo modelo não-linear para predição de porosidade que trata fácies sedimentares como variáveis ocultas ou latentes. Esse modelo, denominado Transductive Conditional Random Field Regression (TCRFR), combina com sucesso os conceitos de Markov random fields, ridge regression e aprendizado transdutivo. O modelo utiliza volumes de impedância sísmica como informação de entrada condicionada aos valores de porosidade disponíveis nos poços existentes no reservatório e realiza de forma simultânea e automática a classificação das fácies e a estimativa de porosidade em todo o volume. O método é capaz de inferir as fácies latentes através da combinação de amostras precisas de porosidade local presentes nos poços com dados de impedância sísmica ruidosos, porém disponíveis em todo o volume do reservatório. A informação precisa de porosidade é propagada no volume através de modelos probabilísticos baseados em grafos, utilizando conditional random fields. Adicionalmente, duas novas técnicas são introduzidas como etapas de pré-processamento para aplicação do método TCRFR nos casos extremos em que somente um número bastante reduzido de amostras rotuladas de porosidade encontra-se disponível em um pequeno conjunto de poços exploratórios, uma situação típica para geólogos durante a fase exploratória de uma nova área. São realizados experimentos utilizando dados de um reservatório sintético e de um reservatório real. Os resultados comprovam que o método apresenta um desempenho consideravelmente superior a outros métodos automáticos de predição em relação aos dados sintéticos e, em relação aos dados reais, um desempenho comparável ao gerado por técnicas tradicionais de geo estatística que demandam grande esforço manual por parte de especialistas. / [en] Estimating porosity in oil and gas reservoirs is a crucial and challenging task in the oil industry. A novel nonlinear model for porosity estimation is proposed, which handles sedimentary facies as latent variables. It successfully combines the concepts of conditional random fields (CRFs), transductive learning and ridge regression. The proposed Transductive Conditional Random Field Regression (TCRFR) uses seismic impedance volumes as input information, conditioned on the porosity values from the available wells in the reservoir, and simultaneously and automatically provides as output the porosity estimation and facies classification in the whole volume. The method is able to infer the latent facies states by combining the local, labeled and accurate porosity information available at well locations with the plentiful but imprecise impedance information available everywhere in the reservoir volume. That accurate information is propagated in the reservoir based on conditional random field probabilistic graphical models, greatly reducing uncertainty. In addition, two new techniques are introduced as preprocessing steps for the application of TCRFR in the extreme but realistic cases where just a scarce amount of porosity labeled samples are available in a few exploratory wells, a typical situation for geologists during the evaluation of a reservoir in the exploration phase. Both synthetic and real-world data experiments are presented to prove the usefulness of the proposed methodology, which show that it outperforms previous automatic estimation methods on synthetic data and provides a comparable result to the traditional manual labored geostatistics approach on real-world data.

Title: Density of Minkowski functionals of stationary random sets Author: Bc. Filip Dohnálek Department: Department of Probability and Mathematical Statistics Supervisor: prof. RNDr. Jan Rataj, CSc., Mathematical Institute of Charles University Abstract: In the presented work we can find the created theory of random closed excursion set generated by means of Gaussian real random field. We specialize in a real random field, which is defined on the regular stratified manifold. The text includes a determination of conditions for a random field and stratified manifold in which densities of the intrinsic volumes for excursion sets exist. Then subsequently attributes and relations of the excursion set are derived for the existence of densities of the intrinsic volumes. Finally, a simulated study is made where we compare theoretical and estimated values of densities. This is followed by a discussion on the results, which we compare to the Boolean model. Keywords: Densities of the intrinsic volume, Excursion set, Manifold, Real random field

Uma etapa de suma importância na análise automática de imagens é a segmentação, que procura dividir uma imagem em regiões cujos pixels exibem um certo grau de similaridade. Uma característica que provê similaridade entre pixels de uma mesma região é a textura, formada geralmente pela combinação aleatória de suas intensidades. Muitos trabalhos vêm sendo realizados com o intuito de estudar técnicas não-supervisionadas de segmentação de imagens por modelos estocásticos, definindo texturas como campos aleatórios de Markov. Um método com esta abordagem que se destaca é o EM/MPM, um algoritmo iterativo que combina a técnica EM para realizar uma estimação de parâmetros por máxima verossimilhança com a MPM, utilizada para segmentação pela minimização do número de pixels erroneamente classificados. Este trabalho desenvolveu um estudo sobre a modelagem e a implementação do algoritmo EM/MPM, juntamente com sua abordagem multiresolução. Foram propostas uma estimação inicial de parâmetros por limiarização e uma combinação com o algoritmo de Annealing. Foi feito também um estudo acerca da validação de classes, ou seja, a busca pelo número de regiões diferentes na imagem, mostrando as principais técnicas encontradas na literatura e propondo uma nova abordagem, baseada na distribuição dos níveis de cinza das classes. Por fim, foi desenvolvida uma extensão do modelo para a segmentação de malhas em duas e três dimensões. / An important stage of the automatic image analysis process is segmentation, that aims to split an image into regions whose pixels exhibit a certain degree of similarity. Texture is known as an efficient feature that provides enough discriminant power to differenciate pixels from distinct regions. It is usually defined as a random combination of pixel intensities. A considerable amount of researches has been done on non-supervised techniques for image segmentation based on stochastic models, in which texture is defined as Markov Random Fields. Such an important method in this category is the EM/MPM, an iterative algorithm that combines the maximum-likelihood parameter estimation model EM with the MPM segmentation algorithm, whose aim is to minimize the number of misclassified pixels in the image. This work has carried out a study on stochastic models for segmentation and shows an implementation for the EM/MPM algorithm, together with a multiresolution approach. A new threshold-based scheme for the estimation of initial parameters for the EM/MPM model has been proposed. This work also shows how to incorporate the concept of annealing to the current EM/MPM algorithm in order to improve segmentation. Additionally, a study on the class validity problem (search for the correct number of classes) has been done, showing the most important techniques available in the literature. As a consequence, a gray level distribution-based approach has been devised. Finally, the work shows an extension of the traditional EM/MPM technique for segmenting 2D and 3D meshes.

No contexto de sistemas de baixa anisotropia, medidas de magnetização para verificar os efeitos magnéticos induzidos pela substituição do íon Mn+2 por Cu+2 em um quase unidimensional antiferromagneto tipo Heisenberg CsMn1-xCuxA3.2H2O (A = Cl, Br) foram feitas. Nas amostras diluídas com derivados de Br observamos o aparecimento de uma magnetização remanente abaixo de TN quando elas são resfriadas em um pequeno campo axial aplicado ao longo do eixo fácil. Isso não ocorre com as amostras diluídas com derivados de Cl. A troca intra-cadeia tanto com os compostos de Cl e Br é antiferromagnética, entretanto a troca entre-cadeias ao longo de eixo fácil é antiferromagnética no composto com Cl e ferromagnética com o Br. Esse fato parece ser determinístico no surgimento de momentos espontâneos abaixo de TN no composto com bromo. Além disso, medidas de magnetização do monocristal antiferromagnético de sítio diluído A2Fe1-xInxCl5.H2O (A = Cs) foram feitas em baixos campos magnéticos (H) aplicados ao longo do eixo de fácil magnetização. Os dados revelaram que uma magnetização remanente Mr se desenvolve abaixo a temperatura de Néel TN. Essa Mr(T) é paralela ao eixo fácil e satura para campos H ~ 1Oe e ela aumenta com decréscimo de T. Ela também possui uma dependência de temperatura como outros sistemas diluídos da mesma família (A = K, Rb). Para todos esses sistemas, a curva normalizada Mr(t)/ Mr(t = 0,3), onde t=T/TN é a temperatura reduzida, é independente de x e acompanha uma curva universal. No contexto de sistemas de alta anisotropia, a dependência da temperatura do excesso de magnetização em baixos e altos campos foi investigada para o antiferromagneto 3D de Ising FexZn1-xF2 (x = 0.72; 0.46 e 0.31) e também o sistema puro FeF2. Verificamos que Mr surge tanto paralela ou perpendicular ao eixo fácil. A magnitude de Mr, para baixos campos (H < 1 Oe) depende de H, mas satura para campos de alguns Oersted. O esperado comportamento de campo aleatório (RF), em campos altos, é observado quando H é aplicado ao longo do eixo fácil. / In the context of low anisotropy, the magnetization measurements to find out the magnetic effects induced by the substitution of Mn+2 by Cu+2 íons in the quaseone-dimensional Heisenberg-like antiferromagnets CsMn1-xCuxA3.2H2O (A = Cl,Br) were made. In the diluted samples of the Br derivative, we observe the appearance of a remanent magnetization (Mr) below TN when they are cooled in a small axial magnetic field applied along the easy axis. This does not occur in the diluted samples of the Cl derivative. The intra-chain exchange both in Cl and Br compounds is antiferromagnetic, however the inter-chain exhange along the easy axis is antiferromagnetic in the chloride compound and ferromagnetic in the bromide. This fact seems to be deterministic in the appearance of the net moments below TN in the bromide. Moreover, the magnetization measurements on single crystals of the sitediluted antiferromagnet A2Fe1-xInxCl5.H2O (A = Cs) were carried out at low magnetic fields (H) applied along the easy axis. The data revealed that a Mr develops below the Néel temperature TN. This Mr(T) is parallel to the easy axis , saturates for H ~ 1 Oe and it increases with decreasing T. It has also temperature dependence as another diluted systems of the same family (A = K, Rb). For all these systems the normalized Mr(t)/Mr(t = 0,3), where t = T/TN is the reduced temperature, is independet of x and follow a universal curve. In the context of high anisotropy, the temperature dependence of the excess magnetization at low and high fields was investigated for the diluted antiferromagnet FexZn1-xF2 (x = 0.72; 0.46 and 0.31) and pure system FeF2 as well. It was found that Mr is either along the easy axis or perpendicular to it. The size of Mr for very low fields (H < 1 Oe) depends on H but it sature for fields of the order of few Oersteds. The expected random field (RF) behaivor is observed when H is applied along the easy axis at higher fields.

Survey propagation (SP) has recently been discovered as an efficient algorithm in solving classes of hard constraint-satisfaction problems (CSP). Powerful as it is, SP is still a heuristic algorithm, and further understanding its algorithmic nature, improving its effectiveness and extending its applicability are highly desirable. Prior to the work in this thesis, Maneva et al. introduced a Markov Random Field (MRF) formalism for k-SAT problems, on which SP may be viewed as a special case of the well-known belief propagation (BP) algorithm. This result had sometimes been interpreted to an understanding that “SP is BP” and allows a rigorous extension of SP to a “weighted” version, or a family of algorithms, for k-SAT problems. SP has also been generalized, in a non-weighted fashion, for solving non-binary CSPs. Such generalization is however presented using statistical physics language and somewhat difficult to access by more general audience. This thesis generalizes SP both in terms of its applicability to non-binary problems and in terms of introducing “weights” and extending SP to a family of algorithms. Under a generic formulation of CSPs, we first present an understanding of non-weighted SP for arbitrary CSPs in terms of “probabilistic token passing” (PTP). We then show that this probabilistic interpretation of non-weighted SP makes it naturally generalizable to a weighted version, which we call weighted PTP. Another main contribution of this thesis is a disproof of the folk belief that “SP is BP”. We show that the fact that SP is a special case of BP for k-SAT problems is rather incidental. For more general CSPs, SP and generalized SP do not reduce from BP. We also established the conditions under which generalized SP may reduce as special cases of BP. To explore the benefit of generalizing SP to a wide family and for arbitrary, particularly non-binary, problems, we devised a simple weighted PTP based algorithm for solving 3-COL problems. Experimental results, compared against an existing non-weighted SP based algorithm, reveal the potential performance gain that generalized SP may bring.

Survey propagation (SP) has recently been discovered as an efficient algorithm in solving classes of hard constraint-satisfaction problems (CSP). Powerful as it is, SP is still a heuristic algorithm, and further understanding its algorithmic nature, improving its effectiveness and extending its applicability are highly desirable. Prior to the work in this thesis, Maneva et al. introduced a Markov Random Field (MRF) formalism for k-SAT problems, on which SP may be viewed as a special case of the well-known belief propagation (BP) algorithm. This result had sometimes been interpreted to an understanding that “SP is BP” and allows a rigorous extension of SP to a “weighted” version, or a family of algorithms, for k-SAT problems. SP has also been generalized, in a non-weighted fashion, for solving non-binary CSPs. Such generalization is however presented using statistical physics language and somewhat difficult to access by more general audience. This thesis generalizes SP both in terms of its applicability to non-binary problems and in terms of introducing “weights” and extending SP to a family of algorithms. Under a generic formulation of CSPs, we first present an understanding of non-weighted SP for arbitrary CSPs in terms of “probabilistic token passing” (PTP). We then show that this probabilistic interpretation of non-weighted SP makes it naturally generalizable to a weighted version, which we call weighted PTP. Another main contribution of this thesis is a disproof of the folk belief that “SP is BP”. We show that the fact that SP is a special case of BP for k-SAT problems is rather incidental. For more general CSPs, SP and generalized SP do not reduce from BP. We also established the conditions under which generalized SP may reduce as special cases of BP. To explore the benefit of generalizing SP to a wide family and for arbitrary, particularly non-binary, problems, we devised a simple weighted PTP based algorithm for solving 3-COL problems. Experimental results, compared against an existing non-weighted SP based algorithm, reveal the potential performance gain that generalized SP may bring.

Segmentation of individual facial soft tissues has received relatively little attention in the literature due to the complicated structures of these tissues. There is a need to incorporate the prior information, which is usually in the form of atlases, in the segmentation process. In this thesis we performed several segmentation methods that take advantage of prior knowledge for facial soft tissue segmentation. An atlas based method and three expectation maximization &ndash / Markov random field (EM-MRF) based methods are tested for two dimensional (2D) segmentation of masseter muscle in the face. Atlas based method uses the manually labeled atlases as prior information. We implemented EM-MRF based method in different manners / without prior information, with prior information for initialization and with using labeled atlas as prior information. The differences between these methods and the influence of the prior information are discussed by comparing the results. Finally a new method based on EM-MRF is proposed in this study. In this method we aim to use prior information without performing manual segmentation, which is a very complicated and time consuming task. 10 MRI sets are used as experimental data in this study and leave-one-out technique is used to perform segmentation for all sets. The test data is modeled as a Markov Random Field where unlabeled training data, i.e., other 9 sets, are used as prior information. The model parameters are estimated by the Maximum Likelihood approach when the Expectation Maximization iterations are used to handle hidden labels. The performance of all segmentation methods are computed and compared to the manual segmented ground truth. Then we used the new 2D segmentation method for three dimensional (3D) segmentation of two masseter and two temporalis tissues in each data set and visualize the segmented tissue volumes.

Bien que souvent présentés comme des configurations atypiques, la classe des milieux diffusifs représente une grande partie des milieux dans lesquels se propagent des ondes aussi bien électromagnétiques qu'acoustiques. Les grandes cavités étant capables de bien approcher ces mêmes caractéristiques, elles sont largement utilisées dans un contexte métrologique, afin d'émuler un grand nombre de configurations pratiques et d'évaluer certaines propriétés de dispositifs électroniques, acoustiques et optiques. Nous nous intéressons à la modélisation statistique de la propagation d'ondes dans les grandes cavités. La pratique courante de modéliser les champs dans une cavité comme diffus est d'abord analysée, afin de montrer comment cette hypothèse n'est pas réaliste en basse fréquence, et les conséquences qui en découlent. L'importance du recouvrement modal et sa nature aléatoire sont discutées, montrant comment l'hypothèse diffusive ne peut pas être décrite comme une propriété certaine. Dans un deuxième temps nous étudions les applications du retournement temporel aux grandes cavités, ce qui nous amène à l'introduction d'une technique généralisée capable de reproduire des fronts d'ondes cohérents dans un environnement diffusif, typiquement regardé comme uniquement capable de supporter une propagation aléatoire.

Survey propagation (SP) has recently been discovered as an efficient algorithm in solving classes of hard constraint-satisfaction problems (CSP). Powerful as it is, SP is still a heuristic algorithm, and further understanding its algorithmic nature, improving its effectiveness and extending its applicability are highly desirable. Prior to the work in this thesis, Maneva et al. introduced a Markov Random Field (MRF) formalism for k-SAT problems, on which SP may be viewed as a special case of the well-known belief propagation (BP) algorithm. This result had sometimes been interpreted to an understanding that “SP is BP” and allows a rigorous extension of SP to a “weighted” version, or a family of algorithms, for k-SAT problems. SP has also been generalized, in a non-weighted fashion, for solving non-binary CSPs. Such generalization is however presented using statistical physics language and somewhat difficult to access by more general audience. This thesis generalizes SP both in terms of its applicability to non-binary problems and in terms of introducing “weights” and extending SP to a family of algorithms. Under a generic formulation of CSPs, we first present an understanding of non-weighted SP for arbitrary CSPs in terms of “probabilistic token passing” (PTP). We then show that this probabilistic interpretation of non-weighted SP makes it naturally generalizable to a weighted version, which we call weighted PTP. Another main contribution of this thesis is a disproof of the folk belief that “SP is BP”. We show that the fact that SP is a special case of BP for k-SAT problems is rather incidental. For more general CSPs, SP and generalized SP do not reduce from BP. We also established the conditions under which generalized SP may reduce as special cases of BP. To explore the benefit of generalizing SP to a wide family and for arbitrary, particularly non-binary, problems, we devised a simple weighted PTP based algorithm for solving 3-COL problems. Experimental results, compared against an existing non-weighted SP based algorithm, reveal the potential performance gain that generalized SP may bring.

In the present thesis, a novel gridding technique, as well as, two new segmentation methods applied to complementary DNA (cDNA) microarray images is proposed. More precise, a new gridding method based on continuous wavelet transform (CWT) was performed. Line profiles of x and y axis were calculated, resulting to 2 different signals. These signals were independently processed by means of CWT at 15 different levels, using daubechies 4 mother wavelet. A summation, point by point, was performed on the processed signals, in order to suppress noise and enhance spot’s differences. Additionally, a wavelet based hard thresholding filter was applied to each signal for the task of alleviating the noise of the signals. 10 real microarray images were used in order to visually assess the performance of our gridding method. Each microarray image contained 4 sub-arrays, each sub-array 40x40 spots, thus, 6400 spots totally. According to our results, the accuracy of our algorithm was 98% in all 10 images and in all spots. Additionally, processing time was less than 3 sec on a 1024×1024×16 microarray image, rendering the method a promising technique for an efficient and fully automatic gridding processing. Following the gridding process, the Gaussian Mixture Model (GMM) and the Fuzzy GMM algorithms were applied to each cell, with the purpose of discriminating foreground from background. In addition, markov random field (MRF), as well as, a proposed wavelet based MRF model (SMRF) were implemented. The segmentation abilities of all the algorithms were evaluated by means of the segmentation matching factor (SMF), the Coefficient of Determination (r2), and the concordance correlation (pc). Indirect accuracy performances were also tested on the experimental images by means of the Mean Absolute Error (MAE) and the Coefficient of Variation (CV). In the latter case, SPOT and SCANALYZE software results were also tested. In the former case, SMRF attained the best SMF, r2, and pc (92.66%, 0.923, and 0.88, respectively) scores, whereas, in the latter case scored MAE and CV, 497 and 0.88, respectively. The results and support the performance superiority of the SMRF algorithm in segmenting cDNA images. / Τα τελευταία χρόνια παρατηρείται ραγδαία ανάπτυξη της τεχνολογίας των μικροσυστοιχιών (microarrays) με αποτέλεσμα την ποιοτική και ποσοτική μέτρηση της έκφρασης χιλιάδων γονιδίων ταυτοχρόνως σ’ ένα και μόνο πείραμα. Εικόνες μικροσυστοιχιών, στις οποίες έχει λάβει χώρα υβριδοποίηση δείγματος DNA, χρησιμοποιούνται ευρέως για την εξαγωγή αξιόπιστων αποτελεσμάτων γονιδιακής έκφρασης και προσδιορισμό των μηχανισμών που ελέγχουν την ενεργοποίηση των γονιδίων σ’ έναν οργανισμό. Συνεπώς, η δημιουργία κατάλληλων υπολογιστικών τεχνικών για την επεξεργασία των εικόνων αυτών συντελεί καθοριστικά στην εξαγωγή ορθών και έγκυρων αποτελεσμάτων. Στη παρούσα Διδακτορική Διατριβή αναπτύχθηκε στο πρώτο στάδια μια νέα πλήρως αυτοματοποιημένη τεχνική διευθυνσιοδότησης και στο δεύτερο στάδιο δύο νέες τεχνικές τμηματοποίησης. Πιο συγκεκριμένα, αναπτύχθηκε μια νέα μέθοδος διευθυνσιοδότησης η οποία βασίζεται στο συνεχή μετασχηματισμό κυματιδίου (Continuous Wavelet Transform CWT) για την αυτόματη εύρεση των κέντρων των κηλίδων, καθώς και των ορίων μεταξύ δύο διαδοχικών κηλίδων. Στη συνέχεια αναπτύχθηκαν δύο νέες μέθοδοι κατάτμησης της εικόνας για τον διαχωρισμό των κηλίδων από το φόντο, οι οποίες βασίζονται στη τεχνική μίξης ασαφών μοντέλων Γκάους (Fuzzy Gaussian Mixture Models FGMM) καθώς και στη τεχνική συνδυασμού τυχαίων πεδίων Μαρκόφ (Markov Random Field MRF) και μετασχηματισμού κυματιδίου (Wavelet Transform WT) (SMRF). Με σκοπό την αξιολόγηση (validation) των προτεινόμενων μεθόδων της παρούσας Διδακτορικής Διατριβής, δημιουργήθηκαν και χρησιμοποιήθηκαν τόσο πραγματικές εικόνες μικροσυστοιχιών, καθώς και απομιμούμενες (simulated) σύμφωνα με μεθοδολογία η οποία προτείνεται απο τη διεθνή βιβλιογραφία. Όσον αφορά την διευθυνσιοδότηση, χρησιμοποιώντας οπτική ανασκόπηση για κάθε κηλίδα χωριστά σε όλες τις πραγματικές εικόνες, δημιουργήθηκαν δύο κατηγορίες, ανάλογα με το αν οι γραμμές του πλέγματος εφάπτονταν πάνω σε κάποια κηλίδα ή όχι. Η προτεινόμενη μεθοδολογία ήταν ακριβής σε ποσοστό 98% στον ακριβή εντοπισμό των κηλίδων σε όλες τις εικόνες. Σύγκριση ανάμεσα στην απόδοση των GMM, FGMM, MRF και SMRF στις απομιμούμενες εικόνες σε διαφορετικά επίπεδα θορύβου πραγματοποιήθηκε και τα αποτελέσματα σε όλα τα μετρικά, segmentation matching factor (SMF), coefficient of variation ( ), και coefficient of determination ( ), μας έδειξαν ότι η μέθοδος SMRF είναι πιο αξιόπιστη στο να μπορέσει να αναδείξει την πραγματική περιφέρεια της κηλίδας, τόσο σε εικόνες με μεγάλο λόγο σήματος προς θόρυβο, όσο και σε μικρό λόγο. Ενδεικτικά αποτελέσματα σε 1 db SNR για την περίπτωση του SMRF είναι SMF = 92.66, =0.923, και = 0.88, ακολουθούμενο από το MRF ( SMF = 92.15, =0.91, και = 0.85), FGMM ( SMF = 91.07, =0.92, και = 0.86)και GMM (SMF = 90.73, =0.89, και = 0.83). Στη συνέχεια πάρθηκαν αποτελέσματα τα οποία προέκυψαν από τη χρήση πραγματικών εικόνων μικροσυστοιχιών. Και σε αυτή τη περίπτωση, αναδείχθηκε η υπεροχή του WMRF, έναντι των άλλων αλγορίθμων ταξινόμησης μέση τιμή MAE = 497 και CV = 0.88. Τέλος, θα πρέπει να τονιστεί ότι τα παραπάνω μετρικά υπολογίστηκαν και σε αποτελέσματα από δύο ευρέως χρησιμοποιούμενα πακέτα επεξεργασίας εικόνων μικροσυστοιχιών, τα οποία χρησιμοποιούνται και είναι διαθέσιμα. Πιο συγκεκριμένα, χρησιμοποιήθηκαν το SCANALYSE και το SPOT, τα οποία χρησιμοποιούν τις τεχνικές τμηματοποίησης Fixed Circle και Seeded Region Growing, αντίστοιχα. Στη περίπτωση αυτή η τεχνική SMRF κατάφερε να υπολογίσει καλύτερα αποτελέσματα από τα δύο αυτά πακέτα. Πιο συγκεκριμένα η τεχνική GMM πέτυχε MAE = 1470 και CV = 1.29, η τεχνική FGMM πέτυχε MAE = 1430 και CV = 1.21, η τεχνική MRF πέτυχε MAE = 1215 και CV = 1.15, η τεχνική WMRF πέτυχε MAE = 497 και CV = 0.88, η τεχνική FC του λογισμικού πακέτου SCANALYZE πέτυχε MAE = 503 και CV = 0.90, και τέλος η τεχνική SRG του λογισμικού πακέτου SPOT πέτυχε MAE = 1180 και CV = 0.93.