DOCSLIB.ORG

Point Process and Graph Cut Applied to 2D and 3D Object Extraction Ahmed Gamal Eldin

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Point Process and Graph Cut Applied to 2D and 3D Object Extraction Ahmed Gamal Eldin Point process and graph cut applied to 2D and 3D object extraction Ahmed Gamal Eldin To cite this version: Ahmed Gamal Eldin. Point process and graph cut applied to 2D and 3D object extraction. Image Processing [eess.IV]. Université Nice Sophia Antipolis, 2011. English. tel-00737988 HAL Id: tel-00737988 https://tel.archives-ouvertes.fr/tel-00737988 Submitted on 3 Oct 2012 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. UNIVERSITY OF NICE - SOPHIA ANTIPOLIS - FRANCE GRADUATE SCHOOL STIC INFORMATION AND COMMUNICATION TECHNOLOGIES AND SCIENCES THESIS to fulfill the requirements for the degree of Doctor of Philosophy in Computer Science from the University of Nice - Sophia Antipolis Specialized in : Control,Signal and Image Processing presented by Ahmed GAMAL ELDIN Point process and graph cut applied to 2D and 3D object extraction Supervised by Xavier Descombes, and Josiane Zerubia and prepared at INRIA Sophia-Antipolis Mediterran´ ee´ in the Ariana research team Defended the 24th of October, 2011 Jury: M. Marc Berthod Emeritus Professor, INRIA President M. Fionn Murtagh Professor, University of London Reviewer Mrs. Florence Tupin Professor, Telecom ParisTech Reviewer M. Jean-Denis Durou Associate Professor, University of Toulouse Reviewer Mrs. Josiane Zerubia Director of Research, INRIA Director M. Xavier Descombes Director of Research, INRIA Supervisor M. Michel Gauthier-Clerc Director of Research, Tour du Vala Examiner M. Guillaume Perrin Research engineer, Thales Alenia Space Examiner Dedication I dedicate this to my very exceptional parents, to my mother who taught me every thing good in my life, I would not be what I am without her, to my father who created for me a beautiful environment where I can live and work, I owe them everything in my life and I will never be able to thank them for all what they did for me. God bless both of you... Acknowledgements I owe a very special acknowledgement to my supervisors, Josiane ZERUBIA and Xavier DESCOMBES. Josiane, thank you for having accepting me as part of your team, for your great support and encouragement. Thank you for always being there during and even after my thesis. Xavier, thank you believing in me even when I did not, thank you for being so understand- ing. I really learned a lot from you. Thank you for giving me all the freedom during my thesis, working with you was a real pleasure for me. After my two supervisors, I want to thank my friend Guillaume CHARPIAT. Thank you Guillaume for all your help, your gen- erous discussions, availability, it was a lot of fun to work with you. This work could not have been accomplished without you all. I would like to thank Professors MARC BERTHOD, Fionn MURTAGH, Florence TUPIN, Jean-Denis DUROU, Michel GAUTHIER-CLERC and Guillaume PERRIN. Thank you for accepting to be members of my thesis jury. Thank you for your effort, your interest and your kind attention during the defence. I owe a special acknowledgement to our ecologist collaborators. I would like to thank Yvon le MAHO, Michel Gauthier-Clerc and Arnaud Bechet´ for this collaboration, for all the interesting discussions and the efforts they made. I would like to thank every researcher on site who participated in this work: Onesime´ PRUD’HOMME, Celine Le BOHEC, Benjamin FRIESS, Yan ROPERT-COUDERT, Maryline Le VAILLANT, Claire SARAUX, Marion RIPOCHE, Remi´ GENER. I would like to start listing by friends who I want to thank with Alexandre FOURNIER who gave me the most significant advices during the early days of my PhD. Thanks to all my friends with whom I shared these three years, work and fun. Thank you Maria, Aymen, Giovanni, Csaba, Praveen, Aurelie,´ Vladmir, Sayma, Ioan, Guillaume Perrin, Mikael and Alexis. A special thank you as well to our very nice project assistants Corinne, Laurie and Christine. I would like to thank Giovanni GHERDOVICH with whom I worked a lot during my first PhD year. I would like to thank Professor Elena Zhizhina and the many other great visitors of our team with whom I had very enriching discussions. I would like to thank every person who helped during these three years. Summary The topic of this thesis is to develop a novel approach for 3D object detection from a 2D image. This approach takes into consideration the occlusions and the perspective effects. This work has been embedded in a marked point process framework, proved to be efficient for solving many challenging problems dealing with high resolution images. The accom- plished work during the thesis can be presented in two parts: First part: We propose a novel probabilistic approach to handle occlusions and perspective effects. The proposed method is based on 3D scene simulation on the GPU using OpenGL. It is an object based method embedded in a marked point process framework. We apply it for the size estimation of a penguin colony, where we model a penguin colony as an unknown number of 3D objects. The main idea of the proposed approach is to sample some can- didate configurations consisting of 3D objects lying on the real plane. A Gibbs energy is define on the configuration space, which takes into account both prior and data information. The proposed configurations are projected onto the image plane, and the configurations are modified until convergence. To evaluate a proposed configuration, we measure the simi- larity between the projected image of the proposed configuration and the real image, by defining a data term and a prior term which penalize objects overlapping. We introduced modifications to the optimization algorithm to take into account new dependencies that ex- ists in our 3D model. Second part: We propose a new optimization method which we call ”Multiple Births and Cut” (MBC). It combines the recently developed optimization algorithm Multiple Births and Deaths (MBD) and the Graph-Cut. MBD and MBC optimization methods are applied for the optimization of a marked point process. We compared the MBC to the MBD algorithms showing that the main advantage of our newly proposed algorithm is the reduction of the number of pa- rameters, the speed of convergence and the quality of the obtained results. We validated our algorithm on the counting problem of flamingos in a colony. Resum´ e´ en Franc¸ais L’objectif de cette these` est de developper´ une nouvelle approche de detection´ d’objets 3D partir d’une image 2D, prenant en compte les occultations et les phenom´ enes` de per- spective. Cette approche est fondee´ sur la theorie´ des processus ponctuels marques,´ qui a fait ses preuves dans la solution de plusieurs problemes` en imagerie haute resolution.´ Le travail de la these` est structure´ en deux parties: Premi`ere partie: Nous proposons une nouvelle methode´ probabiliste pour gerer´ les occultations et les ef- fets de perspective. Le modele` propose´ est fonde´ sur la simulation d’une scene` 3D utilisant OpenGL sur une carte graphique (GPU). C’est une methode´ orientee´ objet, integr´ ee´ dans le cadre d’un processus ponctuel marque.´ Nous l’appliquons pour l’estimation de la taille d’une colonie de manchots, la` ou` nous modelisons´ une colonie de manchots comme un nom- bre inconnu d’objets 3D. L’idee´ principale de l’approche proposee´ consiste echantillonner´ certaines configurations candidat compose´ d’objets 3D s’appuyant sur le plan reel.´ Une densite´ de Gibbs est definie´ sur l’espace des configurations, qui prend en compte des infor- mations a priori et sur les donnees.´ Pour une configuration proposee,´ la scene` est projetee´ sur le plan image, et les configurations sont modifiees´ jusqu’a` convergence. Pour evaluer´ une configuration proposee,´ nous mesurons la similarite´ entre l’image projetee´ de la con- figuration proposee´ et l’image reelle,´ definissant´ ainsi le terme d’attache aux donnees´ et l’a priori penalisant´ les recouvrements entre objets. Nous avons introduit des modifications dans l’algorithme d’optimisation pour prendre en compte les nouvelles dependances´ qui existent dans notre modele` 3D. Deuxi`emepartie: Nous proposons une nouvelle methode´ d’optimisation appelee´ ”Naissances et Coupe multiples” (”Multiple Births and Cut” (MBC) en Anglais). Cette methode´ combine la fois la nouvelle methode´ d’optimisation Naissance et Mort multiples (MBD) et les ”Graph- Cut”. Les methodes´ MBC et MBD sont utilisees´ pour loptimisation d’un processus ponctuel marque.´ Nous avons compare´ les algorithmes MBC et MBD montrant que les princi- paux avantages de notre algorithme nouvellement propose´ sont la reduction´ du nombre de parametres,` la vitesse de convergence et de la qualite´ des resultats´ obtenus. Nous avons valide´ notre algorithme sur le probleme` de denombrement´ des flamants roses dans une colonie. Contents General introduction 3 I Markov Marked Point Process 3 1 Introduction 5 1.1 Remote sensing . 5 1.1.1 Markov Random Field . 5 1.1.2 From MRF to Point Process . 7 1.2 Ecological application . 9 1.2.1 Flamingo counting . 9 1.2.2 Penguin counting . 10 1.3 Thesis organization . 12 2 Point Process 15 2.1 Spatial Point Process . 15 2.1.1 Basics of 1D and 2D Point Process . 16 2.1.2 Marked Point Processes . 17 2.1.3 Point Processes Models . 18 2.2 Markov Point Processes . 21 2.2.1 Conditional Intensity . 21 2.2.2 Cliques and Interactions Order .
Load more

Recommended publications
  • “Graph Cut Based Image Segmentation Using Statistical Priors and Its
    “GRAPH CUT BASED IMAGE SEGMENTATION USING STATISTICAL PRIORS AND ITS APPLICATION TO OBJECT DETECTION AND THIGH CT TISSUE IDENTIFICATION ANALYSIS” by TAPOSH BISWAS A THESIS Submitted in partial fulfillment of the requirements for the degree of Master of Science in the Natural Resources Graduate Program of Delaware State University DOVER, DELAWARE May 2018 This thesis is approved by the following members of the Final Oral Review Committee: Dr. Sokratis Makrogiannis, Committee Chairperson, Department of Mathematical Science, Delaware State University Dr. Thomas A. Planchon, Committee Member, Department of Physics and Engineering, Delaware State University Dr. Qi Lu, Committee Member, Department of Physics and Engineering, Delaware State University Dr. Matthew Tanzy, External Committee Member, Department of Mathematical Science, Delaware State University COPYRIGHT Copyright ©2018 by Taposh Biswas. All rights reserved. DEDICATION This thesis is dedicated to my parents Monoranjan Biswas and Dipti Biswas who have supported curiosity throughout my life. Without their persistent guidance, support, and advice, the successes I have achieved till now would never have come to fruition. ii ACKNOWLEDGEMENTS First, I would like to thank Dr. Sokratis Makrogiannis for giving me the opportunity to be a part of his research group (MIVIC) and supporting me through my thesis. It is an honor to work with him; he was always there for helping me improve my programming skills and assisting me with my research. I really appreciate his contributions of time, ideas and funding to complete my master’s degree. His door was always to discuss about any problem. I would like to thank the Federal Research and Development Matching Grant Program of the Delaware Economic Development Office (DEDO) for the funding and giving me the opportunity to complete my degree.
    [Show full text]
  • Random Fields for Image Registration
    Computer Aided Medical Procedures Prof. Dr. Nassir Navab Dissertation Random Fields for Image Registration Benjamin M. Glocker Fakultät für Informatik Technische Universität München TECHNISCHE UNIVERSITÄT MÜNCHEN Computer Aided Medical Procedures & Augmented Reality / I16 Random Fields for Image Registration Benjamin M. Glocker Vollständiger Abdruck der von der Fakultät für Informatik der Technischen Universität München zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigten Dissertation. Vorsitzender: Univ.-Prof. Dr. Peter O. A. Struss Prüfer der Dissertation: 1. Univ.-Prof. Dr. Nassir Navab 2. Prof. Dr. Nikos Paragios, Ecole Centrale de Paris / Frankreich Die Dissertation wurde am 09.09.2010 bei der Technischen Universität München eingereicht und durch die Fakultät für Informatik am 16.05.2011 angenommen. Abstract Image registration is one of the key components in computer vision and medical image analysis. Motion compensation, multi-modal fusion, atlas matching, image stitching, or optical flow estimation are only some of the applications where efficient registration methods are needed. The task of registration is to recover a spatial transformation which aligns corresponding structures visible in the images. This is commonly formulated as an optimization problem based on an objective function which evaluates the quality of a transformation with respect to the image data and some prior information. So far, mainly classical continuous methods have been considered for the critical part of optimization. In this thesis, discrete labeling of random fields is introduced as a novel promising and powerful alternative. A general framework is derived which allows to represent both linear and non-linear image registration as labeling problems where random variables play the role of transformation parameters.
    [Show full text]
  • Pylon Model for Semantic Segmentation
    A Pylon Model for Semantic Segmentation Victor Lempitsky Andrea Vedaldi Andrew Zisserman Visual Geometry Group, University of Oxford∗ fvilem,vedaldi,[email protected] Abstract Graph cut optimization is one of the standard workhorses of image segmentation since for binary random field representations of the image, it gives globally optimal results and there are efficient polynomial time implementations. Often, the random field is applied over a flat partitioning of the image into non-intersecting elements, such as pixels or super-pixels. In the paper we show that if, instead of a flat partitioning, the image is represented by a hierarchical segmentation tree, then the resulting energy combining unary and boundary terms can still be optimized using graph cut (with all the corresponding benefits of global optimality and efficiency). As a result of such inference, the image gets partitioned into a set of segments that may come from different layers of the tree. We apply this formulation, which we call the pylon model, to the task of semantic seg- mentation where the goal is to separate an image into areas belonging to different semantic classes. The experiments highlight the advantage of inference on a segmentation tree (over a flat partitioning) and demonstrate that the optimization in the pylon model is able to flex- ibly choose the level of segmentation across the image. Overall, the proposed system has superior segmentation accuracy on several datasets (Graz-02, Stanford background) com- pared to previously suggested approaches. 1 Introduction Semantic segmentation (i.e. the task of assigning each pixel of a photograph to a semantic class label) is often tackled via a “flat” conditional random field model [10, 29].
    [Show full text]
  • Global Optimization for Image Segmentation with High-Level Priors
    Noname manuscript No. (will be inserted by the editor) Branch-and-Mincut: Global Optimization for Image Segmentation with High-Level Priors Victor Lempitsky · Andrew Blake · Carsten Rother the date of receipt and acceptance should be inserted later Abstract Efficient global optimization techniques such 1 Introduction as graph cut exist for energies corresponding to binary image segmentation from low-level cues. However, in- Binary image segmentation is often posed as a graph troducing a high-level prior such as a shape prior or partition problem. This is because efficient graph algo- a color-distribution prior into the segmentation pro- rithms such as st-mincut permit fast global optimiza- cess typically results in an energy that is much harder tion of the functionals measuring the quality of the to optimize. The main contribution of the paper is a segmentation. As a result, difficult image segmentation new global optimization framework for a wide class of problems can be solved efficiently, robustly, and inde- such energies. The framework is built upon two power- pendently of initialization. Yet, while graphs can rep- ful techniques: graph cut and branch-and-bound. These resent energies based on localized low-level cues, they techniques are unified through the derivation of lower are much less suitable for representing non-local cues bounds on the energies. Being computable via graph and priors describing the foreground or the background cut, these bounds are used to prune branches within a segment as a whole. branch-and-bound search. Consider, for example, the situation when the shape of the foreground segment is known a priori to be sim- We demonstrate that the new framework can com- ilar to a particular template (segmentation with shape pute globally optimal segmentations for a variety of seg- priors).
    [Show full text]
  • Spatio-Temporal Video Segmentation with Shape Growth Or Shrinkage Constraint Yuliya Tarabalka, Guillaume Charpiat, Ludovic Brucker, Bjoern Menze
    Spatio-Temporal Video Segmentation with Shape Growth or Shrinkage Constraint Yuliya Tarabalka, Guillaume Charpiat, Ludovic Brucker, Bjoern Menze To cite this version: Yuliya Tarabalka, Guillaume Charpiat, Ludovic Brucker, Bjoern Menze. Spatio-Temporal Video Seg- mentation with Shape Growth or Shrinkage Constraint. IEEE Transactions on Image Processing, Institute of Electrical and Electronics Engineers, 2014, 23 (9), pp.3829-3840. hal-01052543 HAL Id: hal-01052543 https://hal.inria.fr/hal-01052543 Submitted on 28 Jul 2014 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 23, NO. 9, SEPTEMBER 2014 3829 Spatio-Temporal Video Segmentation With Shape Growth or Shrinkage Constraint Yuliya Tarabalka, Member, IEEE,GuillaumeCharpiat,LudovicBrucker,andBjoernH.Menze Abstract—We propose a new method for joint segmentation volume [6]–[8]. In this case, the segmentation of the entire of monotonously growing or shrinking shapes in a time sequence image set supports each of the individual segmentations. of noisy images. The task of segmenting the image time series is Graph-based methods gained popularity among omniscient expressed as an optimization problem using the spatio-temporal graph of pixels, in which we are able to impose the constraint approaches, in particular those using hierarchical model [8], of shape growth or of shrinkage by introducing monodirectional normalized cuts [6] or graph cuts [9].
    [Show full text]
  • A Reduction Method for Graph Cut Optimization Nicolas Lermé, François Malgouyres
    A Reduction Method For Graph Cut Optimization Nicolas Lermé, François Malgouyres To cite this version: Nicolas Lermé, François Malgouyres. A Reduction Method For Graph Cut Optimization. Pattern Analysis and Applications, Springer Verlag, 2014, 17 (2), pp.361-378. 10.1007/s10044-013-0337-7. hal-01486804v5 HAL Id: hal-01486804 https://hal.archives-ouvertes.fr/hal-01486804v5 Submitted on 10 Mar 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. PATTERN ANALYSIS AND APPLICATIONS 1 A Reduction Method For Graph Cut Optimization N. Lermé, F. Malgouyres hal-00606921, version 3 - Jul 2012 M. Lermé is with the Laboratoire d’Informatique de Paris Nord, University Paris 13, 99 avenue Jean-Baptiste Clément, 93430 Villetaneuse, France. Phone: +33 (0)1-49-40-32-13. Fax: +33 (0)1-48-26-07-12. E-mail: [email protected] M. Malgouyres is with the Institut Mathématiques de Toulouse, University Paul Sabatier, 118 route de Narbonne, F-31062 Toulouse Cedex 9, France. Phone: +33 (0)5-61-55-85-83. Fax: +33 (0)5-61-55-75-99. E-mail: [email protected] toulouse.fr July 3, 2012 DRAFT PATTERN ANALYSIS AND APPLICATIONS 2 Abstract In a couple of years, graph cuts methods appeared as a leading method in computer vision and graphics due to their efficiency in computing globally optimal solutions.
    [Show full text]
  • Algorithm for Fuzzy Maximum Flow Probdlemin Hyper
    Linli Zhu et al.; Sch. J. Phys. Math. Stat., 2016; Vol-3; Issue-2 (Mar-May); pp-77-83 Scholars Journal of Physics, Mathematics and Statistics ISSN 2393-8056 (Print) Sch. J. Phys. Math. Stat. 2016; 3(2):77-83 ISSN 2393-8064 (Online) ©Scholars Academic and Scientific Publishers (SAS Publishers) (An International Publisher for Academic and Scientific Resources) Algorithm for Fuzzy Maximum Flow Probdlemin Hyper-Network Setting (II) Linli Zhu1*, Yu Pan1, Wei Gao2 1School of Computer Engineering, Jiangsu University of Technology, Changzhou 213001, China 2School of Information, Yunnan Normal University, Kunming 650500, China *Corresponding Author: Linli Zhu Email: [email protected] Abstract: Maximum flow problem on hypergraphs (hyper-networks) is an extension of maximum flow problem on normal graphs. In this report, we discuss a generalized fuzzy version of maximum flow problem in hyper-networks setting, and a new fuzzy maximum flow algorithm in hyper-network setting is obtained. Our algorithm mainly based on fuzzy set theory and incremental graph, and the technology of -cut is also employed to determine the fuzzy maximum flow. The implement procedure is manifested at last. Keywords: Hypergraph, maximum flow problem, incremental graph, -cut. INTRODUCTION AND NOTATIONS There is an important component of graph theory and artificial intelligence which is Maximum flow problem of weighted graph and it shows extensive applications in various fields like: computer network, data mining, image segmentation and ontology computation [1-7]. Hyper-graph, a subset system for limited set, is one of the most general discrete structures, and is the generalization of the common graph. In terms of lots of practical problems, the usage of the concept of hyper-graph shows more effective than the concept of graph.
    [Show full text]
  • Multichannel Phase Unwrapping with Graph-Cuts Giampaolo Ferraioli, Aymen Shabou, Florence Tupin, and Vito Pascazio
    1 Multichannel phase unwrapping with Graph-cuts Giampaolo Ferraioli, Aymen Shabou, Florence Tupin, and Vito Pascazio Abstract—Markovian approaches have proven to be effective minimum Lp norm unwrapping methods. Therefore, they do for solving the multichannel phase unwrapping problem, es- not optimally exploit statistical properties of the noise present pecially when dealing with noisy data and big discontinuities. on the data and they are not optimal from the information This paper presents a markovian approach to solve the phase unwrapping problem based on a new a priori model, the Total theoretical point of view. Moreover, differently from these Variation, and graph-cut based optimization algorithms. The approaches, we propose an algorithm that is able to unwrap proposed method turns to be fast, simple and robust. A set of and restore the solution at the same time. experimental results on both simulated and real data illustrate In the next section, we introduce the multichannel phase un- the effectiveness of our approach. wrapping (MCPU) technique with an inhomogeneous GMRF model. In section III, we present our new approach based on I. INTRODUCTION TV model and graph-cut optimization algorithms. Finally, we present some results showing the reconstruction obtained on In interferometric synthetic aperture radar systems, estima- simulated and real data. tion of the phase is a crucial point since there exists a known relation between InSAR phase and height values of the ground [1]. It is known that the measured phase (wrapped phase) is II. MULTICHANNEL PHASE UNWRAPPING given in the principal interval [−π, π], so phase unwrapping Multichannel phase unwrapping approach consists in com- (PU) problem has to be solved providing the absolute phase bining two or more independent interferograms.
    [Show full text]
  • Graph Cuts for Fast Optimization in Markov Random Field Based Remote Sensing Image Analysis
    Graph cuts for fast optimization in Markov Random Field based Remote Sensing image analysis Abdulmain Karimov March, 2010 Graph cuts for fast optimization in Markov Random Field based Remote Sensing image analysis by Abdulmain Karimov Thesis submitted to the International Institute for Geo-information Science and Earth Observation in partial fulfilment of the requirements for the degree of Master of Science in Geo-information Science and Earth Observation, Specialisation: Geoinformatics Thesis Assessment Board Chair: Ms Dr. Ir. W. Bijker External examiner: Dr. Ir. B.G.H. Gorte Supervisor: Dr. V.A. Tolpekin Second supervisor: Prof. Dr. A. Stein INTERNATIONAL INSTITUTE FOR GEO-INFORMATION SCIENCE AND EARTH OBSERVATION ENSCHEDE, THE NETHERLANDS Disclaimer This document describes work undertaken as part of a programme of study at the International Institute for Geo-information Science and Earth Observation. All views and opinions expressed therein remain the sole responsibility of the author, and do not necessarily represent those of the institute. Abstract Optimization of energy is a challenging issue in Markov Random Field (MRF) based remote sensing image analysis. Traditional energy minimization methods such as Iterated Conditional Modes (ICM) and Simulated Annealing (SA) are widely used to deal with this problem. ICM does not provide a globally best estimation but it concentrates on local area and it does not provide optimal solution. SA is used to find globally optimal solutions for MRF based image analysis problems which allow approximating the global minimum of energy function that produces better quality of solutions, but at it takes long computational time to approximate the global minimum. Therefore, in order to address this problem faster energy minimization methods from vision are proposed.
    [Show full text]
  • Higher-Order Gradient Descent by Fusion-Move Graph Cut
    Higher-Order Gradient Descent by Fusion-Move Graph Cut Hiroshi Ishikawa Nagoya City University Department of Information and Biological Sciences 1 Yamanohata Mizuho, Nagoya 467-8501, Japan Abstract 130 110 Markov Random Field is now ubiquitous in many formu- lations of various vision problems. Recently, optimization 90 of higher-order potentials became practical using higher- -expansion order graph cuts: the combination of i) the fusion move 70 algorithm, ii) the reduction of higher-order binary energy blur & random 50 minimization to first-order, and iii) the QPBO algorithm. In gradient (this paper) the fusion move, it is crucial for the success and efficiency 30 of the optimization to provide proposals that fits the ener- 0 20 40 60 80 100 120 140 sec. gies being optimized. For higher-order energies, it is even Figure 1. Minimization of a third-order energy for denoising of an more so because they have richer class of null potentials. image. The vertical axis is the energy and the horizontal axis is the ffi In this paper, we focus on the e ciency of the higher-order time elapsed for optimization. The three plots are for the same en- graph cuts and present a simple technique for generating ergy discussed in 4.2. Alpha expansion failed to achieve the same proposal labelings that makes the algorithm much more ef- level of minimum energy. Proposals by pixel-wise random label ficient, which we empirically show using examples in stereo and blurring is used in [10]. The new technique by gradient de- and image denoising. scent proposal achieves the same level of minimum energy much faster.
    [Show full text]
  • Multi-View Reconstruction Using Photo-Consistency and Exact Silhouette Constraints: a Maximum-Flow Formulation
    Multi-view Reconstruction using Photo-consistency and Exact Silhouette Constraints: A Maximum-Flow Formulation Sudipta N. Sinha Marc Pollefeys Department of Computer Science, University of North Carolina at Chapel Hill, USA. Abstract when seen from different views must produce pixels with similar colors; this is the color consistency or the photo- This paper describes a novel approach for reconstructing a consistency constraint. In the ill-posed reconstruction prob- closed continuous surface of an object from multiple cali- lem, different scenes can be consistent with the same set of brated color images and silhouettes. Any accurate recon- color images. Theoritically the union of all photo-consistent struction must satisfy (1) photo-consistency and (2) silhou- scenes, the photo hull [12] is a unique reconstruction, but it ette consistency constraints. Most existing techniques treat is sensitive to the sampling rate of 3D voxels, the range of these cues identically in optimization frameworks where sil- textures in the scene and image noise. The reconstructed houette constraints are traded off against photo-consistency shape when re-projected must coincide with the respective and smoothness priors. Our approach strictly enforces sil- silhouettes; this is the silhouette consistency constraint.The houette constraints, while optimizing photo-consistency and exact visual hull’s silhouettes [1, 2] should be considered, smoothness in a global graph-cut framework. We transform when calibration or segmentation errors are present. the reconstruction problem into computing max-flow / min- SFS methods compute the visual hull [1, 14, 2, 5]; the cut in a geometric graph, where any cut corresponds to a maximal shape consistent with a set of silhouettes.
    [Show full text]
  • Multi-Label Markov Random Fields As an Efficient and Effective Tool For
    Numer. Math. Theor. Meth. Appl. Vol. 6, No. 1, pp. 169-198 doi: 10.4208/nmtma.2013.mssvm09 February 2013 Multi-Label Markov Random Fields as an Efficient and Effective Tool for Image Segmentation, Total Variations and Regularization Dorit S. Hochbaum∗ Department of Industrial Engineering and Operations Research, University of California, Berkeley, Ca 94720, USA. Received 6 December 2011; Accepted (in revised version) 12 September 2012 Available online 11 January 2013 Abstract. One of the classical optimization models for image segmentation is the well known Markov Random Fields (MRF) model. This model is a discrete optimization problem, which is shown here to formulate many continuous models used in image segmentation. In spite of the presence of MRF in the literature, the dominant perception has been that the model is not effective for image segmentation. We show here that the reason for the non-effectiveness is due to the lack of access to the optimal solution. Instead of solving optimally, heuristics have been engaged. Those heuristic methods cannot guarantee the quality of the solution nor the running time of the algorithm. Worse still, heuristics do not link directly the input functions and parameters to the output thus obscuring what would be ideal choices of parameters and functions which are to be selected by users in each particular application context. We describe here how MRF can model and solve efficiently several known continuous models for image segmentation and describe briefly a very efficient polynomial time algorithm, which is provably fastest possible, to solve optimally the MRF problem. The MRF algorithm is enhanced here compared to the algorithm in Hochbaum (2001) by allowing the set of assigned labels to be any discrete set.
    [Show full text]