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...ng the classes as well as 2) the variability of the data around the manifold(s). Recent work has demonstrated the advantages of nonparametric statistical modeling for general image segmentation [15], =-=[16]-=-, as well as MR tissue classification [17]. The proposed framework combines results from two very recent developments—one describing a generic (tensor-metric independent) Riemannian kernel pdfs estima...

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...nfortu nately, this type of model is too simple to capture the textures present in a large percentage of real images. This drawback has limited the performance of such models, and motivated datadriven representations. One data-driven strategy is to use image neighborhoods or patches as a feature vector for representing local structure. Image neighborhoods are rich enough to cap ture the local structures of real images, but do not impose an explicit model. This representation has been used as a basis for image denoising [4]—[10], for texture synthesis [11], [12], and for texture segmentation [13]. For both denoising and seg mentation, it has been demonstrated that the accuracy of this Manuscript received August 14, 2008; revised June 24, 2009. First published July 24, 2009; current version published November 13, 2009. This work was supported in part by the National Institutes of Health R01 EB005832 and in part by the National Science Foundation CCF0732227. The associate editor co ordinating the review of this manuscript and approving it for publication was Prof. Kai-Kuang Ma. The author is with the Electrical and Computer Engineering Department and the Scientific Computing and Imagi...

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...ut do not impose an explicit model. This representation has been used as a basis for image denoising [4], [5], [6], [7], [8], [9], [10], for texture synthesis [11], [12], and for texture segmentation =-=[13]-=-. For both denoising and segmentation, it has been demonstrated that the accuracy of this strategy is comparable to state-of-the-art methods in general and exceeds them in particular types of images s...

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...h to capture the local structures of real images, but do not impose an explicit model. This representation has been used as a basis for image denoising [1, 2, 3, 4] and for texture image segmentation =-=[5]-=-. For both denoising and segmentation, it has been demonstrated that the accuracy of this strategy is on the same level as state-of-the-art methods in general and exceeds them in particular types of i...

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...ng a Markov prior distribution, i.e. the glands will be modeled as a Markov random field. The merits of using MRFs to incorporate spatial dependencies have been demonstrated in a variety of computer vision tasks such as clustering (Pappas, 1992), denoising (Besag, 1986; Figueiredo et al., 1997), and texture synthesis (Paget et al., 1998; Zalesny et al., 2001). MRFs are also prevalent in several medical imaging applications: detecting tumors in mammography (Li et al., 1995), identifying cancer in prostate MR imaging (Liu et al., 2009), and segmenting MR images of the brain (Zhang et al., 2001; Awate et al., 2006) and lung (Farag et al., 2006). MRF priors are established through the construction of local conditional probability density functions (LCPDFs). These LCPDFs — one centered about each site — describe the local inter-site dependencies of a random process. In combination, these LCPDFs can establish a joint probability density function (JPDF) relating all sites. (This JPDF is the Markov prior.) However, only LCPDFs of certain functional forms will reconstitute a valid JPDF. Specifically, the Gibbs–Markov equivalence theorem (Besag, 1974) states that the JPDF will be valid if (and only if) it, and...

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...this limitation, non-parametric statistical boundary evolution algorithms have emerged for segmentation and tracking [8, 11, 12]. Using pure intensity distributions [12], complex multivariate texture =-=[1]-=- or motion information [9], these methods follow a common methodology: (a) derive a minimization criterion from informationtheoretic measures on the region distributions, and (b) use the Parzen window...

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...ogeneous class of mud and oriented texture associated to sand ripples (Fig. 6). The last images I6 and I7 are, respectively, a zebra and a leopard image often used in previous works [11], [14], [17], =-=[18]-=-. For the supervised case, for each test image, we first select the most discriminant feature statistics keeping only features that account for more than 90% of the total weight sum. For image I1, thr...

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...her area of focus, like in general image segmentation, concerns robust mechanisms for enforcing geometric smoothness on the segmented-region boundaries [118, 153, 117]. This chapter presents a method =-=[4]-=- that exploits the defining characteristics of a texture coupled with the generality of nonparametric statistical modeling. The method relies on an information-theoretic metric on Markov image statist...