В работе [1.1] предлагается модель изображения, состоящая из нескольких текстур, задаваемых независимыми марковскими случайными полями, и рассмотрена возможность решения задач сегментации на основе этой модели. В [1.2] построен математический аппарат случайных полей, заданных на многомерных сетках. В ряде работ [1.3 – 1.6] предлагаемых авторами варианты статистических моделей исследованы экспериментально путём визуальной оценки качества модельного изображения. Большинство работ посвящено задаче расщепления изображений на компоненты с различными характеристиками случайного распределения значений пикселов при разных условиях, характерных для специфической тематики изображений (медицинские препараты, дистанционное зондирование, опознавание лиц и др.), они отнесены к разделу 3 настоящего обзора. В [1.10] описан алгоритм разделения статистических компонентов естественных изображений, включающий вычисление глобальных параметров, исключение неинформативных и разделение гауссовских распределений. Различные усовершенствования алгоритмов разделения гауссовских распределений предлагаются, например, в работах [1.11 и 1.12], а в [1.13] перейти от гауссовских распределений к распределению Дирихле.
1.1. Текстурная сегментация изображений на основании марковских случайных полей / – http://tka4.org/materials/lib/Articles-Books/Speech%20Recognition/%D0%A2%D0%B5%D0%BA%D1%81%D1%82%D1%83%D1%80%D0%BD%D0%B0%D1%8F%20%D1%81%D0%B5%D0%B3%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%D1%86%D0%B8%D1%8F%20%D0%B8%D0%B7%D0%BE%D0%B1%D1%80%D0%B0%D0%B6%D0%B5%D0%BD%D0%B8%D0%B9%20%D0%BD%D0%B0%20%D0%BE%D1%81%D0%BD%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B8%20%D0%BC%D0%B0%D1%80%D0%BA%D0%BE%D0%B2%D1%81%D0%BA%D0%B8%D1%85.pdf
В данной статье вводится модель изображения, состоящего из нескольких текстур. Особенность введенной модели состоит в том, что сегментация и каждая текстура задаются независимыми марковскими случайными полями. Данная модель позволяет избежать каких-либо дополнительных ограничений на рассматриваемые марковские случайные поля, таких, как авторегрессионность или гауссовость. Также рассматриваются возможные постановки задач сегментации, основанные на указанной модели, и исследуются возможности их решения.
1.2. АНДРИЯНОВ Никита Андреевич. ДВАЖДЫ СТОХАСТИЧЕСКИЕ АВТОРЕГРЕССИОННЫЕ МОДЕЛИ ИЗОБРАЖЕНИЙ. – Дисс. Канд. Наук. - Ульяновский государственный технический университет, .2017 - http://www. ulsu. ru/media/uploads/hairutdinova%40ulsu. ru/2017/09/28/d_AndrijanovNA. pdf
1. Впервые предложены и исследованы математические модели слуайных полей на многомерных сетках.
2. Разработан новый численный метод идентификации параметров дважды стохастических моделей.
3. Синтезированы и исследованы алгоритмы фильтрации дважды стохастических случайных полей, наблюдаемых на фоне белого шума.
4. Разработана и исследована методика восстановления повреждённых участков изображений по реальным данным на основе процедур нелинейной фильтрации дважды стохастических моделей изображений.
5. Синтезирован и исследован алгоритм обнаружения протяжённых детерминированных сигналов на фоне моделей изображений, описываемых с помощью дважды стохастических моделей случайных полей.
6. Впервые в едином программном комплексе реализованы алгоритмы моделирования дважды стохастических авторегрессивных изображений и их обработки
1.3. F.-C. Jeng ; J. W. Woods. Inhomogeneous Gaussian image models for estimation and restoration // IEEE Transactions on Acoustics, Speech, and Signal Processing (Volume: 36, Issue: 8, Aug 1988). – Pages 1305 – 1312. - http://ieeexplore. ieee. org/document/1658/.
Two inhomogeneous Gaussian-image models are presented for estimation and incorporating the local statistics of an image, a homogeneous autoregressive (AR) random field can be extended to an inhomogeneous AR field. This inhomogeneous random field can provide a better description of the image than the homogeneous one. As a consequence of this improved modeling, a minimum-mean-square-error estimator (MMSE), based on the inhomogeneous Gaussian model, can produce good results in both subjective and objective criteria. Two image models are proposed for use in image estimation and restoration: a residual image model (original image minus the space-variant mean) and a normalized image model (residual image divided by space-variant standard variation). The novel aspect of these models is the use of an autoregressive dynamical model for residual and normalized images.
1.4. Lo-Bin Chang, Eran Borenstein, Wei Zhang, and Stuart Geman
Maximum likelihood features for generative image models // Ann. Appl. Stat. Volume 11, Number 3 (2017), 1275-1308. – https://projecteuclid. org/euclid. aoas/1507168830 (abstract)
Here, we focus on the generative or Bayesian approach, which is more model based and, in theory, more efficient. Challenges include latent-variable modeling, computationally efficient inference, and data modeling. We restrict ourselves to the problem of data modeling, which is possibly the most daunting, and specifically to the generative modeling of image patches. We formulate a new approach, which can be broadly characterized as an application of “conditional modeling,” designed to sidestep the high-dimensionality and complexity of image data. A series of experiments, learning appearance models for faces and parts of faces, illustrates the flexibility and effectiveness of the approach.
1/4a. Alexander Kolesnikov, Christoph H. Lampert. PixelCNN Models with Auxiliary Variables for Natural Image Modeling // Proceedings of the 34th International Conference on Machine Learning, PMLR 70:1905-1914, 2017.
We study probabilistic models of natural images and extend the autoregressive family of PixelCNN models by incorporating auxiliary bsequently, we describe two new generative image models that exploit different image transformations as auxiliary variables: a quantized grayscale view of the image or a multi-resolution image pyramid. The proposed models tackle two known shortcomings of existing PixelCNN models: 1) their tendency to focus on low-level image details, while largely ignoring high-level image information, such as object shapes, and 2) their computationally costly procedure for image sampling. We experimentally demonstrate benefits of our models, in particular showing that they produce much more realistically looking image samples than previous state-of-the-art probabilistic models.
1.5. Seyedeh-Zohreh Azimifar (2005). Image Models for Wavelet Domain Statistics // UWSpace. – http://hdl. /10012/938
This thesis presents an empirical study of joint wavelet statistics for textures and other imagery including dependencies across scale, space, and orientation. There is a growing realization that modeling wavelet coefficients as independent, or at best correlated only across scales, may be a poor assumption. While recent developments in wavelet-domain Hidden Markov Models (notably HMT-3S) account for within-scale dependencies, we find that wavelet spatial statistics are strongly orientation dependent, structures which are surprisingly not considered by state-of-the-art wavelet modeling techniques. To demonstrate the effectiveness of the studied wavelet correlation models a novel non-linear correlated empirical Bayesian shrinkage algorithm based on the wavelet joint statistics is proposed. In comparison with popular nonlinear shrinkage algorithms, it improves the denoising results.
1.6. J Anthony Wilson; David H. Brainard. Perceptual evaluation of statistical image models [Abstract] // Journal of Vision. – December 2005, V. 5, No. 12. P, 93. - doi:10.1167/5.12.93. - http://jov. arvojournals. org/article. aspx? articleid=2132907.
Parametric models of the statistical regularities in natural images may be exploited for image processing and for understanding biological vision. Our current knowledge of how well extant models actually characterize natural images is quite limited. Here we present a psychophysical method that quantifies image model quality and report initial baseline results. Methods: The van Hateren database of natural images was analyzed to determine its pixel intensity histogram. A simple first-order model assumes that pixel intensities are iid and drawn according to this histogram. On each trial of the experiment, the observer viewed two image patches. One patch was extracted from a van Hateren image, while the other was generated from the first-order model. The observer's task was to identify the natural image patch. Patch size was varied parametrically. Data have been collected for two observers. Results: Percent correct increased monotonically with patch size. Threshold (75% correct) patch size was approximately 4 by 4 pixels.
1.7. Zhirong Wu, Dahua Lin, Xiaoou Tang. Deep Markov Random Field for Image Modeling // http://dahua. me/publications/dhl16_deepmrf. pdf
In this paper we propose a novel MRF model that uses fully-connected neurons to express the complex interactions among pixels. Through theoretical analysis, we reveal an inherent connection between this model and recurrent neural networks, and thereon derive an approximated feed-forward network that couples multiple RNNs along opposite directions. This formulation combines the expressive power of deep neural networks and the cyclic dependency structure of MRF in a unified model, bringing the modeling capability to a new level. The feed-forward approximation also allows it to be efficiently learned from data.
We present a new class of MRF model whose potential functions are expressed by powerful fully-connected neurons. Through theoretical analysis, we draw close connections between probabilistic deep MRFs and end-to-end RNNs. To tackle the difficulty of inference in cyclic graphs, we derive a new framework that decouples a cyclic graph with multiple coupled acyclic passes.
1.8. Ya Jin, Stuart Geman. Context and Hierarchy in a Probabilistic Image Model // http://vision. stanford. edu/cs598_spring07/papers/JinGemanCVPR2006.pdf.
We propose a mathematical frame-work (a “composition machine”) for constructing probabilistic hierarchical image models, designed to accommodate arbitrary contextual relationships, and we build a demonstration system for reading Massachusetts license plates in an image set collected at Logan Airport. The demonstration system detects and correctly reads more than 98% of the plates, with a negligible rate of false detection. Unlike a formal grammar, the architecture of a composition machine does not exclude the sharing of sub-parts among multiple entities, and does not limit interpretations to single trees (e. g. a scene can have multiple license plates, or no plates at all). In this sense, the architecture is more like a general Bayesian network than a formal grammar. On the other hand, unlike a Bayesian network, the distribution is non-Markovian, and therefore more like a probabilistic context-sensitive grammar. The conceptualization and construction of a composition machine is facilitated by its formulation as the result of a series of non-Markovian perturbations of a “Markov backbone”.
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