C. Bouman and B. Liu, "Multiple resolution segmentation of textured images," IEEE Trans. Pattern Anal. Machine Intell., vol. 13, pp. 99--113, Feb. 1991.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....with the joint class conditional distribution p X u and prior distribution of Eq. 2) the MAP estimates of true class labels as given by Eq. 1) becomes: argmin ln ( upXuVu MAP u c = 3) The minimization of (3) is essential in order to derive a MAP estimate of u, u MAP . In [7], it is pointed out that the one dimensional dynamic programming in [8] or simulated annealing method in [4] are computational expensive, and the global minimization still suffers from falling into a local minimum. In [2] a method called ICM is developed to approximate u MAP using assumptions to ....

C. Bouman and B. Liu, Multiple resolution segmentation of textured images, IEEE Trans. Pattern. Anal. Machine Intell., vol. 13, no. 2, pp. 99-113, 1991.

....the field rapidly decays to zero, a finite support NSHP MA model, would generally provide a more compact representation of the purely indeterministic field. We note that many of the existing texture analysis and synthesis algorithms employ 2 D AR models for texture modeling (see, e.g. 7] IS] [9]) These AR models produce efficient parameterization of the purely indeterministic field, when its spectral density function contains high peaks, and has large dynamic range. The general problem of estimating the parameters of random fields has received considerable attention. Most approaches ....

C. Bouman and B. Liu, "Multiple Resolution Segmentation of Textured Images," IEEE Trans. Pattern Anal. Mach. Intell., vol. PAMI-13, pp. 99-113, 1991.

....emerge: 1. Traditional statistical models, which assume that the statistic of each texture are stationnary, especially in the case of Markov random eld approaches (see [5, 20, 21, 39, 7, 27, 30] 2. Models based on the ltering theory, especially Gabor lters cf [23, 44] or wavelets (cf [53, 16, 6, 24, 19, 50, 10]) We have chosen to use the wavelets approach which give an excellent way to decompose a signal in di erent sub bands in which it is easier to caracterized it. The use of wavelet to analyze textures is not new. There exists mainly two approaches: 1. Models which assume the independence of the ....

C. Bouman. Multiple resolution segmentation of textured images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(2):99113, July 1995.

....an image pyramid, can be used in image classification. The multiscale classification is generally performed in a sequential manner, namely, by utilizing the classification result of a coarse scale, low resolution image to guide classification at a finer scale and higher resolution. Bouman and Liu [3] report a successful classification scheme for textured images that utilizes a multiscale, multiresolution representation in a hierarchical approach. Another hierarchical classification 1057 7149 00 10.00 2000 IEEE method is developed in [14] based on adaptive clustering. In this case, the ....

C. A. Bouman and B. Liu, "Multiple resolution segmentation of textured images," IEEE Trans. Pattern Anal. Machine Intell., vol. 13, pp. 99--113, Feb. 1991.

....and Eschbach [8] have segmented and classified JPEG compressed documents. Morphological closing and opening operations are used to identify and crop individual segments in the compressed domain. A number of multiscale classification and segmentation approaches are reported in the literature [2,3]. Here, multiscale representations are first computed. The segmentation process in these cases is strictly sequential, wherein maximum a posterJori (MAP) estimates at a given resolution are propagated from coarse to fine scales within a quadtree. Also, Bayesian segmentation techniques are used ....

C: Bouman and B. Liu, "Multiple Resolution Segmentation of Textured Images," IEEE Trans. PAMI, vol. 13, no. 2, pp. 99-113, 1991.

....a variety of image configurations and are implicitly the basis for picture parameter estimation. The estimation principle consists of solving a sequence of global optimization problems defined on a sequence of embedded configuration subspaces accepting constraints in form of prior distributions [1,2,8]. 4. THE BASIC CONCEPTS Due to the incommensurability of the images obtained from different sensors and due to the high complexity of the imaged scenes, data fusion systems demands high level representation of information. Thus, scene interpretation is done by augmentation of the data with ....

Bouman, C., B. Liu (1991) Multiple resolution segmentation of textured images, IEEE Tr. PAMI, Vol. 13, pp. 99-113.

....the output of an initial texture model [3] 5] This is usually a computational expensive task requiring simulated annealing or similar iterative schemes. The extension of the MRF model to a multiscale random field (MSRF) that is hierarchically ordered, reduces the computation time significantly [2] [1] 8] 7] 6] 9] As a disadvantage some MSRF models are either not exactly tractable or produce rather blocky regions. In this paper we present a model that avoids both of these drawbacks. We let each random variable of the MSRF choose its parent during segmentation, so that the preferred ....

Charles Bouman and Debe Liu. Multiple resolution segmentation of textured images. IEEE Tr. on PAMI, 13(2):99--113, 2 1991.

....at high resolutions, but are hidden at low resolutions. In contrast, low frequency (global) characteristics are more easily resolved at low resolutions [86] A problem with the single scale relaxation process is that the global image characteristics evolve indirectly in the relaxation process [26, 86, 193]. Typically these global image characteristics only propagated across the image lattice through local interactions. This results in a slow evolution process which is easily disrupted by phase discontinuities, see Section 7.3. Long relaxation times are required to obtain an equilibrium, as defined ....

....By this method, global image characteristics that have been resolved at a low resolution are infused into the relaxation process at the higher resolution. This helps reduce the number of iterations required to obtain equilibrium [193] As a consequence of implementing MR, Bouman and Liu [26] and Derin and Won [55] found, by experimentation, that it helped the ICM algorithm to find convergence to the global maximum of the joint distribution #. Under SR the ICM algorithm tended to cause convergence to a local maximum over # that was dependent on the initial image. This MR observation, ....

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C. Bouman and B. Liu, "Multiple resolution segmentation of textured images," no. 2, pp. 99--113, 1991.

....have been resolved at a low resolution are infused into the relaxation process at the higher resolutions. This helps reduce the number of iterations required to obtain equilibrium [16] MR also helps the ICM algorithm converge to an image closer to the global maximum of the joint distribution # [3], 5] The multiscale model may be best described by a multigrid representation of the image, as shown in Fig. 3. The grid at level l = 0 represents the increasing image resolution Fig. 3. Grid organisation for MR via decimation. image at the original resolution, where each intersection ....

Charles Bouman and Bede Liu, "Multiple resolution segmentation of textured images," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 2, pp. 99--113, 1991.

....low resolution are infused into the relaxation process at the higher resolutions. This helps reduce the number of iterations required to obtain equilibrium [44] Multiscale relaxation also helps the ICM algorithm converge to an image that is closer to the global maximum of the joint distribution # [6], 16] The multiscale model may be described by a multigrid representation of the image, as shown in Fig. 2. The grid at level l = 0 represents the image at the original resolution, where each intersection point . is a site s S. The lower resolutions, or higher grid levels l 0, are ....

Charles Bouman and Bede Liu, "Multiple resolution segmentation of textured images," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 2, pp. 99--113, 1991.

....resolution are infused into the relaxation process at the higher resolutions. This helps reduce the number of iterations required to obtain equilibrium [46] Multiscale relaxation also helps the ICM algorithm converge to an image that is closer to the global maximum of the joint distribution II [6, 15]. The multiscale model may be described by a multigrid representation of the image, as shown in Fig. 2. The grid at level I = 0 represents the image at the original resolution, where each intersection point e is a site s C . The lower resolutions, or higher grid levels I 0, are decimated ....

C. Bouman and B. Liu, "Multiple resolution segmentation of textured images," IEEE Transactions on Pattern AnMysis and Machine Intelligence, 13, no. 2, pp. 99-113, 1991.

.... for the optimal estimates for such models is computationally demanding, requiring methods such as simulated annealing for their solution or leading to suboptimal methods such as iterated conditional mode (ICM) 36] These problems have led a variety of authors to consider MR algorithms and models [48, 14, 135, 40, 144, 179, 180, 42, 59, 53, 58]. We will describe how some of these methods fall directly into the framework on which we focus and how others relate to it. 2.6 Multisensor Fusion for Groundwater Hydrology As we mentioned in Section 1, one of the motivations for using multiresolution methods comes from applications in which ....

....coarser 2x2 blocks, this fine scale detail could then be used to correct for the erroneous averaging at the coarser scale, allowing new, coarser scale estimates to be computed. This is exactly what the fine to coarse multigrid correction step does. In a number of other MRF estimation algorithms [135, 40, 145, 257, 144, 140, 195, 126] the full multigrid structure is not used, and only coarse to fine operations are performed. In some of these (e.g, see [40, 145, 144, 140] the problems that are solved at coarser scales correspond exactly to the original problems but with a constrained set of allowed reconstructions (e.g. ....

[Article contains additional citation context not shown here]

C. A. Bouman and B. Liu. Multiple resolution segmentation of textured images. IEEE Trans. on Pattern Analysis and Machine Intelligence, 13(2):99--113, February 1991.

....methods relying on a priori knowledge of the number of textures in a given image [8] 11] 9] often fail, because if any unexpected texture region appears, like the ones related to shadows or boundaries, a wrong fusion of two non related regions is forced. Unsupervised segmentation [4] 6] [2] does not rely on such a knowledge, but it is slower because it requires a computationally expensive additional stage to calculate the correct number of regions in the image [4] A common choice to speed up segmentation processes is to use multiresolution structures. Most multiresolution methods ....

....but it is slower because it requires a computationally expensive additional stage to calculate the correct number of regions in the image [4] A common choice to speed up segmentation processes is to use multiresolution structures. Most multiresolution methods work in a coarse to ne way [8] 9] [2] [10] Their main problem is that they typically adopt the same cost functions at all scales [8] 2] Unfortunately, cost functions tend to work ne either at high or at low resolution. Our eorts have been focused on implementing an unsupervised texture based segmentation algorithm to achieve a ....

[Article contains additional citation context not shown here]

C. Bouman and B. Liu, "Multiple resolution segmentation of textured images", IEEE Trans. on Pattern Anal. Machine Intel l., 13 (2), 99-113, 1991

....such classes, the problem of segmenting textured images is particularly challenging. A primary reason for this is that a well posed definition of texture has only begun to emerge. Many recent successful techniques have been based on multiband filtering [7, 15,25,26] or on purely stochastic models [1, 4, 17, 19, 21,27]. In this paper, we take a distinct approach by characterizing texture in terms of nonstationary amplitude and frequency modulations. We model textured images as sums of nonstationary AM FM functions, or components,ofthe form ######### ##########. By definition, the instantaneous amplitude #### ....

C. Bouman and B. Liu. Multiple resolution segmentation of textured images. IEEE. Trans. Pattern Anal. Machine Intell., 13(2):99--113, February 1991.

....concerns the subsampling of MRF s. The general properties of several subsampling schemes are examined. It is shown that most standard subsampling schemes lead Alternate approaches, involving various kind of coarsening operators on a single resolution model, have also been developed recently [7], 19] 20] 27] 34] 36] 37] These approaches are not subject to a loss of locality and hence will not be considered in this paper. to a loss of locality. Examples of subsampling schemes which preserve a local Markov property are also presented. The statistical properties of MRF models defined ....

C. Bouman and B. Liu, "Multiple resolution segmentation of textured images," IEEE Trans. Pattern Anal. Machine Intell., vol. 13, no. 2, pp. 99-113, 1991.

....complexity. To reduce the computational complexity and improve the classification accuracy, researchers proposed multiscale techniques which apply contextual behavior in the coarser scale to guide the decision in the finer scale and retain the underlying MRF model in each fixed scale, e.g. [3, 4]. In particular, in [4] Markovian dependencies are assumed across scales to capture interscale dependencies of multiscale class labels with a causal MRF structure, so that a non iterative segmentation algorithm was developed where a sequential MAP (SMAP) estimator replaces the MAP estimator. ....

C. A. Bouman and B. Liu, "Multiple resolution segmentation of textured images," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 2, pp. 99--113, February 1991.

....segmentation fields, and many algorithms have employed MRF models in tackling the segmentation problem. However, such treatments are usually computationally intensive. Multiresolution techniques have been integrated into such methods, in order to reduce computation load and to improve precision [7, 8]. All the multiresolution segmentation algorithms employ a lowpass filter to construct a multiscale representation of the original image. Segmentation then proceeds in a coarse to fine scheme. In this work we use the DCLT to characterize the image, and develop a corresponding algorithm for texture ....

....scale 1, d) e) scale 0 used for the minimization process, such as simulated annealing (SA) 10] and iterated conditional modes (ICM) 11] algorithms. Multiresolution algorithms based on MRF scheme have been used in several reports, primarily for the purpose of efficient computation. Some authors [8] have used multiresolution label fields. Others [7] have used both multiresolution observation fields and multiresolution label fields. Image segmentation is obtained through a coarse tofine process. In this work, we will employ the DCLT to construct a multiresolution representation of the ....

C.Bouman and B.Liu, "Multiple resolution segmentation of textured images", IEEE Trans. Pattern Anal. Machine Intell., vol.13, no.2, pp.99-113, 1991.

....[20] and the two dimensional Markovian model [27] These approaches assume a local dependency of a pixel on its neighbors and it is incorporated into the decision rule in addition to the spectral information. As a result, these are also referred to as simultaneous contextual classification methods [20, 27 30], or Bayesian contextual classification because the theoretical foundation of simultaneous classification is based on the Bayesian formulation. Bayesian contextual approaches involve the formulation of a distribution model for both the underlying class labels and the class conditional model so ....

....specification of spatially local interaction (short distance statistical dependence) using a set of local parameters. This greatly reduces the complexity of the model. It has been shown that classification performance of multispectral remotely sensed images has been improved with these approaches [30] [35] Although the Bayesian contextual MAP estimation is neatly formulated, the MAP estimation still involves huge computational complexity due to the size of the image lattice wherein the image is confined. Also, the exact maximization of the posterior probability is intractable. As a result, ....

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C. Bouman and B. Liu, Multiple resolution segmentation of textured images, IEEE Trans. Pattern. Anal. Machine Intell., vol. 13, no. 2, pp. 99-113, 1991

....of the image. Second, it usually also improves robustness; the pyramid has a smoothing effect on the criterion to be optimized which often reduces the likelihood of getting trapped in local optima. There are numerous examples of the application of this principle in the literature. Bouman et al. [5] employ a quadtreelike pyramid for unsupervised texture segmentation and Kato et al. 12] uses a multiscale relaxation algorithm applied to image classification. Pyramids have also been used in [4] to compute time varying motion parameters and in [18] a Haar pyramid is used for segmentation of ....

....to the next (Fig. 1) Naturally, a one pixel wide label should lead to a two pixel wide label at the finer level that has twice the resolution of the coarser level. The centered topology guarantees a clearly defined way of propagating labels across scales. This advantage has been exploited in [5], 11] 12] 18] which employ quadtree like pyramids. The down side of the Haar pyramid, however, is that it has very poor approximation power because the underlying model is piecewise constant, hence one operates on a bad replica of the original image at coarser resolutions. The purpose of ....

C. Bouman and B. Liu, "Multiple resolution segmentation of textured images," IEEE Trans. Pattern Anal. Machine Intell., vol. 13, pp. 99--113, Feb. 1991.

.... their characteristic symmetric structures are usually described by real feature vectors [10] Further developments aim at reducing computational costs and adapting this technique to specific classification tasks [8, 13] Alternatively, texture can be regarded as a hierarchical pattern [2] because a characteristic structure can be part of a larger structure that again may be periodic. The basic idea behind this approach is that information in a signal cannot be extracted at only one scale. Therefore it is appropriate to chose a multiscale representation of the image to decompose ....

C. Bouman, B. Liu. Multiple resolution segmentation of textured images. IEEE PAMI, 13:99--113, 1991.

....models and can be readily applied to other grouping and segmentation tasks. Most approaches employed local optimization techniques like iterative conditional mode (ICM) 2, 3, 8, 9, 13, 12] or annealing techniques [1, 4] Multi resolution optimization techniques have been used only occasionally [25]. For other vision applications, several previous optimization approaches rely on coarse versions of a cost function. Similar techniques are employed by multi grid algorithms, which have rst been developed for the solution of partial di erential equations [26] Multi grid methods have been ....

....of the cost function. In contrast, most multi resolution techniques developed for image processing tasks are semantic multi resolution techniques. They adopt the same model class for feature sets extracted from di erent image scales. An example for texture segmentation is the approach of Bouman [25], who used Gaussian autoregressive features extracted on multiple image scales to design a coarse to ne optimization strategy. Note that there is no guarantee that coarse grid solutions are good initializations for ner levels, as di erent cost functions are optimized and interactions between ....

C. Bouman and B. Liu, \Multiple resolution segmentation of textured images," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, pp. 99-113, 1991.

....quadtree method of Spann and Wilson [11] and also in [12, 13, 14] used clustering of a historgram at a low spatial resolution, followed by boundary refinement. Recently, a multiresolution stochastic image model was used by Bouman and Shapiro in the development of a Bayesian segmentation algorithm[15]. Although region based methods have their attractions, it is quite hard to define region models which are sufficiently robust and general to allow just enough intra region variation, without causing ambiguities in what constitutes a region. Correspondingly, the importance of line and edge ....

....of advantages over previously reported methods. It is computationally fast, flexible with respect to region and boundary models and uses only local processing. There are a number of features of the segmentation method presented here which differentiate it from work reported elsewhere (e.g. 23] [15], 25] The inhomogeneous block tessellation used by 20 (a) b) c) d) e) f) Figure 12: Results on natural images table and Lena image. a) table 1 original, b) Regions result, c) Boundary result, d) Lena image, e) Regions result, c) Boundary result. Off links highlighted in ....

C. Bouman and B. Liu. Multiple Resolution Segmentation of Textured Images. IEEE Trans. PAMI., 13:99--113, 1991.

....Because of the multiresolution estimation, the overall number of iterations required to attain convergence was low in the examples shown in gure 16, the number of iterations pixel was of the order of 4. We have compared these results with those presented by a number of authors, including [16] [4], 5] 17] 27] and [20] The results presented here are superior in terms of error rates to those and compare well with any we 21 have seen in the literature on image segmentation. 3 Conclusions In this paper, we have presented a new model for image analysis, which combines the notions of ....

C. A. Bouman and B. Liu. Multiple Resolution Segmentation of Textured Images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(2):99-113, 1991.

....and pattern forming behaviors of the model. The results allow more accurate and flexible control when the GRF is used as an image model. 1 Introduction Gibbs random fields (GRF) and their equivalent Markov random fields, have recently been applied to image segmentation [1] 2] 3] 4] 5] [6], 7] edge detection [8] restoration [9] 10] 11] 12] 13] reconstruction [14] 15] coding [16] 17] and motion estimation [18] Underlying these applications is the notion of representing an image as a random field of primarily local interactions, i.e. using the GRF as an image ....

....GRF as an image model. However it has proven difficult to control scale and patterning within the GRF model. Meanwhile, alternate models that provide multiscale representations such as wavelets, pyramids, quadtrees, etc. have achieved noteworthy success. Although there are recent efforts [10] [6], 19] 20] to develop multiscale random fields or to combine them with another multiscale model, these methods assume a discrete number of scales. None facilitate continuous control over scale. In nature, however, multiresolution pattern formation does not occur by discrete quadtrees or ....

C. Bouman and B. Liu, "Multiple resolution segmentation of textured images," IEEE T. Patt. Analy. and Mach. Intell. , vol. PAMI-13, no. 2, pp. 99--113, 1991.

....for a description of the second approach. A split, merge and group (SMG) approach is proposed by Strasters and Gerbrands [122] In this approach, an M Theta M , M = 2 n , image is represented by a quadtree structure in which each leaf node corresponds to a block of pixels in the image [8, 110, 111, 112, 38, 41, 94, 3, 73, 12]. Figure 2.15 depicts a quadtree rooted at level 0. The quadtree is expanded to an initial level, s, in which each leaf node represents pixel blocks of size 2 n Gammas Theta 2 n Gammas where 0 s n. Next, a merging phase is performed in which nodes at level s 0 , 0 s 0 s Gamma 1, are ....

C. Bouman and B. Liu. Multiple resolution segmentation of textured images. IEEE Transactions On Pattern Analysis and Machine Intelligence, 13(2):99-- 113, 1991.

....to region growing is to consider an image as consisting of a number of blocks. Each of these blocks can be characterized by the texture within it and can be identified with some sort of label. A multiresolution approach takes the view that an image can be broken into blocks of different sizes [3]. By using different block sizes it is possible for each block to represent only 1 texture in the image, thus producing the strongest texture feature measures. When a 19 block has a weak measure, it can be split up into more blocks at a higher resolution (smaller size) In this way, the optimal ....

C. Bouman and B. Liu. Multiple resolution segmentation of textured images. IEEE Transactions On Pattern Recognition and Machine Intelligence, 13(2):99-- 113, 1991.

....is available. Deterministic approaches converge to configurations corresponding to local minima of the global energy function. On the other hand, 2 E. Memin, F. Heitz and F. Charot it is known that multigrid methods can significantly improve the convergence rate of iterative relaxation schemes [6, 22, 37]. The major drawback of relaxation algorithms is the amount of computation required to update the image. For real world applications the computation time quickly becomes prohibitive on workstations. On the other hand, in low level vision, the global energy functions usually adopted decompose into ....

....This algorithm is described in Fig. 3. It is used in this paper as a standard example of non linear deterministic relaxation. 2.2. 3 Multigrid relaxation It is well known that multigrid methods can significantly improve the convergence rate of linear and non linear iterative relaxation schemes [6, 19, 22, 27, 37]. Multigrid methods may also be useful when the energy to be minimized has many local minima, as is often the case with non linear models. It has indeed been conjectured that multigrid analysis may, to a certain extent, smooth the energy landscape. Fast deterministic relaxation schemes can then be ....

[Article contains additional citation context not shown here]

C. BOUMAN and B. LIU. -- Multiple resolution segmentation of textured images. -- IEEE Trans. Pattern Anal. Machine Intell., Vol. 13, No 2: pages 99--113, Feb. 1991.

....Field model because the continuous models suffer from problems of non stationarity, sensitivity to noise and initial conditions, and visualisation. During the past decade, there has been a strong trend towards the use of stochastic models in image segmentation problems, Lakshmanan Derin 1989, Bouman 1991, Cohen Cooper 1987, Geman 1984) Several of the earlier studies showed that when the parameters of the candidate texture model were assumed to be known, stochastic model based image segmentation yielded good results. In our approach we assume no a priori knowledge of the texture parameters. we ....

Bouman, C. (1991). "Multiple Resolution Segmentation of Textured Images", IEEE,Trans. Pattern Anal. Machine Intell. , Vol. 13, No. 2, pp. 99-113.

....way like for intensity images [14] 1] 4] However the fundamental drawback of this modeling is that it requires the number of labels. This number is supposed known in supervised segmentation [12] 26] But in unsupervised segmentation, it must be estimated from an estimation learning phase [6] [22] 32] Most estimation methods of this number are based on clustering technique. However in general this estimation requires prior information or hypothesis, and is usually unreliable and in particular for real images containing complex scene. Also, m could be taken as an upper bound of the ....

.... is doubly stochastic : X is a Markov Random field defined by a priori regularities of the distribution of the regions, the texture features or natures of homogeneous regions are described by the conditional distribution P (Y = y j X = x) of the intensity image given homogeneous regions, 12] [6], 22] 26] 32] The image is segmented by maximizing the conditional probability of X given the intensity image Y , i.e. the MAP estimate : x = arg max x P (X = x j Y = y) Using Bayes rule, we have x = arg max x P (Y = y j X = x)P (X = x) Let U y (x) Gamma log P (Y = y j X = x) ....

C. Bouman, B. Liu, "Multiple resolution segmentation of textured images", IEEE Trans. Pattern Anal. Machine Intell., vol. 13, pp. 99-113, Feb. 1991.

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C. A. Bouman and B. Liu, "Multiple resolution segmentation of textured images," IEEE Trans. Pattern Anal. Machine Intell., vol. 13, pp. 99--113, Feb. 1991.

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C. Bouman and B. Liu, "Multiple resolution segmentation of textured images," IEEE Trans. Pattern Anal. Machine Intell., vol. 13, pp. 99--113, Feb. 1991.

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C. Bouman and B. Liu. Multiple resolution segmentation of textured images. IEEE Trans. Pattern Anal. Machine Intell., 13(2):99--113, February 1991.

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C. Bouman and B. Liu, "Multiple resolution segmentation of textured images," no. 2, pp. 99--113, 1991.

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C. Bouman, B. Liu, Multiple resolution segmentation of textured images, IEEE Transactions on Pattern Analysis and Machine Intelligence 13 (2) (1991) 99 -- 113.

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C. Bouman and B. Liu, "Multiple resolution segmentation of textured images," IEEE Trans. Pattern Anal. Machine Intell., vol. 13, pp. 99--113, 1991.

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Charles Bouman and Bede Liu, "Multiple resolution segmentation of textured images", IEEE Trans. on PAMI, Vol. 13, No. 2, Feb. 1991.

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Bouman, C., Liu, B.: Multiple Resolution Segmentation of Textured Images. IEEE Transactions on Pattern Analysis and Machine Intelligence 13(2) (1991) 99--113

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C.A. Bouman and B. Liu, "Multiple Resolution Segmentation of Textured Images," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 2, pp. 99-113, Feb. 1991.

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C. Bouman and B. Liu, "Multiple Resolutions Segmentation of Textured Images," IEEE transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 2, pp. 99--113, 1991.

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C. Bouman and B. Liu, "Multiple resolution segmentation of textured images," IEEE Trans. Pattern Anal. Machine Intell., vol. 13, no. 2, pp. 99--113, 1991.

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C. Bouman and B. Liu, \Multiple Resolution Segmentation of Textured Images," IEEE Trans. PAMI, vol. 13, no. 2, pp. 99-113, Feb. 1991.

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C. Bouman and Bede Liu, "Multiple resolution segmentation of textured images," IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 13, No. 2, pp. 99-113, February 1991.

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C. Bouman and B. Liu, "Multiple resolution segmentation of textured images," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 2, pp. 99-113, 1991.

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Charles Bouman and Bede Liu. Multiple resolution segmentation of textured images. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-13(2):99-113, 1991.

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C. Bouman and B. Liu, "Multiple resolution segmentation of textured images", IEEE Transactions on Pattern Anal. Machine Intel l., 13 (2), pages 99-113, 1991

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C. Bouman and B. Liu. Multiple resolution segmentation of textured images. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-13(2):99--113, February 1991.

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C. Bouman and B. Liu, \Multiple resolution segmentation of textured images," IEEE Trans. on Pattern Anal. and Mach. Intell. 13, pp. 99-113, Feb. 1991.

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C. Bouman and B. Liu, "Multiple resolution segmentation of textured images," IEEE Trans. Pattern Anal. Machine Intell., vol. 13, pp. 99--113, Feb. 1991.

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C. Bouman and B. Liu, "Multiple resolution segmentation of textured images," no. 2, pp. 99--113, 1991.

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C. Bouman and B. Liu, "Multiple resolution segmentation of textured images," IEEE Trans. on Pattern Anal. and Mach. Intell. 13, pp. 99--113, Feb. 1991.

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