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Beyond trees: MRF inference via outer-planar decomposition

Dhruv Batra, A. C. Gallagher, Devi Parikh, Tsuhan Chen
2010 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition  
We leverage a new class of graphs amenable to exact inference, called outerplanar graphs, and propose an approximate inference algorithm called Outer-Planar Decomposition (OPD).  ...  Maximum a posteriori (MAP) inference in Markov Random Fields (MRFs) is an NP-hard problem, and thus research has focussed on either finding efficiently solvable subclasses (e.g. trees), or approximate  ...  We thank Pedro Felzenszwalb for pointing out the connections between outer-planar graphs and k-trees, and Carlos Guestrin and Ramin Zabih for helpful discussions.  ... 
doi:10.1109/cvpr.2010.5539951 dblp:conf/cvpr/BatraGPC10 fatcat:zpodxtnqabbm7c6w5ozwgfq7qe

Oblique view individual tree crown delineation

Christian Kempf, Jiaojiao Tian, Franz Kurz, Pablo D'Angelo, Thomas Schneider, Peter Reinartz
2021 International Journal of Applied Earth Observation and Geoinformation  
Individual tree crown (ITC) segmentation supports numerous applications in forest management and ecology.  ...  In the second step, the contour of the visible part of a candidate tree in images with known orientation is obtained by means of ray casting and concave hull calculation.  ...  On the one hand, TM, MPP and MRF methods only detect trees and do not produce precise boundaries.  ... 
doi:10.1016/j.jag.2021.102314 fatcat:qvatzp24rbg5rgnw3bqn332jqy

(Hyper)-Graphs Inference through Convex Relaxations and Move Making Algorithms: Contributions and Applications in Artificial Vision

Nikos Komodakis, M. Pawan Kumar, Nikos Paragios
2016 Foundations and Trends in Computer Graphics and Vision  
Modularity, scalability and portability are the main strength of these methods which once combined with efficient inference algorithms they could lead to state of the art results.  ...  To this end, computer vision tasks are often reformulated as mathematical inference problems where the objective is to determine the set of parameters corresponding to the lowest potential of a task-specific  ...  of binary slave problems that are defined over loopy planar graphs (of arbitrary tree-width) [55, 67] • and submodular decompositions [48, 24] .  ... 
doi:10.1561/0600000066 fatcat:5nj6rc6vy5ek5ct3fulfpch7si

Human Attention in Visual Question Answering: Do Humans and Deep Networks Look at the Same Regions?

Abhishek Das, Harsh Agrawal, Larry Zitnick, Devi Parikh, Dhruv Batra
2017 Computer Vision and Image Understanding  
Beyond trees: MRF Inference via Outer- Planar Decomposition. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2010. 56.  ...  Tighter Relaxations for MAP-MRF Inference: A Local Primal-Dual Gap based Separation Algorithm. International Conference on Artificial Intelligence and Statistics (AISTATS), 2011. 54.  ... 
doi:10.1016/j.cviu.2017.10.001 fatcat:nzvodvk5pbb3bicchq57vlimca

Factor Graphs for Robot Perception

Frank Dellaert, Michael Kaess
2017 Foundations and Trends in Robotics  
on graphical models, introducing the Bayes tree in the process.  ...  They provide a powerful abstraction that gives insight into particular inference problems, making it easier to think about and design solutions, and write modular software to perform the actual inference  ...  In what follows we will frequently refer to the undirected graph G of the MRF associated with an inference problem. However, we will not use the MRF graphical model much beyond that.  ... 
doi:10.1561/2300000043 fatcat:flxlfe5aerg7ha4zasswzerj3e

Submodular Relaxation for Inference in Markov Random Fields

Anton Osokin, Dmitry P. Vetrov
2015 IEEE Transactions on Pattern Analysis and Machine Intelligence  
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.  ...  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  ...  In this paper we focus on one important type of inference: maximum a posteriori (MAP) inference, often referred to as MRF energy minimization.  ... 
doi:10.1109/tpami.2014.2369046 pmid:26352444 fatcat:wvatnp5d4zemvm5c7zfydtbptq

HOP-MAP: Efficient Message Passing with High Order Potentials

Daniel Tarlow, Inmar E. Givoni, Richard S. Zemel
2010 Journal of machine learning research  
Message passing inference in such models generally takes time exponential in the size of the interaction, but in some cases maximum a posteriori (MAP) inference can be carried out efficiently.  ...  Importantly, we present both new and existing HOPs in a common representation; performing inference with any combination of these HOPs requires no change of representations or new derivations.  ...  We emphasize that several "outer loop" inference routines can take advantage of these messagecomputation subroutines.  ... 
dblp:journals/jmlr/TarlowGZ10 fatcat:yoxle4smlrggrdilog5zrnlzcq

Model Reductions for Inference: Generality of Pairwise, Binary, and Planar Factor Graphs

Frederik Eaton, Zoubin Ghahramani
2013 Neural Computation  
We investigate the expressive power of three classes of model-those with binary variables, with pairwise factors, and with planar topology-as well as their four intersections.  ...  We formalize a notion of "simple reduction" for the problem of inferring marginal probabilities and consider whether it is possible to "simply reduce" marginal inference from general discrete factor graphs  ...  Only Gibbs sampling was able to track exact marginals beyond k = 1.  ... 
doi:10.1162/neco_a_00441 pmid:23547951 fatcat:at7uw6ftafdbhkr3jzbjgwrypa

Graphical Models, Exponential Families, and Variational Inference

Martin J. Wainwright, Michael I. Jordan
2007 Foundations and Trends® in Machine Learning  
Beyond its use as a language for formulating models, graph theory also plays a fundamental role in assessing computational 3 7  ...  The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in large-scale statistical models.  ...  and the other via node 3, and so on down the tree.  ... 
doi:10.1561/2200000001 fatcat:3f33bwasgvg5ndjfqezocaxxfa

Saliency Sequential Surface Organization for Free-Form Object Recognition

Kim L. Boyer, Ravi Srikantiah, Patrick J. Flynn
2002 Computer Vision and Image Understanding  
Henderson [26] used a sequential region-growing algorithm (via a planarity test) that creates convex planar surfaces from initial sets of three close noncollinear points.  ...  The bumps show up as λ segments, and most of the outer part of the torus is of type µ.  ... 
doi:10.1006/cviu.2002.0973 fatcat:emjby3cn2rcghfo7z3zg73suzq

Methods for Inference in Graphical Models

Adrian Weller
2017
We derive new results for this approach, including a general decomposition theorem for models of any order and number of labels, extensions of results for binary pairwise models with submodular cost functions  ...  However, inference is computationally intractable in general.  ...  However, Barahona (1982) demonstrated that even MAP inference on general planar binary pairwise models (with arbitrary singleton potentials) is NP-hard via a reduction to planar MWSS, which is NP-hard  ... 
doi:10.7916/d8jd4vdc fatcat:g7sqtasi7jgclnauxiui5u4yvy

Statistical Methods and Models for Video-Based Tracking, Modeling, and Recognition

Rama Chellappa
2009 Foundations and Trends® in Signal Processing  
In the pinhole camera model, rays (or photons) from the scene are projected onto a planar screen after passing through a pinhole, as illustrated in Figure 2 .4.  ...  In the presence of noisy observations and other uncertainties, computer vision algorithms make use of statistical methods for robust inference.  ...  To generate an actual shape, we need to first choose a two-frame for the generated subspace which can be performed via singular value decomposition (SVD) of the projection matrix.  ... 
doi:10.1561/2000000007 fatcat:o5hmdnzbqvbdzjdu72jkojl5ya

Knowledge Augmented Machine Learning with Applications in Autonomous Driving: A Survey [article]

Julian Wörmann, Daniel Bogdoll, Etienne Bührle, Han Chen, Evaristus Fuh Chuo, Kostadin Cvejoski, Ludger van Elst, Tobias Gleißner, Philip Gottschall, Stefan Griesche, Christian Hellert, Christian Hesels (+34 others)
2022 arXiv   pre-print
The outer meta-objective consists in finding the optimal parameters θ across several tasks drawn from p(T ), i.e. min θ Ti∼p(T ) L Ti (f θ−α∇L T i (f θ ) ). (16) Via optimizing the outer criterion ( 16  ...  It uses decision trees to describe a NN's performance based on the units in its hidden layer. Then, it builds up new decision trees to describe the split points of the first decision trees.  ... 
arXiv:2205.04712v1 fatcat:u2bgxr2ctnfdjcdbruzrtjwot4

Towards spatial and temporal analysis of facial expressions in 3D data

Georgia Rajamanoharan, Stefanos Zafeiriou, Maja Pantic, Engineering And Physical Sciences Research Council
2016
Intensity Inference In order to minimise Equation 5.10, a method based on the well known Viterbi algorithm, and exploited in [49] for efficient inference on MRF structures, is employed.  ...  This was determined to give adequate quad-tree decomposition results from preliminary testing.  ... 
doi:10.25560/31549 fatcat:dcdjihf3sjbq5e5fxkn6ilvkri

SDCA-Powered Inexact Dual Augmented Lagrangian Method for Fast CRF Learning SDCA-Powered Inexact Dual Augmented Lagrangian Method for Fast CRF Learning

Shell Hu, Guillaume Obozinski, Shell Hu, Guillaume, Shell Hu, Guillaume Obozinski
2018 unpublished
Our algorithm, which can be interpreted as an inexact gradient descent algorithm on the multiplier, does not require to perform global inference iteratively, and requires only a fixed number of stochastic  ...  MRF optimization via dual decomposition: Messagepassing revisited. In ICCV, pages 1-8. Kulesza, A. and Pereira, F. (2007). Structured learning with approximate inference.  ...  Convergent propagation algorithms via oriented trees. In UAI, pages 133-140. Hazan, T. and Urtasun, R. (2010).  ... 
fatcat:3ag6bjjwmnh5tnu6alkrfjeczy
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