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Using greedy algorithm to learn graphical model for digit recognitionYang, Jisong 20 January 2015 (has links)
Graphical model, the marriage between graph theory and probability theory, has been drawing increasing attention because of its many attractive features. In this paper, we consider the problem of learning the structure of graphical model based on observed data through a greedy forward-backward algorithm and with the use of learned model to classify the data into different categories. We establish the graphical model associated with a binary Ising Markov random field. And model selection is implemented by adding and deleting edges between nodes. Our experiments show that: compared with previous methods, the proposed algorithm has better performance in terms of correctness rate and model selection. / text
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Make it Flat : Detection and Correction of Planar Regions in Triangle Meshes / Detektion och tillrättning av plana ytor i triangelmodellerJonsson, Mikael January 2016 (has links)
The art of reconstructing a real-world scene digitally has been on the mind of researchers for decades. Recently, it has attracted more and more attention from companies seeing a chance to bring this kind of technology to the market. Digital reconstruction of buildings in particular is a niche that has both potential and room for improvement. With this background, this thesis will present the design and evaluation of a pipeline made to find and correct approximately flat surfaces in architectural scenes. The scenes are 3D-reconstructed triangle meshes based on RGB images. The thesis will also comprise an evaluation of a few different components available for doing this, leading to a choice of best components. The goal is to improve the visual quality of the reconstruction. The final pipeline is designed with two blocks - one to detect initial plane seeds and one to refine the detected planes. The first block makes use of a multi-label energy formulation on the graph that describes the reconstructed surface. Penalties are assigned to each vertex and each edge of the graph based on the vertex labels, effectively describing a Markov Random Field. The energy is minimized with the help of the alpha-expansion algorithm. The second block uses heuristics for growing the detected plane seeds, merging similar planes together and extracting deviating details. Results on several scenes are presented, showing that the visual quality has been improved while maintaining accuracy compared with ground truth data. / Konsten att digitalt rekonstruera en verklig miljö har länge varit intressant för forskare. Nyligen har området även tilldragit sig mer och mer uppmärksamhet från företag som ser en möjlighet att föra den här typen av teknik till produkter på marknaden. I synnerhet är digital rekonstruktion av byggnader en nisch som har både stor potential och möjlighet till förbättring. Med denna bakgrund så presenterar detta examensarbete designen för och utvärderingen av en pipeline som skapats för att detektera och rätta till approximativt platta regioner i arkitektoniska miljöer. Miljöerna är 3D-rekonstruerade triangelmeshar skapade från RGB-bilder. Examensarbetet omfattar även utvärdering av olika komponenter för att uppnå detta, som avslutas med att de mest lämpliga komponenterna presenteras. Målet i korthet är att förbättra den visuella kvaliteten av en rekonstruerad modell. Den slutgiltiga pipelinen består av två övergripande block - ett för att detektera initiala plan och ett för att förbättra de funna planen. Det första blocket använder en multi-label energiformulering på grafen som beskriver den rekonstruerade ytan. Straffvärden tilldelas varje vertex och varje båge i grafen baserade på varje vertex label. På så sätt beskriver grafen ett Markov Random Field. Energin är sedan minimerad med alpha-expansion-algoritmen. Det andra blocket använder heuristiker för att låta planen växa, slå ihop närliggande plan och för att extrahera avvikande detaljer. Resultat på flera miljöer presenteras också för att påvisa att den visuella kvaliteten har förbättrats utan att rekonstruktionens noggrannhet har försämrats jämfört med ground truth-data.
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The transformation of one-dimensional and two-dimensional autoregressive random fields under coordinate scaling and rotationKennedy, Ian Douglas January 2008 (has links)
A practical problem in computer graphics is that of representing a textured surface at arbitrary scales. I consider the underlying mathematical problem to be that of interpolating autoregressive random fields under arbitrary coordinate transformations. I examine the theoretical basis for the transformations that autoregressive parameters exhibit when the associated stationary random fields are scaled or rotated. The basic result is that the transform takes place in the continuous autocovariance domain, and that the spectral density and associated autoregressive parameters proceed directly from sampling the continuous autocovariance on a transformed grid. I show some real-world applications of these ideas, and explore how they allow us to interpolate into a random field. Along the way, I develop interesting ways to estimate simultaneous autoregressive parameters, to calculate the distorting effects of linear interpolation algorithms, and to interpolate random fields without altering their statistics.
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Optimal Design of Experiments Subject to Correlated ErrorsPazman, Andrej, Müller, Werner January 2000 (has links) (PDF)
In this paper we consider optimal design of experiments in the case of correlated observations, when no replications are possible. This situation is typical when observing a random process or random field with known covariance structure. We present a theorem which demonstrates that the computation of optimum exact designs corresponds to solving minimization problems in terms of design measures. (author's abstract) / Series: Forschungsberichte / Institut für Statistik
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The transformation of one-dimensional and two-dimensional autoregressive random fields under coordinate scaling and rotationKennedy, Ian Douglas January 2008 (has links)
A practical problem in computer graphics is that of representing a textured surface at arbitrary scales. I consider the underlying mathematical problem to be that of interpolating autoregressive random fields under arbitrary coordinate transformations. I examine the theoretical basis for the transformations that autoregressive parameters exhibit when the associated stationary random fields are scaled or rotated. The basic result is that the transform takes place in the continuous autocovariance domain, and that the spectral density and associated autoregressive parameters proceed directly from sampling the continuous autocovariance on a transformed grid. I show some real-world applications of these ideas, and explore how they allow us to interpolate into a random field. Along the way, I develop interesting ways to estimate simultaneous autoregressive parameters, to calculate the distorting effects of linear interpolation algorithms, and to interpolate random fields without altering their statistics.
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The study of the phase transition from first-order to second-order in the two dimensional Potts model due to random applied fieldsHuang, Shih-Yuan 17 July 2003 (has links)
Abstract
In this paper, we study the nature of phase transition of the two-dimensional six-state Potts model under the external random magnetic field.
The six-state Potts model exist temperature-dependent first-order phase transition. When the external random field is applied, the nature of phase can be altered from first-order to second-order.By employing the Monte Carlo simulation method, we inspected the energy histogram and Binder parameter of the six-state Potts model under the external random magnetic field. According to our analyses, the evidences reveal that the phase transition does not change until the external magnetic field is greater then 0.02
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Optimum design for correlated processes via eigenfunction expansionsFedorov, Valery V., Müller, Werner January 2004 (has links) (PDF)
In this paper we consider optimum design of experiments for correlated observations. We approximate the error component of the process by an eigenvector expansion of the corresponding covariance function. Furthermore we study the limit behavior of an additional white noise as a regularization tool. The approach is illustrated by some typical examples. (authors' abstract) / Series: Research Report Series / Department of Statistics and Mathematics
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Bayesian Analysis for Large Spatial DataPark, Jincheol 2012 August 1900 (has links)
The Gaussian geostatistical model has been widely used in Bayesian modeling of spatial data. A core difficulty for this model is at inverting the n x n covariance matrix, where n is a sample size. The computational complexity of matrix inversion increases as O(n3). This difficulty is involved in almost all statistical inferences approaches of the model, such as Kriging and Bayesian modeling. In Bayesian inference, the inverse of covariance matrix needs to be evaluated at each iteration in posterior simulations, so Bayesian approach is infeasible for large sample size n due to the current computational power limit.
In this dissertation, we propose two approaches to address this computational issue, namely, the auxiliary lattice model (ALM) approach and the Bayesian site selection (BSS) approach. The key feature of ALM is to introduce a latent regular lattice which links Gaussian Markov Random Field (GMRF) with Gaussian Field (GF) of the observations. The GMRF on the auxiliary lattice represents an approximation to the Gaussian process. The distinctive feature of ALM from other approximations lies in that ALM avoids completely the problem of the matrix inversion by using analytical likelihood of GMRF. The computational complexity of ALM is rather attractive, which increase linearly with sample size.
The second approach, Bayesian site selection (BSS), attempts to reduce the dimension of data through a smart selection of a representative subset of the observations. The BSS method first split the observations into two parts, the observations near the target prediction sites (part I) and their remaining (part II). Then, by treating the observations in part I as response variable and those in part II as explanatory variables, BSS forms a regression model which relates all observations through a conditional likelihood derived from the original model. The dimension of the data can then be reduced by applying a stochastic variable selection procedure to the regression model, which selects only a subset of the part II data as explanatory data. BSS can provide us more understanding to the underlying true Gaussian process, as it directly works on the original process without any approximations involved.
The practical performance of ALM and BSS will be illustrated with simulated data and real data sets.
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Learning object segmentation from video dataRoss, Michael G., Kaelbling, Leslie Pack 08 September 2003 (has links)
This memo describes the initial results of a project to create a self-supervised algorithm for learning object segmentation from video data. Developmental psychology and computational experience have demonstrated that the motion segmentation of objects is a simpler, more primitive process than the detection of object boundaries by static image cues. Therefore, motion information provides a plausible supervision signal for learning the static boundary detection task and for evaluating performance on a test set. A video camera and previously developed background subtraction algorithms can automatically produce a large database of motion-segmented images for minimal cost. The purpose of this work is to use the information in such a database to learn how to detect the object boundaries in novel images using static information, such as color, texture, and shape. This work was funded in part by the Office of Naval Research contract #N00014-00-1-0298, in part by the Singapore-MIT Alliance agreement of 11/6/98, and in part by a National Science Foundation Graduate Student Fellowship.
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Fragment Based Protein Active Site Analysis Using Markov Random Field Combinations of Stereochemical Feature-Based ClassificationsPai Karkala, Reetal 2009 May 1900 (has links)
Recent improvements in structural genomics efforts have greatly increased the
number of hypothetical proteins in the Protein Data Bank. Several computational
methodologies have been developed to determine the function of these proteins but
none of these methods have been able to account successfully for the diversity in
the sequence and structural conformations observed in proteins that have the same
function. An additional complication is the
flexibility in both the protein active site
and the ligand.
In this dissertation, novel approaches to deal with both the ligand flexibility
and the diversity in stereochemistry have been proposed. The active site analysis
problem is formalized as a classification problem in which, for a given test protein,
the goal is to predict the class of ligand most likely to bind the active site based
on its stereochemical nature and thereby define its function. Traditional methods
that have adapted a similar methodology have struggled to account for the
flexibility
observed in large ligands. Therefore, I propose a novel fragment-based approach to
dealing with larger ligands. The advantage of the fragment-based methodology is
that considering the protein-ligand interactions in a piecewise manner does not affect
the active site patterns, and it also provides for a way to account for the problems
associated with
flexible ligands. I also propose two feature-based methodologies to account for the diversity observed
in sequences and structural conformations among proteins with the same function.
The feature-based methodologies provide detailed descriptions of the active site
stereochemistry and are capable of identifying stereochemical patterns within the
active site despite the diversity.
Finally, I propose a Markov Random Field approach to combine the individual
ligand fragment classifications (based on the stereochemical descriptors) into a single
multi-fragment ligand class. This probabilistic framework combines the information
provided by stereochemical features with the information regarding geometric constraints
between ligand fragments to make a final ligand class prediction.
The feature-based fragment identification methodology had an accuracy of 84%
across a diverse set of ligand fragments and the mrf analysis was able to succesfully
combine the various ligand fragments (identified by feature-based analysis) into one
final ligand based on statistical models of ligand fragment distances. This novel
approach to protein active site analysis was additionally tested on 3 proteins with very
low sequence and structural similarity to other proteins in the PDB (a challenge for
traditional methods) and in each of these cases, this approach successfully identified
the cognate ligand. This approach addresses the two main issues that affect the
accuracy of current automated methodologies in protein function assignment.
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