Higher Order Energies for Image Segmentation

A novel energy minimization method for general higher-order binary energy functions is proposed in this paper. We first relax a discrete higher-order function to a continuous one, and use the Taylor expansion to obtain an approximate lower-order function, which is optimized by the quadratic pseudo-boolean optimization (QPBO) or other discrete optimizers. The minimum solution of this lower-order function is then used as a new local point, where we expand the original higher-order energy function again. Our algorithm does not restrict to any specific form of the higher-order binary function or bring in extra auxiliary variables. For concreteness, we show an application of segmentation with the appearance entropy, which is efficiently solved by our method. Experimental results demonstrate that our method outperforms state-of-the-art methods

Discrete-Continuous ADMM for Transductive Inference in Higher-Order MRFs

This paper introduces a novel algorithm for transductive inference in higher-order MRFs, where the unary energies are parameterized by a variable classifier. The considered task is posed as a joint optimization problem in the continuous classifier parameters and the discrete label variables. In contrast to prior approaches such as convex relaxations, we propose an advantageous decoupling of the objective function into discrete and continuous subproblems and a novel, efficient optimization method related to ADMM. This approach preserves integrality of the discrete label variables and guarantees global convergence to a critical point. We demonstrate the advantages of our approach in several experiments including video object segmentation on the DAVIS data set and interactive image segmentation

Shape Calculus for Shape Energies in Image Processing

Many image processing problems are naturally expressed as energy minimization or shape optimization problems, in which the free variable is a shape, such as a curve in 2d or a surface in 3d. Examples are image segmentation, multiview stereo reconstruction, geometric interpolation from data point clouds. To obtain the solution of such a problem, one usually resorts to an iterative approach, a gradient descent algorithm, which updates a candidate shape gradually deforming it into the optimal shape. Computing the gradient descent updates requires the knowledge of the first variation of the shape energy, or rather the first shape derivative. In addition to the first shape derivative, one can also utilize the second shape derivative and develop a Newton-type method with faster convergence. Unfortunately, the knowledge of shape derivatives for shape energies in image processing is patchy. The second shape derivatives are known for only two of the energies in the image processing literature and many results for the first shape derivative are limiting, in the sense that they are either for curves on planes, or developed for a specific representation of the shape or for a very specific functional form in the shape energy. In this work, these limitations are overcome and the first and second shape derivatives are computed for large classes of shape energies that are representative of the energies found in image processing. Many of the formulas we obtain are new and some generalize previous existing results. These results are valid for general surfaces in any number of dimensions. This work is intended to serve as a cookbook for researchers who deal with shape energies for various applications in image processing and need to develop algorithms to compute the shapes minimizing these energies

Markov mezők a képmodellezésben, alkalmazásuk az automatikus képszegmentálás területén = Markovian Image Models: Applications in Unsupervised Image Segmentation

1) Kifejlesztettünk egy olyan szín és textúra alapú szegmentáló MRF algoritmust, amely alkalmas egy kép automatikus szegmentálását elvégezni. Az eredményeinket az Image and Vision Computing folyóiratban publikáltuk. 2) Kifejlesztettünk egy Reversible Jump Markov Chain Monte Carlo technikán alapuló automatikus képszegmentáló eljárást, melyet sikeresen alkalmaztunk színes képek teljesen automatikus szegmentálására. Az eredményeinket a BMVC 2004 konferencián és az Image and Vision Computing folyóiratban publikáltuk. 3) A modell többrétegű továbbfejlesztését alkalmaztuk video objektumok szín és mozgás alapú szegmentálására, melynek eredményeit a HACIPPR 2005 illetve az ACCV 2006 nemzetközi konferenciákon publikáltuk. Szintén ehhez az alapproblémához kapcsolódik Horváth Péter hallgatómmal az optic flow szamításával illetve szín, textúra és mozgás alapú GVF aktív kontúrral kapcsoltos munkáink. TDK dolgozata első helyezést ért el a 2004-es helyi versenyen, az eredményeinket pedig a KEPAF 2004 konferencián publikáltuk. 4) Horváth Péter PhD hallgatómmal illetve az franciaországi INRIA Ariana csoportjával, kidolgoztunk egy olyan képszegmentáló eljárást, amely a szegmentálandó objektum alakját is figyelembe veszi. Az eredményeinket az ICPR 2006 illetve az ICCVGIP 2006 konferencián foglaltuk össze. A modell előzményeként kidolgoztunk továbbá egy alakzat-momemntumokon alapuló aktív kontúr modellt, amelyet a HACIPPR 2005 konferencián publikáltunk. | 1) We have proposed a monogrid MRF model which is able to combine color and texture features in order to improve the quality of segmentation results. We have also solved the estimation of model parameters. This work has been published in the Image and Vision Computing journal. 2) We have proposed an RJMCMC sampling method which is able to identify multi-dimensional Gaussian mixtures. Using this technique, we have developed a fully automatic color image segmentation algorithm. Our results have been published at BMVC 2004 international conference and in the Image and Vision Computing journal. 3) A new multilayer MRF model has been proposed which is able to segment an image based on multiple cues (such as color, texture, or motion). This work has been published at HACIPPR 2005 and ACCV 2006 international conferences. The work on optic flow computation and color-, texture-, and motion-based GVF active contours doen with my student, Mr. Peter Horvath, won a first price at the local Student Research Competition in 2004. Results have been presented at KEPAF 2004 conference. 4) A new shape prior, called 'gas of circles' has been introduced using active contour models. This work is done in collaboration with the Ariana group of INRIA, France and my PhD student, Mr. Peter Horvath. Results are published at the ICPR 2006 and ICCVGIP 2006 conferences. A preliminary study on active contour models using shape-moments has also been done, these results are published at HACIPPR 2005

Efficient MRF Energy Propagation for Video Segmentation via Bilateral Filters

Segmentation of an object from a video is a challenging task in multimedia applications. Depending on the application, automatic or interactive methods are desired; however, regardless of the application type, efficient computation of video object segmentation is crucial for time-critical applications; specifically, mobile and interactive applications require near real-time efficiencies. In this paper, we address the problem of video segmentation from the perspective of efficiency. We initially redefine the problem of video object segmentation as the propagation of MRF energies along the temporal domain. For this purpose, a novel and efficient method is proposed to propagate MRF energies throughout the frames via bilateral filters without using any global texture, color or shape model. Recently presented bi-exponential filter is utilized for efficiency, whereas a novel technique is also developed to dynamically solve graph-cuts for varying, non-lattice graphs in general linear filtering scenario. These improvements are experimented for both automatic and interactive video segmentation scenarios. Moreover, in addition to the efficiency, segmentation quality is also tested both quantitatively and qualitatively. Indeed, for some challenging examples, significant time efficiency is observed without loss of segmentation quality.Comment: Multimedia, IEEE Transactions on (Volume:16, Issue: 5, Aug. 2014

Efficient Relaxations for Dense CRFs with Sparse Higher Order Potentials

Dense conditional random fields (CRFs) have become a popular framework for modelling several problems in computer vision such as stereo correspondence and multi-class semantic segmentation. By modelling long-range interactions, dense CRFs provide a labelling that captures finer detail than their sparse counterparts. Currently, the state-of-the-art algorithm performs mean-field inference using a filter-based method but fails to provide a strong theoretical guarantee on the quality of the solution. A question naturally arises as to whether it is possible to obtain a maximum a posteriori (MAP) estimate of a dense CRF using a principled method. Within this paper, we show that this is indeed possible. We will show that, by using a filter-based method, continuous relaxations of the MAP problem can be optimised efficiently using state-of-the-art algorithms. Specifically, we will solve a quadratic programming (QP) relaxation using the Frank-Wolfe algorithm and a linear programming (LP) relaxation by developing a proximal minimisation framework. By exploiting labelling consistency in the higher-order potentials and utilising the filter-based method, we are able to formulate the above algorithms such that each iteration has a complexity linear in the number of classes and random variables. The presented algorithms can be applied to any labelling problem using a dense CRF with sparse higher-order potentials. In this paper, we use semantic segmentation as an example application as it demonstrates the ability of the algorithm to scale to dense CRFs with large dimensions. We perform experiments on the Pascal dataset to indicate that the presented algorithms are able to attain lower energies than the mean-field inference method

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

Hierarchy construction schemes within the Scale set framework

Segmentation algorithms based on an energy minimisation framework often depend on a scale parameter which balances a fit to data and a regularising term. Irregular pyramids are defined as a stack of graphs successively reduced. Within this framework, the scale is often defined implicitly as the height in the pyramid. However, each level of an irregular pyramid can not usually be readily associated to the global optimum of an energy or a global criterion on the base level graph. This last drawback is addressed by the scale set framework designed by Guigues. The methods designed by this author allow to build a hierarchy and to design cuts within this hierarchy which globally minimise an energy. This paper studies the influence of the construction scheme of the initial hierarchy on the resulting optimal cuts. We propose one sequential and one parallel method with two variations within both. Our sequential methods provide partitions near the global optima while parallel methods require less execution times than the sequential method of Guigues even on sequential machines

A discrete approximation of Blake & Zisserman energy in image denoising and optimal choice of regularization parameters

We consider a multi-scale approach for the discrete approximation of a functional proposed by Bake and Zisserman (BZ) for solving image denoising and segmentation problems. The proposed method is based on simple and effective higher order varia-tional model. It consists of building linear discrete energies family which Γ-converges to the non-linear BZ functional. The key point of the approach is the construction of the diffusion operators in the discrete energies within a finite element adaptive procedure which approximate in the Γ-convergence sense the initial energy including the singular parts. The resulting model preserves the singularities of the image and of its gradient while keeping a simple structure of the underlying PDEs, hence efficient numerical method for solving the problem under consideration. A new point to make this approach work is to deal with constrained optimization problems that we circumvent through a Lagrangian formulation. We present some numerical experiments to show that the proposed approach allows us to detect first and second-order singularities. We also consider and implement to enhance the algorithms and convergence properties, an augmented Lagrangian method using the alternating direction method of Multipliers (ADMM)