Texture synthesis via a noncausal nonparametric multiscale Markov random field

Paget, R.; Longstaff, I.D.

doi:10.1109/83.679446

Cited by 160 publications

(118 citation statements)

References 12 publications

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“…The range of applicability of the procedural approaches [6,9,10] remains sparse, leading mostly to algorithms hard to optimize [6,[22][23][24]. In opposition to the global growth procedure involved in the procedural methods, the local methods [1][2][3][4][11][12][13] generate the texture one voxel/patch at a time maintaining the coherence of the local texture with its vicinity. Some of the most underlined synthesis methods based on local optimization are the exemplar-based synthesis algorithms.…”

Section: Introductionmentioning

confidence: 99%

Non-parametric synthesis of laminar volumetric textures from a 2D sample

Urs¹,

Costa²,

Leyssale³

et al. 2012

Procedings of the British Machine Vision Conference 2012

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The goal of this paper is to evaluate non-parametric algorithms that achieve 3D texture synthesis from a single 2D sample. The algorithms under study are variants of the algorithm proposed by Wei and Levoy [1]. Several authors have proposed different algorithms that intend to better reproduce, in the output texture, the diversity learned in the input sample. Hence, we turn our attention to the improved algorithm proposed by Kopf et al. [2] and the particular histogram matching approach of Chen and Wang [3]. In addition, we propose to visit the voxels during synthesis according to the 3D extension of space filling curves. We investigate the algorithms capability to reproduce anisotropic textures. In particular we are interested in laminar textures, i.e. textures made of anisotropic sheets stacked along a given direction. Examples of such textures are snapshots of dense carbons observed by high resolution transmission electronic microscopy (HRTEM). Beyond the traditional subjective evaluation of the synthesized textures, we propose a genuine quantitative benchmark for the analysis of the synthesized textures which consists in comparing input and output gray level statistics and patterns morphology.

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Section: Introductionmentioning

confidence: 99%

Non-parametric synthesis of laminar volumetric textures from a 2D sample

Urs¹,

Costa²,

Leyssale³

et al. 2012

Procedings of the British Machine Vision Conference 2012

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“…Such approaches have lacked the representational power needed to capture the rich statistics of natural scenes. The second line of research involves improving the expressive power of MRFs with higher-order models that are learned from data [7,8,9]. These approaches better capture the rich statistics of the natural world and…”

Section: Introductionmentioning

confidence: 99%

Efficient Belief Propagation with Learned Higher-Order Markov Random Fields

Lan

Roth

Huttenlocher

et al. 2006

Lecture Notes in Computer Science

166

167

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Abstract. Belief propagation (BP) has become widely used for low-level vision problems and various inference techniques have been proposed for loopy graphs. These methods typically rely on ad hoc spatial priors such as the Potts model. In this paper we investigate the use of learned models of image structure, and demonstrate the improvements obtained over previous ad hoc models for the image denoising problem. In particular, we show how both pairwise and higher-order Markov random fields with learned clique potentials capture rich image structures that better represent the properties of natural images. These models are learned using the recently proposed Fields-of-Experts framework. For such models, however, traditional BP is computationally expensive. Consequently we propose some approximation methods that make BP with learned potentials practical. In the case of pairwise models we propose a novel approximation of robust potentials using a finite family of quadratics. In the case of higher order MRFs, with 2 × 2 cliques, we use an adaptive state space to handle the increased complexity. Extensive experiments demonstrate the power of learned models, the benefits of higher-order MRFs and the practicality of BP for these problems with the use of simple principled approximations.

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“…MRFs have been used in computer vision and image processing for texture synthesis (Cross and Jain, 1983;Efros and Leung, 1999;Paget and Longstaff, 1998), image segmentation (Derin and Elliott, 1987), and image restoration (Geman and Geman, 1984;Li, 1995). The states of MRF texture models are all possible gray levels and directly observable.…”

Section: Related Workmentioning

confidence: 99%

“…The states of MRF texture models are all possible gray levels and directly observable. A sample texture is regarded as a realization of the MRF model and is used to estimate the conditional distribution of the model through either parametric (Cross and Jain, 1983) or nonparametric methods (Efros and Leung, 1999;Paget and Longstaff, 1998). Texture can be then synthesized by sampling from the conditional distribution.…”

Section: Related Workmentioning

confidence: 99%

Markov Random Field Modeling of the Spatial Distribution of Proteins on Cell Membranes

Zhang¹

2007

Bull. Math. Biol.

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Cell membranes display a range of receptors that bind ligands and activate signaling pathways. Signaling is characterized by dramatic changes in membrane molecular topography, including the co-clustering of receptors with signaling molecules and the segregation of other signaling molecules away from receptors. Electron microscopy of immunogold-labeled membranes is a critical technique to generate topographical information at the 5-10 nm resolution needed to understand how signaling complexes assemble and function. However, due to experimental limitations, only two molecular species can usually be labeled at a time. A formidable challenge is to integrate experimental data across multiple experiments where there are from 10 to 100 different proteins and lipids of interest and only the positions of two species can be observed simultaneously. As a solution, we propose the use of Markov random field (MRF) modeling to reconstruct the distribution of multiple cell membrane constituents from pair-wise data sets. MRFs are a powerful mathematical formalism for modeling correlations between states associated with neighboring sites in spatial lattices. The presence or absence of a protein of a specific type at a point on the cell membrane is a state. Since only two protein types can be observed, i.e., those bound to particles, and the rest cannot be observed, the problem is one of deducing the conditional distribution of a MRF with unobservable (hidden) states. Here, we develop a multiscale MRF model and use mathematical programming techniques to infer the conditional distribution of a MRF for proteins of three types from observations showing the spatial relationships between only two types. Application to synthesized data shows that the spatial distributions of three proteins can be reliably estimated. Application to experimental data provides the first maps of the spatial relationship between groups of three different signaling molecules. The work is an important step toward a more complete understanding of membrane spatial organization and dynamics during signaling.

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Texture synthesis via a noncausal nonparametric multiscale Markov random field

Cited by 160 publications

References 12 publications

Non-parametric synthesis of laminar volumetric textures from a 2D sample

Non-parametric synthesis of laminar volumetric textures from a 2D sample

Efficient Belief Propagation with Learned Higher-Order Markov Random Fields

Markov Random Field Modeling of the Spatial Distribution of Proteins on Cell Membranes

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