3D RECONSTRUCTION FROM STEREO/RANGE IMAGES

3D reconstruction from stereo/range image is one of the most fundamental and extensively researched topics in computer vision. Stereo research has recently experienced somewhat of a new era, as a result of publically available performance testing such as the Middlebury data set, which has allowed researchers to compare their algorithms against all the state-of-the-art algorithms. This thesis investigates into the general stereo problems in both the two-view stereo and multi-view stereo scopes. In the two-view stereo scope, we formulate an algorithm for the stereo matching problem with careful handling of disparity, discontinuity and occlusion. The algorithm works with a global matching stereo model based on an energy minimization framework. The experimental results are evaluated on the Middlebury data set, showing that our algorithm is the top performer. A GPU approach of the Hierarchical BP algorithm is then proposed, which provides similar stereo quality to CPU Hierarchical BP while running at real-time speed. A fast-converging BP is also proposed to solve the slow convergence problem of general BP algorithms. Besides two-view stereo, ecient multi-view stereo for large scale urban reconstruction is carefully studied in this thesis. A novel approach for computing depth maps given urban imagery where often large parts of surfaces are weakly textured is presented. Finally, a new post-processing step to enhance the range images in both the both the spatial resolution and depth precision is proposed

Learning the dynamics and time-recursive boundary detection of deformable objects

We propose a principled framework for recursively segmenting deformable objects across a sequence of frames. We demonstrate the usefulness of this method on left ventricular segmentation across a cardiac cycle. The approach involves a technique for learning the system dynamics together with methods of particle-based smoothing as well as non-parametric belief propagation on a loopy graphical model capturing the temporal periodicity of the heart. The dynamic system state is a low-dimensional representation of the boundary, and the boundary estimation involves incorporating curve evolution into recursive state estimation. By formulating the problem as one of state estimation, the segmentation at each particular time is based not only on the data observed at that instant, but also on predictions based on past and future boundary estimates. Although the paper focuses on left ventricle segmentation, the method generalizes to temporally segmenting any deformable object

Approximate inference in Gaussian graphical models

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 161-169).The focus of this thesis is approximate inference in Gaussian graphical models. A graphical model is a family of probability distributions in which the structure of interactions among the random variables is captured by a graph. Graphical models have become a powerful tool to describe complex high-dimensional systems specified through local interactions. While such models are extremely rich and can represent a diverse range of phenomena, inference in general graphical models is a hard problem. In this thesis we study Gaussian graphical models, in which the joint distribution of all the random variables is Gaussian, and the graphical structure is exposed in the inverse of the covariance matrix. Such models are commonly used in a variety of fields, including remote sensing, computer vision, biology and sensor networks. Inference in Gaussian models reduces to matrix inversion, but for very large-scale models and for models requiring distributed inference, matrix inversion is not feasible. We first study a representation of inference in Gaussian graphical models in terms of computing sums of weights of walks in the graph -- where means, variances and correlations can be represented as such walk-sums. This representation holds in a wide class of Gaussian models that we call walk-summable. We develop a walk-sum interpretation for a popular distributed approximate inference algorithm called loopy belief propagation (LBP), and establish conditions for its convergence. We also extend the walk-sum framework to analyze more powerful versions of LBP that trade off convergence and accuracy for computational complexity, and establish conditions for their convergence. Next we consider an efficient approach to find approximate variances in large scale Gaussian graphical models.(cont.) Our approach relies on constructing a low-rank aliasing matrix with respect to the Markov graph of the model which can be used to compute an approximation to the inverse of the information matrix for the model. By designing this matrix such that only the weakly correlated terms are aliased, we are able to give provably accurate variance approximations. We describe a construction of such a low-rank aliasing matrix for models with short-range correlations, and a wavelet based construction for models with smooth long-range correlations. We also establish accuracy guarantees for the resulting variance approximations.by Dmitry M. Malioutov.Ph.D

Combining Features and Semantics for Low-level Computer Vision

Visual perception of depth and motion plays a significant role in understanding and navigating the environment. Reconstructing outdoor scenes in 3D and estimating the motion from video cameras are of utmost importance for applications like autonomous driving. The corresponding problems in computer vision have witnessed tremendous progress over the last decades, yet some aspects still remain challenging today. Striking examples are reflecting and textureless surfaces or large motions which cannot be easily recovered using traditional local methods. Further challenges include occlusions, large distortions and difficult lighting conditions. In this thesis, we propose to overcome these challenges by modeling non-local interactions leveraging semantics and contextual information. Firstly, for binocular stereo estimation, we propose to regularize over larger areas on the image using object-category specific disparity proposals which we sample using inverse graphics techniques based on a sparse disparity estimate and a semantic segmentation of the image. The disparity proposals encode the fact that objects of certain categories are not arbitrarily shaped but typically exhibit regular structures. We integrate them as non-local regularizer for the challenging object class 'car' into a superpixel-based graphical model and demonstrate its benefits especially in reflective regions. Secondly, for 3D reconstruction, we leverage the fact that the larger the reconstructed area, the more likely objects of similar type and shape will occur in the scene. This is particularly true for outdoor scenes where buildings and vehicles often suffer from missing texture or reflections, but share similarity in 3D shape. We take advantage of this shape similarity by localizing objects using detectors and jointly reconstructing them while learning a volumetric model of their shape. This allows to reduce noise while completing missing surfaces as objects of similar shape benefit from all observations for the respective category. Evaluations with respect to LIDAR ground-truth on a novel challenging suburban dataset show the advantages of modeling structural dependencies between objects. Finally, motivated by the success of deep learning techniques in matching problems, we present a method for learning context-aware features for solving optical flow using discrete optimization. Towards this goal, we present an efficient way of training a context network with a large receptive field size on top of a local network using dilated convolutions on patches. We perform feature matching by comparing each pixel in the reference image to every pixel in the target image, utilizing fast GPU matrix multiplication. The matching cost volume from the network's output forms the data term for discrete MAP inference in a pairwise Markov random field. Extensive evaluations reveal the importance of context for feature matching.Die visuelle Wahrnehmung von Tiefe und Bewegung spielt eine wichtige Rolle bei dem Verständnis und der Navigation in unserer Umwelt. Die 3D Rekonstruktion von Szenen im Freien und die Schätzung der Bewegung von Videokameras sind von größter Bedeutung für Anwendungen, wie das autonome Fahren. Die Erforschung der entsprechenden Probleme des maschinellen Sehens hat in den letzten Jahrzehnten enorme Fortschritte gemacht, jedoch bleiben einige Aspekte heute noch ungelöst. Beispiele hierfür sind reflektierende und texturlose Oberflächen oder große Bewegungen, bei denen herkömmliche lokale Methoden häufig scheitern. Weitere Herausforderungen sind niedrige Bildraten, Verdeckungen, große Verzerrungen und schwierige Lichtverhältnisse. In dieser Arbeit schlagen wir vor nicht-lokale Interaktionen zu modellieren, die semantische und kontextbezogene Informationen nutzen, um diese Herausforderungen zu meistern. Für die binokulare Stereo Schätzung schlagen wir zuallererst vor zusammenhängende Bereiche mit objektklassen-spezifischen Disparitäts Vorschlägen zu regularisieren, die wir mit inversen Grafik Techniken auf der Grundlage einer spärlichen Disparitätsschätzung und semantischen Segmentierung des Bildes erhalten. Die Disparitäts Vorschläge kodieren die Tatsache, dass die Gegenstände bestimmter Kategorien nicht willkürlich geformt sind, sondern typischerweise regelmäßige Strukturen aufweisen. Wir integrieren sie für die komplexe Objektklasse 'Auto' in Form eines nicht-lokalen Regularisierungsterm in ein Superpixel-basiertes grafisches Modell und zeigen die Vorteile vor allem in reflektierenden Bereichen. Zweitens nutzen wir für die 3D-Rekonstruktion die Tatsache, dass mit der Größe der rekonstruierten Fläche auch die Wahrscheinlichkeit steigt, Objekte von ähnlicher Art und Form in der Szene zu enthalten. Dies gilt besonders für Szenen im Freien, in denen Gebäude und Fahrzeuge oft vorkommen, die unter fehlender Textur oder Reflexionen leiden aber ähnlichkeit in der Form aufweisen. Wir nutzen diese ähnlichkeiten zur Lokalisierung von Objekten mit Detektoren und zur gemeinsamen Rekonstruktion indem ein volumetrisches Modell ihrer Form erlernt wird. Dies ermöglicht auftretendes Rauschen zu reduzieren, während fehlende Flächen vervollständigt werden, da Objekte ähnlicher Form von allen Beobachtungen der jeweiligen Kategorie profitieren. Die Evaluierung auf einem neuen, herausfordernden vorstädtischen Datensatz in Anbetracht von LIDAR-Entfernungsdaten zeigt die Vorteile der Modellierung von strukturellen Abhängigkeiten zwischen Objekten. Zuletzt, motiviert durch den Erfolg von Deep Learning Techniken bei der Mustererkennung, präsentieren wir eine Methode zum Erlernen von kontextbezogenen Merkmalen zur Lösung des optischen Flusses mittels diskreter Optimierung. Dazu stellen wir eine effiziente Methode vor um zusätzlich zu einem Lokalen Netzwerk ein Kontext-Netzwerk zu erlernen, das mit Hilfe von erweiterter Faltung auf Patches ein großes rezeptives Feld besitzt. Für das Feature Matching vergleichen wir mit schnellen GPU-Matrixmultiplikation jedes Pixel im Referenzbild mit jedem Pixel im Zielbild. Das aus dem Netzwerk resultierende Matching Kostenvolumen bildet den Datenterm für eine diskrete MAP Inferenz in einem paarweisen Markov Random Field. Eine umfangreiche Evaluierung zeigt die Relevanz des Kontextes für das Feature Matching

Deformable shape matching

Deformable shape matching has become an important building block in academia as well as in industry. Given two three dimensional shapes A and B the deformation function f aligning A with B has to be found. The function is discretized by a set of corresponding point pairs. Unfortunately, the computation cost of a brute-force search of correspondences is exponential. Additionally, to be of any practical use the algorithm has to be able to deal with data coming directly from 3D scanner devices which suffers from acquisition problems like noise, holes as well as missing any information about topology. This dissertation presents novel solutions for solving shape matching: First, an algorithm estimating correspondences using a randomized search strategy is shown. Additionally, a planning step dramatically reducing the matching costs is incorporated. Using ideas of these both contributions, a method for matching multiple shapes at once is shown. The method facilitates the reconstruction of shape and motion from noisy data acquired with dynamic 3D scanners. Considering shape matching from another perspective a solution is shown using Markov Random Fields (MRF). Formulated as MRF, partial as well as full matches of a shape can be found. Here, belief propagation is utilized for inference computation in the MRF. Finally, an approach significantly reducing the space-time complexity of belief propagation for a wide spectrum of computer vision tasks is presented.Anpassung deformierbarer Formen ist zu einem wichtigen Baustein in der akademischen Welt sowie in der Industrie geworden. Gegeben zwei dreidimensionale Formen A und B, suchen wir nach einer Verformungsfunktion f, die die Deformation von A auf B abbildet. Die Funktion f wird durch eine Menge von korrespondierenden Punktepaaren diskretisiert. Leider sind die Berechnungskosten für eine Brute-Force-Suche dieser Korrespondenzen exponentiell. Um zusätzlich von einem praktischen Nutzen zu sein, muss der Suchalgorithmus in der Lage sein, mit Daten, die direkt aus 3D-Scanner kommen, umzugehen. Bedauerlicherweise leiden diese Daten unter Akquisitionsproblemen wie Rauschen, Löcher sowie fehlender Topologieinformation. In dieser Dissertation werden neue Lösungen für das Problem der Formanpassung präsentiert. Als erstes wird ein Algorithmus gezeigt, der die Korrespondenzen mittels einer randomisierten Suchstrategie schätzt. Zusätzlich wird anhand eines automatisch berechneten Schätzplanes die Geschwindigkeit der Suchstrategie verbessert. Danach wird ein Verfahren gezeigt, dass die Anpassung mehrerer Formen gleichzeitig bewerkstelligen kann. Diese Methode ermöglicht es, die Bewegung, sowie die eigentliche Struktur des Objektes aus verrauschten Daten, die mittels dynamischer 3D-Scanner aufgenommen wurden, zu rekonstruieren. Darauffolgend wird das Problem der Formanpassung aus einer anderen Perspektive betrachtet und als Markov-Netzwerk (MRF) reformuliert. Dieses ermöglicht es, die Formen auch stückweise aufeinander abzubilden. Die eigentliche Lösung wird mittels Belief Propagation berechnet. Schließlich wird ein Ansatz gezeigt, der die Speicher-Zeit-Komplexität von Belief Propagation für ein breites Spektrum von Computer-Vision Problemen erheblich reduziert

MRF Stereo Matching with Statistical Estimation of Parameters

For about the last ten years, stereo matching in computer vision has been treated as a combinatorial optimization problem. Assuming that the points in stereo images form a Markov Random Field (MRF), a variety of combinatorial optimization algorithms has been developed to optimize their underlying cost functions. In many of these algorithms, the MRF parameters of the cost functions have often been manually tuned or heuristically determined for achieving good performance results. Recently, several algorithms for statistical, hence, automatic estimation of the parameters have been published. Overall, these algorithms perform well in labeling, but they lack in performance for handling discontinuity in labeling along the surface borders. In this dissertation, we develop an algorithm for optimization of the cost function with automatic estimation of the MRF parameters – the data and smoothness parameters. Both the parameters are estimated statistically and applied in the cost function with support of adaptive neighborhood defined based on color similarity. With the proposed algorithm, discontinuity handling with higher consistency than of the existing algorithms is achieved along surface borders. The data parameters are pre-estimated from one of the stereo images by applying a hypothesis, called noise equivalence hypothesis, to eliminate interdependency between the estimations of the data and smoothness parameters. The smoothness parameters are estimated applying a combination of maximum likelihood and disparity gradient constraint, to eliminate nested inference for the estimation. The parameters for handling discontinuities in data and smoothness are defined statistically as well. We model cost functions to match the images symmetrically for improved matching performance and also to detect occlusions. Finally, we fill the occlusions in the disparity map by applying several existing and proposed algorithms and show that our best proposed segmentation based least squares algorithm performs better than the existing algorithms. We conduct experiments with the proposed algorithm on publicly available ground truth test datasets provided by the Middlebury College. Experiments show that results better than the existing algorithms’ are delivered by the proposed algorithm having the MRF parameters estimated automatically. In addition, applying the parameter estimation technique in existing stereo matching algorithm, we observe significant improvement in computational time

The feasibility of using feature-flow and label transfer system to segment medical images with deformed anatomy in orthopedic surgery

In computer-aided surgical systems, to obtain high fidelity three-dimensional models, we require accurate segmentation of medical images. State-of-art medical image segmentation methods have been used successfully in particular applications, but they have not been demonstrated to work well over a wide range of deformities. For this purpose, I studied and evaluated medical image segmentation using the feature-flow based Label Transfer System described by Liu and colleagues. This system has produced promising results in parsing images of natural scenes. Its ability to deal with variations in shapes of objects is desirable. In this paper, we altered this system and assessed its feasibility of automatic segmentation. Experiments showed that this system achieved better recognition rates than those in natural-scene parsing applications, but the high recognition rates were not consistent across different images. Although this system is not considered clinically practical, we may improve it and incorporate it with other medical segmentation tools

Estimation in Gaussian Graphical Models Using Tractable Subgraphs: A Walk-Sum Analysis

Graphical models provide a powerful formalism for statistical signal processing. Due to their sophisticated modeling capabilities, they have found applications in a variety of fields such as computer vision, image processing, and distributed sensor networks. In this paper, we present a general class of algorithms for estimation in Gaussian graphical models with arbitrary structure. These algorithms involve a sequence of inference problems on tractable subgraphs over subsets of variables. This framework includes parallel iterations such as embedded trees, serial iterations such as block Gauss-Seidel, and hybrid versions of these iterations. We also discuss a method that uses local memory at each node to overcome temporary communication failures that may arise in distributed sensor network applications. We analyze these algorithms based on the recently developed walk-sum interpretation of Gaussian inference. We describe the walks ldquocomputedrdquo by the algorithms using walk-sum diagrams, and show that for iterations based on a very large and flexible set of sequences of subgraphs, convergence is guaranteed in walk-summable models. Consequently, we are free to choose spanning trees and subsets of variables adaptively at each iteration. This leads to efficient methods for optimizing the next iteration step to achieve maximum reduction in error. Simulation results demonstrate that these nonstationary algorithms provide a significant speedup in convergence over traditional one-tree and two-tree iterations

Exponential families on resource-constrained systems

This work is about the estimation of exponential family models on resource-constrained systems. Our main goal is learning probabilistic models on devices with highly restricted storage, arithmetic, and computational capabilities—so called, ultra-low-power devices. Enhancing the learning capabilities of such devices opens up opportunities for intelligent ubiquitous systems in all areas of life, from medicine, over robotics, to home automation—to mention just a few. We investigate the inherent resource consumption of exponential families, review existing techniques, and devise new methods to reduce the resource consumption. The resource consumption, however, must not be reduced at all cost. Exponential families possess several desirable properties that must be preserved: Any probabilistic model encodes a conditional independence structure—our methods keep this structure intact. Exponential family models are theoretically well-founded. Instead of merely finding new algorithms based on intuition, our models are formalized within the framework of exponential families and derived from first principles. We do not introduce new assumptions which are incompatible with the formal derivation of the base model, and our methods do not rely on properties of particular high-level applications. To reduce the memory consumption, we combine and adapt reparametrization and regularization in an innovative way that facilitates the sparse parametrization of high-dimensional non-stationary time-series. The procedure allows us to load models in memory constrained systems, which would otherwise not fit. We provide new theoretical insights and prove that the uniform distance between the data generating process and our reparametrized solution is bounded. To reduce the arithmetic complexity of the learning problem, we derive the integer exponential family, based on the very definition of sufficient statistics and maximum entropy estimation. New integer-valued inference and learning algorithms are proposed, based on variational inference, proximal optimization, and regularization. The benefit of this technique is larger, the weaker the underlying system is, e.g., the probabilistic inference on a state-of-the-art ultra-lowpower microcontroller can be accelerated by a factor of 250. While our integer inference is fast, the underlying message passing relies on the variational principle, which is inexact and has unbounded error on general graphs. Since exact inference and other existing methods with bounded error exhibit exponential computational complexity, we employ near minimax optimal polynomial approximations to yield new stochastic algorithms for approximating the partition function and the marginal probabilities. Changing the polynomial degree allows us to control the complexity and the error of our new stochastic method. We provide an error bound that is parametrized by the number of samples, the polynomial degree, and the norm of the model’s parameter vector. Moreover, important intermediate quantities can be precomputed and shared with the weak computational device to reduce the resource requirement of our method even further. All new techniques are empirically evaluated on synthetic and real-world data, and the results confirm the properties which are predicted by our theoretical derivation. Our novel techniques allow a broader range of models to be learned on resource-constrained systems and imply several new research possibilities