## Texture Synthesis and Non-Parametric Resampling of Random Fields

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Citations: | 8 - 0 self |

### BibTeX

@MISC{Levina_texturesynthesis,

author = {Elizaveta Levina and Peter J. Bickel},

title = {Texture Synthesis and Non-Parametric Resampling of Random Fields},

year = {}

}

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### Abstract

This paper introduces a non-parametric algorithm for bootstrapping a sta-tionary random field and proves certain consistency properties of the algorithm for the case of mixing random fields. The motivation for this paper comes from relating a heuristic texture synthesis algorithm popular in computer vision to general non-parametric bootstrap of stationary random fields. We give a for-mal resampling scheme for the heuristic texture algorithm and prove that it produces a consistent estimate of the joint distribution of pixels in a window of certain size under mixing and regularity conditions on the random field. The joint distribution of pixels is the quantity of interest here because theories of human perception of texture suggest that two textures with the same joint distribution of pixel values in a suitably chosen window will appear similar to a human. Thus we provide theoretical justification for an algorithm that has already been very successful in practice, and suggest an explanation for its perceptually good results. AMS 2000 subject classifications. Primary 62M40, Secondary 62G09. Key words and phrases. Bootstrap, Markov random fields, Markov mesh models,

### Citations

1224 |
Spatial interaction and the statistical analysis of lattice systems
- Besag
- 1973
(Show Context)
Citation Context ...ifferent methods of texture synthesis can be broadly divided into three categories. The first and oldest group of methods is model-based, with the main modeling tool being Markov Random Fields (MRF) (=-=Besag, 1974-=-; Cross and Jain, 1983). In the early MRF work only a few parameters could be fitted because of computational difficulties, and those models usually did not capture the complexity of real textures. As... |

810 | Texture Synthesis by Non-Parametric Sampling
- Efros, Leung
- 1999
(Show Context)
Citation Context ...e compression, where the whole texture can be recreated from a small sample. The point of departure for our research is a simple and very popular heuristic resampling algorithm for texture synthesis (=-=Efros and Leung, 1999-=-) which produces excellent visual results but has no theoretical justification or statistical framework. We formalize this algorithm in the framework of resampling from random fields and prove that it... |

540 | Image quilting for texture synthesis and transfer
- Efros, Freeman
- 2001
(Show Context)
Citation Context ...ears, started by the algorithm of Efros and Leung (1999). Many variations of their method have been published that speed up and optimize the original algorithm in different ways (Wei and Levoy, 2000; =-=Efros and Freeman, 2001-=-; Liang et al., 2001). In all these works however, the basic resampling principle of Efros and Leung (1999) remains unchanged, and even the original version has been very successful on a wider range o... |

447 | Fast texture synthesis using tree-structured vector quantization
- Wei, Levoy
- 2000
(Show Context)
Citation Context ...d over the past few years, started by the algorithm of Efros and Leung (1999). Many variations of their method have been published that speed up and optimize the original algorithm in different ways (=-=Wei and Levoy, 2000-=-; Efros and Freeman, 2001; Liang et al., 2001). In all these works however, the basic resampling principle of Efros and Leung (1999) remains unchanged, and even the original version has been very succ... |

397 | Pyramid-based texture analysis/synthesis
- Heeger, Bergen
- 1995
(Show Context)
Citation Context ...sed on feature matching. Typically, these methods start from a white noise image and force it to match some set of statistics of the original texture image, such as distributions of filter responses (=-=Heeger and Bergen, 1995-=-; Simoncelli and Portilla, 1998; Portilla and Simoncelli, 2000; De Bonet, 1997). Feature matching methods tend to work well on stochastic textures but have difficulties with highly structured textures... |

338 | Preattentive texture discrimination with early vision mechanisms
- Malik, Perona
- 1990
(Show Context)
Citation Context ...th texture boundaries corresponding to sudden changes in the intensity of “firing” of some of the filters. A comprehensive texture perception model based on this idea was proposed by Malik and Perona =-=[19]-=-, and many filter-based methods were developed subsequently. This view also supports the claim that the joint distribution of k neighboring pixels determines texture appearance, since the joint distri... |

301 | A parametric texture model based on joint statistics of complex wavelet coefficients
- Portilla, Simoncelli
- 2000
(Show Context)
Citation Context ...from a white noise image and force it to match some set of statistics of the original texture image, such as distributions of filter responses (Heeger and Bergen, 1995; Simoncelli and Portilla, 1998; =-=Portilla and Simoncelli, 2000-=-; De Bonet, 1997). Feature matching methods tend to work well on stochastic textures but have difficulties with highly structured textures. Another difficulty is that they typically require some numbe... |

298 |
Textons, the elements of texture perception and their interactions
- Julesz
- 1981
(Show Context)
Citation Context ...s in a window comes from theories of human perception of texture. The study of human preattentive texture discrimination was pioneered by Julesz in the 60s and 70s (Julesz, 1962; Julesz et al., 1973; =-=Julesz, 1981-=-). His original conjecture was that textures appear indistinguishable to humans if they have identical first- and second-order statistics, and was later extended to higher-order statistics (i.e., join... |

292 |
Markov random field texture models
- Cross, Jain
- 1983
(Show Context)
Citation Context ...ods of texture synthesis can be broadly divided into three categories. The first and oldest group of methods is model-based, with the main modeling tool being Markov Random Fields (MRF) (Besag, 1974; =-=Cross and Jain, 1983-=-). In the early MRF work only a few parameters could be fitted because of computational difficulties, and those models usually did not capture the complexity of real textures. As the number of paramet... |

265 | The Jacknife and the bootstrap for general stationary observations Annals of Statistics 17
- Künsch
- 1989
(Show Context)
Citation Context ... very different from synthesis or estimating the joint distribution. The main tool used in this context is the moving block bootstrap (MBB) and its variants. MBB was first introduced for time series (=-=Künsch, 1989-=-; Liu and Singh, 1992) and extended to general random fields by Politis and Romano (1993). It is based on resampling blocks independently and concatenating them, rather than resampling by conditioning... |

260 |
Mixing: Properties and Examples
- Doukhan
- 1995
(Show Context)
Citation Context ...Before proceeding to the proofs of our results, we state a moment inequality for mixing random fields which we will need below. The proof of this inequality and many other useful ones can be found in =-=[7]-=-. LEMMA A.1 (Moment inequality). Let Ft be a real-valued random field indexed by I ⊂ Zd satisfying conditions (A1). If EFt = 0, Ft ∈ Lτ+ε and τ ≥ 2, then there is a constant C depending only on τ and ... |

240 | Multiresolution sampling procedure for analysis and synthesis of texture images
- Bonet
- 1997
(Show Context)
Citation Context ...ased on feature matching. Typically, these methods start from a white noise image and force it to match some set of statistics of the original texture image, such as distributions of filter responses =-=[5, 10, 23, 25]-=-. Feature matching methods tend to work well on stochastic textures but have difficulties with highly structured textures. Another difficulty is that they typically require some number of iterations t... |

202 | Filters, random fields and maximum entropy (FRAME): Towards a unified theory for texture modeling
- Zhu, Wu, et al.
- 1998
(Show Context)
Citation Context ... Efros and Leung can be expected to produce good visual results. To the best of our knowledge, the only other texture synthesis algorithm in the literature with a mathematical justification is FRAME (=-=Zhu et al., 1998-=-), but, unfortunately, it does not produce very good visual results in practice, whereas the algorithm considered here does. This paper converts the Efros and Leung algorithm into a formal bootstrap s... |

138 |
Visual pattern discrimination
- Julesz
- 1962
(Show Context)
Citation Context ...the joint distribution of pixels in a window comes from theories of human perception of texture. The study of human pre-attentive texture discrimination was pioneered by Julesz in the 1960s and 1970s =-=[12, 13, 14]-=-. His original conjecture was that textures appear indistinguishable to humans if they have identical first- and second-order statistics, and was later extended to higher-order statistics (i.e., joint... |

128 | Real-time texture synthesis by patch-based sampling
- Liang, Liu, et al.
(Show Context)
Citation Context ...rithm of Efros and Leung (1999). Many variations of their method have been published that speed up and optimize the original algorithm in different ways (Wei and Levoy, 2000; Efros and Freeman, 2001; =-=Liang et al., 2001-=-). In all these works however, the basic resampling principle of Efros and Leung (1999) remains unchanged, and even the original version has been very successful on a wider range of textures than any ... |

104 | Texture characterization via joint statistics of wavelet coefficient magnitudes
- Simoncelli, Portilla
- 1998
(Show Context)
Citation Context ...Typically, these methods start from a white noise image and force it to match some set of statistics of the original texture image, such as distributions of filter responses (Heeger and Bergen, 1995; =-=Simoncelli and Portilla, 1998-=-; Portilla and Simoncelli, 2000; De Bonet, 1997). Feature matching methods tend to work well on stochastic textures but have difficulties with highly structured textures. Another difficulty is that th... |

80 |
The Earth Mover’s Distance is the Mallows Distance: Some Insights from Statistics
- Levina, Bickel
(Show Context)
Citation Context ...xels rather than to estimate the mean. One could use cross-validation, that is, compare the synthesized texture to the original for several window sizes using a texture similarity measure (see, e.g., =-=[16]-=-), and pick the window size that maximizes this similarity. This approach is somewhat computationally expensive, and there is no guarantee that the similarity measures used for classification and segm... |

76 |
Moving Block Jackknife and bootstrap capture weak dependence, in Exploring the Limits of Bootstrap , eds, by Lepage and Billard
- Liu, Singh
- 1992
(Show Context)
Citation Context ...t from synthesis or estimating the joint distribution. The main tool used in this context is the moving block bootstrap (MBB) and its variants. MBB was first introduced for time series (Künsch, 1989; =-=Liu and Singh, 1992-=-) and extended to general random fields by Politis and Romano (1993). It is based on resampling blocks independently and concatenating them, rather than resampling by conditioning on the neighboring b... |

71 | Novel cluster-based probability model for texture synthesis, classification, and compression
- Popat, Picard
- 1993
(Show Context)
Citation Context ...thm for Markov mesh models. MMM’s (also known as Picard random fields) were introduced by Abend, Harley and Kanal [1] and have been used for a variety of applications. In particular, Popat and Picard =-=[22]-=- used a parametric MMM model for texture synthesis, and so did Cressie and Davidson [3]. In both cases, however, results for natural textures were of low quality due to the small size of the condition... |

64 | Binocular interaction in striate cortex of kittens reared with artificial squint
- Hubel, Wiesel
- 1965
(Show Context)
Citation Context ...chophysical and neurophysiological experiments suggest that the brain performs multi-channel spatial frequency and orientation initial analysis of any image formed on the retina and not just texture (=-=Hubel and Wiesel, 1965-=-; De Valois 2set al., 1982). These and other similar findings inspired the multi-channel filtering approaches, which use distributions of filter responses for texture discrimination, with texture boun... |

48 |
L.N.Kanal, “ Classification of binary random Patterns
- Abend, Harley
- 1965
(Show Context)
Citation Context ...general MRF on the plane, has a natural notion of the past. 3.1. The resampling algorithm for Markov mesh models. MMM’s (also known as Picard random fields) were introduced by Abend, Harley and Kanal =-=[1]-=- and have been used for a variety of applications. In particular, Popat and Picard [22] used a parametric MMM model for texture synthesis, and so did Cressie and Davidson [3]. In both cases, however, ... |

46 |
Inability of humans to discriminate between visual textures that agree in second-order statistics-revisited
- Julesz, Gilbert, et al.
- 1973
(Show Context)
Citation Context ...distribution of pixels in a window comes from theories of human perception of texture. The study of human preattentive texture discrimination was pioneered by Julesz in the 60s and 70s (Julesz, 1962; =-=Julesz et al., 1973-=-; Julesz, 1981). His original conjecture was that textures appear indistinguishable to humans if they have identical first- and second-order statistics, and was later extended to higher-order statisti... |

22 |
Image analysis with partially ordered Markov models. Computational Statistics and Data Analysis
- Cressie, Davidson
- 1998
(Show Context)
Citation Context ...y Abend, Harley and Kanal [1] and have been used for a variety of applications. In particular, Popat and Picard [22] used a parametric MMM model for texture synthesis, and so did Cressie and Davidson =-=[3]-=-. In both cases, however, results for natural textures were of low quality due to the small size of the conditioning neighborhood. Fitting all the parameters required for a larger neighborhood was com... |

21 |
Spatial-frequency selectivity of cells in macaque visual cortex
- DeValois, Albrecht, et al.
- 1982
(Show Context)
Citation Context ...sychophysical and neurophysiological experiments suggest that the brain performs multichannel spatial frequency and orientation initial analysis of any image formed on the retina and not just texture =-=[6, 11]-=-. These and other similar findings inspired the multichannel filtering approaches, which use distributions of filter responses for texture discrimination, with texture boundaries corresponding to sudd... |

19 | Equivalence of julesz ensembles and frame models
- Wu, Zhu, et al.
- 2000
(Show Context)
Citation Context ...that use both MRF models and feature matching, such as the FRAME model by Zhu, Wu and Mumford [28]. It provides a solid theoretical base for combining MRF’s with feature matching, and Wu, Zhu and Liu =-=[27]-=- showed that FRAME is the natural way to establish equivalence between these two approaches. However, its visual results on real textures are unfortunately far from perfect. A new class of heuristic m... |

14 | The local bootstrap for markov processes
- Paparoditis, Politis
- 2002
(Show Context)
Citation Context ... our bootstrap algorithm and MBB. For time series, bootstrapping bysTEXTURE AND RESAMPLING RANDOM FIELDS 1753 conditioning on the past has been introduced by Rajarshi [24] and Paparoditis and Politis =-=[20]-=-; here we extend their methods to stationary random fields. This paper is organized as follows. In Section 2 we give some background on texture synthesis and introduce the algorithm of Efros and Leung... |

10 |
Nonparametric resampling for homogeneous strong mixing random fields
- Politis, Romano
- 1993
(Show Context)
Citation Context ... The main tool used in this context is the moving block bootstrap (MBB) and its variants. MBB was first introduced for time series [15, 18] and extended to general random fields by Politis and Romano =-=[21]-=-. It is based on resampling blocks independently and concatenating them, rather than resampling by conditioning on the neighboring blocks, which is the main difference between our bootstrap algorithm ... |

8 |
Bootstrap in markov sequences based on estimates of transition density
- Rajarshi
- 1990
(Show Context)
Citation Context ...ch is the main difference between our bootstrap algorithm and MBB. For time series, bootstrapping bysTEXTURE AND RESAMPLING RANDOM FIELDS 1753 conditioning on the past has been introduced by Rajarshi =-=[24]-=- and Paparoditis and Politis [20]; here we extend their methods to stationary random fields. This paper is organized as follows. In Section 2 we give some background on texture synthesis and introduce... |

3 | Equivalence of Julesz texture ensembles and FRAME models - Wu, Zhu, et al. - 2000 |

2 | Mixing: properties and examples, number 85 - Doukhan - 1994 |

1 |
Visual pattern discrimination, IRE transactions on information theory 8(2): 84–92
- Julesz
- 1962
(Show Context)
Citation Context ... in the joint distribution of pixels in a window comes from theories of human perception of texture. The study of human preattentive texture discrimination was pioneered by Julesz in the 60s and 70s (=-=Julesz, 1962-=-; Julesz et al., 1973; Julesz, 1981). His original conjecture was that textures appear indistinguishable to humans if they have identical first- and second-order statistics, and was later extended to ... |