J. Portilla and E. P. Simoncelli, "A parametric texture model based on joint statistics of complex wavelet coefficients," Int. J. Comput. Vis., vol. 40, no. 1, pp. 49--71, Dec. 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....nonseparable filters with real coefficients to attain approximate shiftability and improved directionality. To obtain phase information, Simoncelli et al. 20] and van Spaendonck and Baraniuk [35] created complex steerable pyramids that use analytic non separable filters. Portilla and Simoncelli [36] developed a model that in corporated the cross scale phase statistics of complex steerable pyramid coefficients. This model proved useful in a texture synthesis application. Van Spaendonck and Baraniuk [35] demon strated that the smooth envelope of the complex steerable pyramid basis functions ....

....the non redundant CWT. To the best of our knowledge, no other complex wavelet transform is simultaneously directional and non redundant. These properties make the non redundant CWT particularly attractive for use in image coding systems. Reeves and Kingsbury [42] Portilla and Simoncelli [36], and Romberg et al. 33] have derived accurate statistical models for complex wavelet coefficients. These models have proven useful in various different signal processing applications. However, none of these models may be used for image coding, due to the redundancy of the transforms on which ....

J. Portilla and E. P. Simoncelli, "A parametric texture model based on joint statistics of complex wavelet coefficients," International Journal of Computer Vision, 2000.

....we cannot appeal to the marginal histogram of derivative filters to explain the percept of transparency in this image. There are two ways to go beyond marginal histograms of derivative filters. We can either look at joint statistics of derivative filters at different locations or ori entations [6] or look at marginal statistics of more complicated feature detectors (e.g. 11] We looked at the marginal statistics of a corner detector . The output of the corner detector at a given location x0, Y0 is defined as: I2(x,y) Ix(x,y)Iy(x,y) c(xo, Yo) da(y. w(x, y) x( y)y( y) y) ....

J. Portilla and E. P. Simoncelli. A parametric texture model based on joint statistics of complex wavelet coefficients. Int'l J. Cornput. Vision, 40(1):49-71, 2000.

....of the parameters, or perceptual primaries, which are extracted by the visual system and the way they are translated to higher level perceptual units. Besides the pioneering work of Heeger and Bergen [1] particularly relevant in this respect are the contributions of Portilla and Simoncelli [2] and Zhu and Mumford [3] These probabilistic texture models have grown on the insights coming from neurosciences. The main guidelines are in the assumption that the visual system responds to the statistics of the stimuli to which it is exposed and processes the visual information in order to ....

....in fig. 2. The three detail subbands of the DWT are used as the local descriptors of the frequency bands. In order to reproduce the characteristic structure of a texture, the statistical intra and inter scale relationships observed in the original sample between coefficients 6 must be preserved [2]. In that regard, we define the terms of parent, tree and parent vector as follows. Given the total number N of levels in the pyramid, let F be the coefficient of coordinates x y of the feature image F of level 0 i N and orientation 0 j 3, i . Then, the parent of this ....

J. Portilla, E. Simoncelli, A parametric texture model based on joint statistics of wavelet coefficients, International Journal of Computer Vision 40 (1) (2000) 49--71.

....of the parameters, or perceptual primaries, which are extracted by the visual system and the way they are translated to higher level perceptual units. Besides the pioneering work of Heeger and Bergen [1] particularly relevant in this respect are the contributions of Portilla Simoncelli [2] and Zhu [3] These probabilistic texture models have grown on the insights coming from neural sciences. The main guidelines are in the assumption that the visual system responds to the statistics of the stimuli to which it is exposed and processes the visual information in order to maximize the ....

....and is allowed to vary to ensure it that it englobes a su#cient amount of samples (we refer to the Appendix for further explanations) Linking model parameters to perceptual features is a very di#cult problem. Even though many statistical parameters have been proposed by di#erent authors [1] [2], 3] as those relevant to texture in terms of visual appearance , the way each of such parameters maps to perception and to higher visual cues is still unknown. Namely, the gap between low level parameters and mid to high level visual features is still unsolved. The fact that non parametric ....

[Article contains additional citation context not shown here]

J. Portilla and E. P. Simoncelli, "A parametric texture model based on joint statistics of wavelet coe#cients," International Journal of Computer Vision, vol. 40, no. 1, pp. 49--71, December 2000.

....is still unsolved. Two main guidelines can be identified. The first is based on the assumption that there exists a set of statistics which is necessary and sufficient to identify a texture class. Under such an hypothesis, a pair of textures sharing those statistics are perceptually equivalent [4, 8]. The problem is faced in an information theoretic manner, and leads to the definition of models based on statistical parameters. The way such parameters map to the hypothesized necessary and sufficient set is still unknown. The second consists in looking at the problem in a different perspective ....

Portilla J and Simoncelli E P, A parametric texture model based on joint statistics of wavelet coefficients, International Journal of Computer Vision, 40(1), 49-71, Dec. 2000

....segmentation; and (4) shape from texture. Significant progress was made during the 1990s on the first three areas (with shape from texture receiving comparatively less attention) The success in these areas was largely due to learning a fuller statistical representation of filter bank responses [1, 2, 10, 11, 13, 17]. It was fuller in three respects: firstly, the filter response distribution was learnt (as opposed to recording just the low order moments of the distribution) secondly, the joint distribution, or cooccurrence, of filter responses was learnt (as opposed to independent distributions for each ....

J. Portilla and E. Simoncelli. A parametric texture model based on joint statistics of complex wavelet coefficients. IJCV, 40(1):49 70, 2000.

....using this representation with D: 80 PCs. Each example shows one image and an equivalent textured image that shares the same 80 global features. The textured images are generated by coercing noise to have the same features as the original image, while matching the statistics of natural images [6]. 3. Place recognition In this section we describe the context based place recognition system. We start by describing the set up used to capture the image sequences used in this paper. Then we study the problem of recognition of familiar places. Finally Figure 2: Two images from our data set, ....

J. Portilla and E. P. Simoncelli. A parametric texture model based on joint statistics of complex wavelets coefficients. Intl. J of Computer Vision, 40:49 71, 2000.

....model ( Cro83] of an input texture; the synthesis is then obtained by a suitable sampling. The main drawback of these methodologies is the computational complexity that tends to be impractical for real time applications [Wu00] More efficient techniques tend to properly match texture features ([Por00]) measured at different resolution levels ( Bur83] a series of heuristics are used without explicitly derive a real mathematical model. In [Heg95] and [Deb97] impressive results using marginal histograms of image pyramids and maintaining cross scale dependencies are obtained (see also [Bat00a] ....

J. Portilla, E.P. Simoncelli, A Parametric Texture Model based on Joint Statistics of Complex Wavelet Coefficients, Int. J. of Comp. Vision, Vol. 40, No. 1,. 2000;

....distributions for images based on lter histograms obtained from a dataset of images. This work gave an elegant connection between E mail: coughlan ski.org, yuille ski.org generative models on images (e.g. 12] 11] and empirical studies of the statistical properties of images, for example see [7], 6] 5] Learning MRF distributions from empirical image data requires calculating the values of the potential functions that result in a distribution which is consistent with the empirical data. This corresponds to the classic problem of estimating the parameters of a log linear model. ....

J. Portilla and E. P. Simoncelli. \Parametric Texture Model based on Joint Statistics of Complex Wavelet Coecients". International Journal of Computer Vision. October 2000.

....of the parameters, or perceptual primaries, which are extracted by the visual system and the way they are translated to higher level perceptual units. Besides the pioneering work of Heeger and Bergen [1] particularly relevant in this respect are the contributions of Portilla Simoncelli [2] and Zhu [3] These probabilistic texture models have grown on the insights coming from neural sciences. The main guidelines are in the assumption that the visual system responds to the statistics of the stimuli to which it is exposed and processes the visual information in order to maximize the ....

....and is allowed to vary to ensure it that it englobes a sucient amount of samples (we refer to the Appendix for further explanations) Linking model parameters to perceptual features is a very dicult problem. Even though many statistical parameters have been proposed by di erent authors [1] [2], 3] as those relevant to texture in terms of visual appearance , the way each of such parameters maps to perception and to higher visual cues is still unknown. Namely, the gap between low level parameters and mid to high level visual features is still unsolved. The fact that non parametric ....

[Article contains additional citation context not shown here]

J. Portilla and E. P. Simoncelli, \A parametric texture model based on joint statistics of wavelet coecients," International Journal of Computer Vision, vol. 40, no. 1, pp. 49-71, December 2000.

....The desire to build vision systems capable of recognizing materials provides the primary motivation for the present work. Reflectance and texture both di#erentiate materials. Over the past several years, researchers have taken significant strides toward characterization and recognition of texture [43, 81]. We wish to do the same for reflectance, creating vision systems capable of distinguishing materials based on their reflectance properties. While this thesis focuses on analysis of visible spectrum photographs, other imaging modalities pose analogous material recognition problems. One may wish ....

....deviations were computed on log power values. natural images translate into predictable relationships between wavelet coe#cient distributions at di#erent scales. The regular nature of these distributions facilitates image denoising [82, 99] image compression [13] and texture characterization [43, 81], and has also proven useful in understanding neural representations in biological visual systems [96, 101] Previous analysis of natural images and textures has assumed that the data is defined on a planar domain. Because illumination maps are defined as functions of orientation, they are most ....

J. Portilla and E. P. Simoncelli. A parametric texture model based on joint statistics of complex wavelet coe#cients. International Journal of Computer Vision, 40:49--71, 2000.

....simulations. 1 Introduction There has recently been a lot of interest in learning probability models for vision. The most common approach is to learn histograms of lter responses or, equivalently, to learn probability distributions on features (see right panel of gure (1) See, for example, [6], 5] 4] In this paper the features we are considering will be extracted from the image by lters hence we use the terms features and lters synonymously. An alternative approach, however, is to learn probability distributions on the images themselves. The Minimax Entropy Learning ....

J. Portilla and E. P. Simoncelli. \Parametric Texture Model based on Joint Statistics of Complex Wavelet Coecients". International Journal of Computer Vision. October 2000.

....reflectance estimation. 3.2. A machine learning approach We apply machine learning techniques to determine relationships between surface reflectance and statistics of the observed image. Our choice of statistics is inspired by the natural image statistics and texture analysis literatures [8, 10, 14, 13, 19]. Figure 4 illustrates our approach in the case where the observed surface is spherical. We first project the observed data, defined as a function of surface orientation, onto a plane. Next, we compute a set of statistics on the pixel intensity distribution of the image itself and on distributions ....

J. Portilla and E. P. Simoncelli. A parametric texture model based on joint statistics of complex wavelet coefficients. Int. J. Computer Vision, 40:49--71, 2000.

....community (for a survey of this earlier literature see the paper by Haralick [8] Not surprisingly, that work mainly emphasized the aspects of textures useful for the vision problem, such as their great value for object recognition. Several general texture synthesis algorithms have been developed [5, 7, 9, 13] but until recently both running time [7] and, in many cases, quality [5, 9] of synthesized textures has left much to be desired. In addition we are aware of no published attempt to make the texture synthesis process more end user friendly . The only control the user usually has is a candidate ....

PORTILLA, J., AND SIMONCELLI, E. P. A parametric texture model based on joint statistics of complex wavelet coefficients. International Journal of Computer Vision 39, 3 (October 2000). to appear.

....in [3] In this paper, we present a general parametric model to characterize and detect geons based on statistical constraints that are originated from popular object recognition theories. Portilla and Simoncelli proposed a parametric model based on joint statistics of complex wavelet coecients [5], and successfully demonstrated their algorithms capability of analysing and synthesising visual textures. A brief review of this method would be given in section 2. Then, in section 3, we apply this parametric model as a representation for geons, and reason the appropriateness. Following these ....

....and contain repeated elements, which subject to statistical description. Based on the use of linear kernels at multiple scales and orientations, recent year s development of wavelet representations enabled design of more practical and powerful statistical models. 2. 1 Steerable Pyramid In [5], Portilla and Simoncelli designed a universal statistical model that enforces four statistical constraints on a multi scale multi orientation wavelet decomposition of images. The set of wavelet lters they adopted is known as steerable pyramid [6, 7] named after their properties of ....

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J. Portilla, E. P. Simoncelli, A Parametric Texture Model based on Joint Statistics of Complex Wavelet Coecients, International Journal of Computer Vision, Vol. 40, issue 1, pages 49-71, 2000.

....a theoretical justification) However, since the histograms measure marginal, not joint, statistics they do not capture important relationships across scales and orientations, thus the algorithm fails for more structured textures. By also matching these pairwise statistics, Portilla and Simoncelli [17] were able to substantially improve synthesis results for structured textures at the cost of a more complicated optimization procedure. In the above approaches, texture is synthesized by taking a random noise image and coercing it to have the same relevant statistics as in the input image. An ....

....source drawing; or to transfer material surface texture onto a new image (see Figure 5) For the orange texture the correspondence maps are the source and target image luminance values; for Picasso the correspondence maps are the blurred luminance values. input texture Portilla Simoncelli [17] Xu et.al. 21] Wei Levoy [20] Image Quilting Figure 6: Comparison of various texture synthesis methods on structured textures. Our results are virtually the same as Efros Leung [6] not shown) but at a much smaller computational cost. 4 Conclusion In this paper we have introduced image ....

J. Portilla and E. P. Simoncelli. A parametric texture model based on joint statistics of complex wavelet coefficients. International Journal of Computer Vision, 40(1):49--71, December 2000.

....showed that a nearest neighbor search can perform high quality texture synthesis in a single pass, using multiscale and single scale neighborhoods, respectively. This search may be viewed as an approximation to sampling from an MRF, an approach used by Zhu et al. 54] and Portilla and Simoncelli [40]. Wei and Levoy [49] unify these approaches, using neighborhoods consisting of pixels both at the same scale and at coarser scales. Vector quantization [20] or other clustering may be used to summarize and accelerate the nearest neighbors computation [17, 34, 35, 39, 49] In unpublished work, ....

J. Portilla and E. P. Simoncelli. A Parametric Texture Model based on Joint Statistics of Complex Wavelet Coefficients. International Journal of Computer Vision, 40(1):49--71, December 2000.

....reflectance estimation. 3.2. A machine learning approach We apply machine learning techniques to determine relationships between surface reflectance and statistics of the observed image. Our choice of statistics is inspired by the natural image statistics and texture analysis literatures [9, 11, 15, 14, 19]. Figure 4 illustrates our approach in the case where the observed surface is spherical. We first project the observed data, defined as a function of surface orientation, onto a plane. Next, we compute a set of statistics on the pixel intensity distribution of the image itself and on distributions ....

J. Portilla and E. P. Simoncelli. A parametric texture model based on joint statistics of complex wavelet coefficients. Int. J. Computer Vision, 40:49--71, 2000.

....and orientations share a great deal of structure from image to image, as do joint distributions of wavelet coefficients at different scales, orientations, or spatial positions. A number of authors have used properties of these distributions for image denoising [18, 22] texture characterization [9, 17], or reflectance classification [6] Previous analysis of natural images and textures has assumed that the data is defined on a planar domain. One could use spherical wavelets [20] to analyze the statistics of spherical illumination maps. In order to better compare our results with those of the ....

J. Portilla and E. P. Simoncelli. A parametric texture model based on joint statistics of complex wavelet coefficients. Int. J. Computer Vision, 40:49--71, 2000.

....minimax entropy learning[13] deformable 1 This work is supported by a NSF grant IIS 98 77 127, and a NASA grant NAG 13 00039. We refer to a web site www.cis.ohiostate. edu oval for a detailed report and more results. models. For example, recent work on texture modeling fall in this category[13, 11]. These models are built on pixel intensities through complex interactions between image features, which are often re ected by complicated Gibbs potential functions. The shortcoming is that they do not capture high level semantics in the patterns. For example, a Gibbs model of texture can realize ....

J. Portilla and E. P. Simoncelli, \ A parametric texture model based on joint statistics of complex wavelet coecients", IJCV, 40(1), 2000.

....synthesis with joint statistics of filter responses. For example, De Bonet, 1997) synthesized textures by matching joint histogram of a long vector of filter response [2] Portilla and Simoncelli, 2000) studied an iterative projection method for matching the correlations of some filter responses[9]. These methods, among many other work in the literature, represent two distinct paths of texture synthesis. The first path learns analytical models of texture using Markov random fields, and synthesize texture by stochastic sampling from the model[1, 15] The second path synthesize texture by ....

....represent two distinct paths of texture synthesis. The first path learns analytical models of texture using Markov random fields, and synthesize texture by stochastic sampling from the model[1, 15] The second path synthesize texture by matching statistics without deriving analytical texture model[2, 9, 14]. The two paths are unified by the equivalence between the Julesz ensemble and FRAME models [12] More recently, several algorithms have also been proposed to synthesize textures by matching only local distributions. For example, a non parametric estimation of MRF models is introduced by (Efros ....

[Article contains additional citation context not shown here]

J. Portilla and E. Simoncelli. A parametric texture model based on joint statistics of complex wavelet coefficients. Int. Journal of Comp. Vision, (40(1)):49--71, 2000.

....performance gains may be attained through the use of a more general feature set. The features we use at present do not explicitly model image edges. Features which capture dependencies between wavelet coe#cients at neighboring scales and orientations have proven useful in texture modeling [19]. Such features could be incorporated into our classification scheme and feature selection algorithm. 18 Finally, our method for feature selection may prove more widely applicable to texture classification problems. Our approach bears some similarity to the work of Zhu, Wu, and Mumford [33] who ....

J. Portilla and E. P. Simoncelli. A parametric texture model based on joint statistics of complex wavelet coe#cients. IJCV, pages 49--71, 2000.

....characterizes textures as probability distributions from random fields. Recently, wavelet domain statistical image modeling, which combines the above two aspects, has attracted many attentions and was found useful for various applications, including texture analysis [3, 4, 5, 6, 7] and synthesis [8, 9]. Wavelet domain hidden Markov models (HMM) in particular, the hidden Markov tree (HMT) have been recently proposed in [10, 11] and applied to image processing, e.g. denoising [12] and segmentation [13] The HMT can effectively characterize the This work was partially supported by the 1998 ....

....classification (PCC) upon 55 Brodatz textures. As said before, texture synthesis require more accurate and complete characterization than texture analysis. Since the 2 D HMT 3 only captures the cross correlations of the wavelet transform, we combine the 2 D HMT 3 and the auto correlation used in [8] for complete texture modeling. We formulate the problem of texture synthesis using the HMT as a constrained optimization problem which is further simplified into an unconstrained optimization one by using the penalty function technique. The solution can be easily obtained by the steepest ascent ....

[Article contains additional citation context not shown here]

J. Portilla and E. P. Simoncelli, "A parametric texture model based on joint statistics of complex wavelet coefficients," International Journal of Computer Vision, 2000, to appear.

....are independent. However, it has been shown that wavelet coefficients of textural images may have some dependencies across the three subbands due to regular or homogeneous spatial structures and patterns. The characteristics across subbands are found useful for texture analysis and synthesis in [17]. Therefore, we propose a new wavelet domain HMM by adopting the grouping techniques [15, 11] to further capture the dependencies across subbands, where the three wavelet coefficients of the same spatial location and from the three subbands are grouped into one node. Thus a new tree structured ....

J. Portilla and E. P. Simoncelli. A parametric texture model based on joint statistics of complex wavelet coefficients. International Journal of Computer Vision, 2000. to appear.

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J. Portilla and E. P. Simoncelli, "A parametric texture model based on joint statistics of complex wavelet coefficients," Int'l J Computer Vision, vol. 40, pp. 49--71, Dec 2000.

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J. Portilla and E. P. Simoncelli, "A parametric texture model based on joint statistics of complex wavelet coefficients," Int'l J Computer Vision, vol. 40, pp. 49--71, 2000.

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J. Portilla and E. P. Simoncelli, "A parametric texture model based on joint statistics of complex wavelet coefficients," Int'l J Computer Vision, vol. 40, pp. 49--71, Dec 2000.

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J. Portilla and E. P. Simoncelli, "A parametric texture model based on joint statistics of complex wavelet coe#cients," Int'l Journal of Computer Vision 40, pp. 49--71, December 2000.

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J. Portilla and E. P. Simoncelli, "A parametric texture model based on joint statistics of complex wavelet coe#cients," Int'l Journal of Computer Vision 40, pp. 49--71, December 2000.

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J. Portilla and E. P. Simoncelli, "A parametric texture model based on joint statistics of complex wavelet coefficients," Int. J. Comput. Vis., vol. 40, no. 1, pp. 49--71, 2000.

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J Portilla and E P Simoncelli, "A parametric texture model based on joint statistics of complex wavelet coefficients," Int'l Journal of Computer Vision, vol. 40, no. 1, pp. 49--71, 2000.

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J. Portilla and E. P. Simoncelli, "A parametric texture model based on joint statistics of complex wavelet coefficients," Int'l J Computer Vision, vol. 40, pp. 49--71, 2000.

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J Portilla and E P Simoncelli, "A parametric texture model based on joint statistics of complex wavelet coe#cients," Int'l Journal of Computer Vision, vol. 40, no. 1, pp. 49--71, 2000.

....Plotted along the second row of Fig. 6 are joint contours of log probability for pairs of steerable pyramid wavelet coefficients [51] taken from the mountain image shown at the top. In this example, we used a complex valued transform, which incorporates both even and odd phase coefficients (see [41]) Coefficient pairs are at the same spatial scale and orientation, but with a varying spatial separation of # pixels. The third row shows the same plots for coefficients of the simulated GSM random cascade. The shapes of the joint contours of image data and simulated model are strikingly similar. ....

....parametric forms of nonlinearity. Using a nonparametric form of this nonlinearity would allow the model to further adapt to the image under consideration, with no loss of efficiency. Thirdly, using the information about phase provided by a complex valued multiresolution decomposition (see, e.g. [41]) should lead to even better image models. Finally, in order to overcome the well known limitations of tree structured models, we are investigating GSM processes defined on graphs with cycles (i.e. non trees) The addition of extra edges to the graph leads to more powerful models, but also ....

J. Portilla and E. P. Simoncelli, A parametric texture model based on joint statistics of complex wavelet coefficients, Internat. J. Comput. Vision 40, No. 1 (2000), 49--70.

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J. Portilla and E. P. Simoncelli, "A parametric texture model based on joint statistics of complex wavelet coefficients," Int. J. Comput. Vis., vol. 40, no. 1, pp. 49--71, Dec. 2000.

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J. Portilla and E. Simoncelli. A parametric texture model based on joint statistics of complex wavelet coefficients. International Journal of Computer Vision, 40(1), 2000.

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J. Portilla and E. P. Simoncelli. A parametric texture model based on joint statistics of complex wavelet coe#cients. Int'l J. Comput. Vision, 40(1):49--71, 2000.

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J. Portilla and E. P. Simoncelli. A parametric texture model based on joint statistics of complex wavelet coecients. Int'l J. Comput. Vision, 40(1):49-71, 2000.

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J. Portilla and E. P. Simoncelli. A parametric texture model based on joint statistics of complex wavelet coefficients. Int. J. of Comp. Vision, 40(1):49--71, 2000.

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J. Portilla and E. P. Simoncelli. A parametric texture model based on joint statistics of complex wavelet coefficients. International Journal of Computer Vision, 40(1):49--71, 2000.

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J. Portilla and E.P. Simoncelli, "A Parametric Texture Model Based on Joint Statistics of Complex Wavelet Coefficients," Int'l J. Computer Vision, vol. 40, no. 1, pp. 49-71, 2000.

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J. PORTILLA AND E. P. SIMONCELLI, A parametric texture model based on joint statistics of complex wavelet coefficients, Int'l Journal of Computer Vision, 40 (2000), pp. 49--71.

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J. Portilla and E. P. Simoncelli. A parametric texture model based on joint statistics of compex wavelet coecients. IJCV, 40(1):49-71, 2000.

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Javier Portilla and Eero Simoncelli. A Parametric Texture Model based on Joint Statistics of Complex Wavelet Coefficients. In Int'l Journal of Computer Vision 40(1), pp. 49-71. October, 2000.

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J. Portilla and E. Simoncelli, "A parametric texture model based on joint statistics of complex wavelet coefficients," IJCV, vol. 40, no. 1, pp. 149--71, Dec. 2000.

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Portilla, J., and Simoncelli, E. P. A parametric texture model based on joint statistics of complex wavelet coe#cients. Int'l Journal of Computer Vision (2000).

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J. Portilla and E. P. Simoncelli, \ A parametric texture model based on joint statistics of complex wavelet coecients", IJCV, 40(1), 2000.

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