Doğrusal olmayan manifoldlar üzerinde gürbüz yüz tanıma

Tez (Doktora) -- İstanbul Teknik Üniversitesi, Bilişim Enstitüsü, 2012Günümüze dek yapılmış tüm çalışmalara rağmen, yüz tanıma konusu hala kontrollü ortamlarda gösterdiği başarının ötesinde bir ilerlemeye ihtiyaç duymaktadır. Görüntüleme sırasında etkin olan, ışıklandırma, poz, yüz ifadeleri gibi değişimler tanıma etkinliğini olumsuz yönde ve yoğun bir biçimde etkilemektedir. Belli değişimler karşısında başarı gösteren yöntemler geliştirilmiş olmasına karşın, farklı değişimleri aynı yaklaşım ile modelleyebilen bir çalışmadan bahsetmek pek mümkün olamamaktadır. Bu çalışmanın amacı, farklı değişimleri modelleyebilecek genel bir yaklaşımın tasarlanması ve başarımının ölçülmesidir. Sunulan yaklaşımın, değişimlere özel ayarlamalara ihtiyaç duymadan, yalın hali ile kullanılabilmesi ve böylece farklı alt uzay incelemelerini aynı çatı altında toplayabilmesi hedeflenmektedir. Önerilen yöntem, genel hatları ile, alt uzay tasarımlarına dayanmaktadır ve böylece gelecekte yöntemin ne şekilde geliştirilebileceği, açık bir şekilde sunulmaktadır. Bu çalışmada, olasılık tabanlı PCA benzeri bir çerçeve kullanılarak, doğrusallıktan belli düzeyde uzak değişimlerin modellenebilmesi ve bu değişimlerin var olduğu durumlarda sınıflandırma yapılabilmesi için genel amaçlı bir yöntem geliştirilmiştir. Yöntem iki temel aşamadan oluşmaktadır: (1) Manifold öğrenimi ve (2) olasılık temelli üretim modeli. İlk aşamada elde edilen düşük boyutlu alt uzay konaçları, ikinci aşamada sınıfa özel altuzayların belirlenmesinde kullanılmaktadır. Yöntemin en belirgin üstünlüğü, her sınıf için ayrı bir alt uzay elde edilmesi ve eğitim aşamasında her sınıfın tek bir örneğinin yeterli olmasıdır. Sınıfların bağımsız alt uzaylar içerisinde modellenmesi, yöntemin ayrım gücünü oldukça arttırmaktadır. Yöntemin farklı değişimler altında çalışabildiğini göstermek amacıyla, ışıklandırma, poz ve ifade farklılıkları söz konusuyken yüz tanıma deneyleri yapılmıştır. Yöntem, mevcut yazında başarılı olarak nitelendirilen yöntemlerle yarışan başarım oranları elde etmiş ve yüksek boyutlu veritabanları için de uygun olduğunu kanıtlamıştır. Önerilen yöntemin bazı temel artı değerleri şu şekilde sıralanabilir: (1) Manifoldlar üzerinde tanımlı farklı değişimler, yöntem üzerinde yenilemeye ihtiyaç duyulmadan kontrol altına alınabilmektedir. (2) Geleneksel etmen çözümlemesi yaklaşımının etkinliği ve ölçeklenebilirliği, sınıf temelli bir yaklaşım ile arttırılmıştır. (3) Karar verme süreci tamamen olasılıksaldır ve böylece yüksek boyutlu veritabanlarına yönelik olarak öncül olasılıkların devreye sokulması ve alınacak kararın alan bilgisi ile kuvvetlendirilmesi mümkündür. (4) Üç boyutlu modellemeler ile kıyaslandığında, ön inceleme aşamasının zaman karmaşıklığı daha düşüktür. (5) Her kişinin tek bir örneğinin bulunması tanıma için yeterliyken, birden çok görüntünün bulunması durumunda başarımı arttıracak eklentiler de tanımlanmıştır.The face recognition is one of the most studied, yet one of the most incomplete topic due to the nonlinearity and the diversity of variations which are effective during the data acquisition. Developing an algorithm that can handle illumination, pose, expression, occlusion etc. altogether still seems to be a very challenging job. There exist lots of study concerning invariant representations to handle certain variations, yet a generic approach to model different variations at once still seems to be a task to accomplish. In this study, we define a baseline framework to handle different types of variations. The main attention is to propose a guideline that can be used for different types of variations without requiring any modifications depending on the physical or geometric characteristics of the concerned variation. In other words, the methodology can be utilized for recognition under illumination, pose changes or expression changes. The proposed method is established over the subspace analysis; therefore, the direction of the future works is also defined explicitly. A general framework is developed to model nonlinear variations in object appearances and to enable object classification under such variations, which is similar in essence to the probabilistic interpretation of PCA. The proposed method can be summarized as a two-step probabilistic framework. The first step is a bootstrap phase in which the useful statistics are calculated. A manifold learning technique is employed at this step to define the geometry of the subspace. The second step includes regular training and testing tasks. Images of a person under a certain variation are assumed to be generated by a linear generative model. The identity of a novel observation is determined by the likelihood of being generated by this model. The main advantage of the proposed method is the fact that it models each class in a separate subspace and it requires a single instance of each class to do so. Defining different subspaces for individual classes increases the separation capacity of the method. Numerous experiments were performed to analyze the performance of the proposed method against different variation types and with relatively large databases. In both cases, the results are very promising. Several advantages of the method can be summarized as follows: (1) different types of variation that lie on smooth manifolds can be handled by the method, (2) the scalability of the classical factor analysis is improved by a class dependent scheme, (3) the decision process is fully probabilistic, and posterior probabilities can be utilized for large scale and domain specific real life applications by incorporating priors on the identities, (4) bootstrap has less time complexity compared to 3D rendering approaches, and finally (5) a single observation for each identity is sufficient to perform reliable recognition while a way to use more images is also introduced.DoktoraPh.D

Unifying Inference of Meso-Scale Structures in Networks.

Networks are among the most prevalent formal representations in scientific studies, employed to depict interactions between objects such as molecules, neuronal clusters, or social groups. Studies performed at meso-scale that involve grouping of objects based on their distinctive interaction patterns form one of the main lines of investigation in network science. In a social network, for instance, meso-scale structures can correspond to isolated social groupings or groups of individuals that serve as a communication core. Currently, the research on different meso-scale structures such as community and core-periphery structures has been conducted via independent approaches, which precludes the possibility of an algorithmic design that can handle multiple meso-scale structures and deciding which structure explains the observed data better. In this study, we propose a unified formulation for the algorithmic detection and analysis of different meso-scale structures. This facilitates the investigation of hybrid structures that capture the interplay between multiple meso-scale structures and statistical comparison of competing structures, all of which have been hitherto unavailable. We demonstrate the applicability of the methodology in analyzing the human brain network, by determining the dominant organizational structure (communities) of the brain, as well as its auxiliary characteristics (core-periphery)

Model comparisons with different ground-truth meso-scale network structures.

<p>The proposed inference algorithm was run with different number of communities (x-axis) and the log-likelihood (y-axis) was calculated for each. The maximum log-likelihood is marked with the gray circle indicating the predicted number of communities. Dashed gray line shows the log-likelihood for a random network. The ground-truth meso-scale structure was (a) the hybrid structure 2 (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0143133#pone.0143133.e013" target="_blank">Eq 8</a>), (b) the community structure (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0143133#pone.0143133.e009" target="_blank">Eq 4</a>), (c) the hybrid structure 2 (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0143133#pone.0143133.e013" target="_blank">Eq 8</a>). Vertical bars show standard deviation for repeated experiments; some lines are shifted slightly along the x-axis to prevent overlaps. The true models achieved higher likelihood in all pairwise comparisons, with the true number of communities achieving the maximum value in each case.</p

Networks with different meso-scale structures and their generative models.

<p>Networks are illustrated by their connectivity matrices depicting weights of edges between nodes. (a) A network with core-periphery structure. (b) A network with community structure. (c) A hybrid network model including both.</p

Results of simulation studies on predicting the number of communities.

<p>The true number of communities is given in parenthesis next to each curve. The proposed inference algorithm was run with different number of communities (x-axis) and the log-likelihood (y-axis) was calculated for each. The maximum log-likelihood is marked with the gray circle indicating the predicted number of communities. (a) Networks were generated using the pure community structure defined in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0143133#pone.0143133.e009" target="_blank">Eq 4</a>. (b) Networks were generated using the hybrid structure defined in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0143133#pone.0143133.e012" target="_blank">Eq 7</a>. Vertical bars show standard deviation for repeated experiments; some lines are shifted slightly along the x-axis to prevent overlaps. The true number of communities was predicted successfully for all experiments.</p

Meso-scale structures of the human brain network.

<p>(a) The connectivity matrix of the brain that defined the network. Edges between nodes were weighted by the number of streamlines (normalized so as to have values between 0 and 100). (b) Model fits with different candidate meso-scale structures; three structures were compared. The proposed inference algorithm was run with different number of communities (x-axis) and the log-likelihood (y-axis) was calculated for each. The upper panel gives the modularity measure (Q) for different number of communities. Comparison with Q shows that the change in the likelihood value as we increase the number of communities, is similar to the change in the traditionally used modularity measure.</p

Community and core-periphery structures of the human brain network.

<p>(a) Distribution of coreness among nodes when a pure core-periphery structure is assumed. (b) Communities of the network with 5 communities. (c) A hybrid structure. The hybrid model integrates the decisions from two distinct models.</p

Implementing multiphysics models in FEniCS: Viscoelastic flows, poroelasticity, and tumor growth

The open-source finite element code FEniCS is considered as an alternative to commercial finite element codes for evaluating complex constitutive models of multiphysics phenomena. FEniCS deserves this consideration because it is well-suited for encoding weak forms corresponding to partial differential equations arising from the fundamental balance laws and constitutive equations. It is shown how FEniCS can be adopted for solving boundary-value problems describing viscoelastic flows, poroelasticity, and tumor growth. Those problems span a wide range of models of continuum mechanics, and involve Eulerian, Lagrangian, and combined Eulerian-Lagrangian descriptions. Thus it is demonstrated that FEniCS is a viable computational tool capable of transcending traditional barriers between computational fluid and solid mechanics. Furthermore, it is shown that FEniCS implementations are straightforward, and do not require advanced knowledge of finite element methods and/or coding skills