333 research outputs found
Advances in Graph-Cut Optimization: Multi-Surface Models, Label Costs, and Hierarchical Costs
Computer vision is full of problems that are elegantly expressed in terms of mathematical optimization, or energy minimization. This is particularly true of low-level inference problems such as cleaning up noisy signals, clustering and classifying data, or estimating 3D points from images. Energies let us state each problem as a clear, precise objective function. Minimizing the correct energy would, hypothetically, yield a good solution to the corresponding problem. Unfortunately, even for low-level problems we are confronted by energies that are computationally hard—often NP-hard—to minimize. As a consequence, a rather large portion of computer vision research is dedicated to proposing better energies and better algorithms for energies. This dissertation presents work along the same line, specifically new energies and algorithms based on graph cuts.
We present three distinct contributions. First we consider biomedical segmentation where the object of interest comprises multiple distinct regions of uncertain shape (e.g. blood vessels, airways, bone tissue). We show that this common yet difficult scenario can be modeled as an energy over multiple interacting surfaces, and can be globally optimized by a single graph cut. Second, we introduce multi-label energies with label costs and provide algorithms to minimize them. We show how label costs are useful for clustering and robust estimation problems in vision. Third, we characterize a class of energies with hierarchical costs and propose a novel hierarchical fusion algorithm with improved approximation guarantees. Hierarchical costs are natural for modeling an array of difficult problems, e.g. segmentation with hierarchical context, simultaneous estimation of motions and homographies, or detecting hierarchies of patterns
Submodular relaxation for inference in Markov random fields
In this paper we address the problem of finding the most probable state of a
discrete Markov random field (MRF), also known as the MRF energy minimization
problem. The task is known to be NP-hard in general and its practical
importance motivates numerous approximate algorithms. We propose a submodular
relaxation approach (SMR) based on a Lagrangian relaxation of the initial
problem. Unlike the dual decomposition approach of Komodakis et al., 2011 SMR
does not decompose the graph structure of the initial problem but constructs a
submodular energy that is minimized within the Lagrangian relaxation. Our
approach is applicable to both pairwise and high-order MRFs and allows to take
into account global potentials of certain types. We study theoretical
properties of the proposed approach and evaluate it experimentally.Comment: This paper is accepted for publication in IEEE Transactions on
Pattern Analysis and Machine Intelligenc
Inference by Learning: Speeding-up Graphical Model Optimization via a Coarse-to-Fine Cascade of Pruning Classifiers
We propose a general and versatile framework that significantly speeds-up graphical model optimization while maintaining an excellent solution accuracy. The
proposed approach, refereed as Inference by Learning or in short as IbyL, relies on a multi-scale pruning scheme that progressively reduces the solution space by
use of a coarse-to-fine cascade of learnt classifiers. We thoroughly experiment with classic computer vision related MRF problems, where our novel framework
constantly yields a significant time speed-up (with respect to the most efficient inference methods) and obtains a more accurate solution than directly optimizing
the MRF. We make our code available on-line [4]
Rich probabilistic models for semantic labeling
Das Ziel dieser Monographie ist es die Methoden und Anwendungen des semantischen Labelings zu erforschen. Unsere Beiträge zu diesem sich rasch entwickelten Thema sind bestimmte Aspekte der Modellierung und der Inferenz in probabilistischen Modellen und ihre Anwendungen in den interdisziplinären Bereichen der Computer Vision sowie medizinischer Bildverarbeitung und Fernerkundung
Higher-order inference in conditional random fields using submodular functions
Higher-order and dense conditional random fields (CRFs) are expressive graphical
models which have been very successful in low-level computer vision applications
such as semantic segmentation, and stereo matching. These models are able to
capture long-range interactions and higher-order image statistics much better
than pairwise CRFs. This expressive power comes at a price though - inference
problems in these models are computationally very demanding. This is a
particular challenge in computer vision, where fast inference is important and
the problem involves millions of pixels.
In this thesis, we look at how submodular functions can help us designing
efficient inference methods for higher-order and dense CRFs. Submodular
functions are special discrete functions that have important properties from
an optimisation perspective, and are closely related to convex functions. We
use submodularity in a two-fold manner: (a) to design efficient MAP inference
algorithm for a robust higher-order model that generalises the widely-used
truncated convex models, and (b) to glean insights into a recently proposed
variational inference algorithm which give us a principled approach for applying
it efficiently to higher-order and dense CRFs
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