nils-herrmann/clean_scirepeval huggingface dataset:
Integrating bottom-up/top-down for object recognition by data driven Markov chain Monte Carlo

This article presents a mathematical paradigm called Data Driven Markov Chain Monte Carlo (DDMCMC) for object recognition. The objectives of this paradigm are two-fold. Firstly, it realizes traditional "hypothesis-and-test" methods through well-balanced Markov chain Monte Carlo (MCMC) dynamics, thus it achieves robust and globally optimal solutions. Secondly, it utilizes data-driven (bottom-up) methods in computer vision, such as Hough transform and data clustering, to design effective transition probabilities for Markov chain dynamics. This drastically improves the effectiveness of traditional MCMC algorithms in terms of two standard metrics: "burn-in" period and "mixing" rate. The article proceeds in three steps. Firstly, we analyze the structures of the solution space /spl Omega/ for object recognition. /spl Omega/ is decomposed into a large number of subspaces of varying dimensions in a hierarchy. Secondly, we use data-driven techniques to compute importance proposal probabilities in these spaces, each expressed in a non-parametric form using weighted samples or particles. Thirdly, Markov chains are designed to travel in such heterogeneous structured solution space, with both jump and diffusion dynamics. We use possibly the simplest objects-the "/spl Psi/-world" as an example to illustrate the concepts, and we briefly present results on an application of traffic sign detection.
Exploring Texture Ensembles by Efficient Markov Chain Monte Carlo-Toward a 'Trichromacy' Theory of Texture

I E E E Trans on P A M ! , (accepted), 1999. Exploring Texture Ensembles by Efficient Markov Chain Monte Carlo - T o w a r d s a T r i e h r o m a e y T h e o r y of Texture Song C h u n Z h u , X i u Wen Liu, Ying Nian W u Abstract T h i s article presents a m a t h e m a t i c a l definition of texture - the Julesz ensemble 0(h), w h i c h is the set of a l l images (defined on Z ) that share identical statistics h. T h e n texture m o d e l i n g is posed as a n inverse problem: given a set of images sampled from a n u n k n o w n Julesz ensemble fi(h*), we search for the statistics h* w h i c h define the ensemble. A Julesz ensemble fi(h) has a n associated p r o b a b i l i t y d i s t r i b u t i o n g(I;h), w h i c h is uniform over the images i n the ensemble a n d has zero p r o b a b i l i t y outside. I n a c o m p a n i o n paper[32], q(I; h) is shown to be the limit distribution of the F R A M E ( F i l t e r , R a n d o m F i e l d , A n d M i n i m a x E n t r o p y ) model[35] as the image lattice A -~ 7r. T h i s conclusion establishes the intrinsic link between the scientific definition of texture o n Z models of texture o n finite lattices. a n d the m a t h e m a t i c a l It brings two advantages to computer vision. T h e engineering practice of synthesizing texture images by m a t c h i n g statistics has been put o n a m a t h e m a t i c a l foundation. 2). W e are released from the b u r d e n of learning the expensive F R A M E m o d e l i n feature pursuit, m o d e l selection a n d texture synthesis. In this paper, a n efficient M a r k o v chain M o n t e C a r l o a l g o r i t h m is proposed for s a m p l i n g Julesz ensembles. T h e a l g o r i t h m generates r a n d o m texture images by m o v i n g along the directions of filter coefficients a n d thus extends the t r a d i t i o n a l single site G i b b s sampler. T h i s paper also compares four p o p u l a r statistical measures i n the literature, namely, moments, rectified functions, m a r g i n a l histograms a n d joint histograms of linear filter responses i n terms of their descriptive abilities. O u r experiments suggest that a s m a l l number of bins i n m a r g i n a l histograms are sufficient for c a p t u r i n g a variety of texture patterns. W e illustrate our theory a n d a l g o r i t h m by successfully synthesizing a number of n a t u r a l textures.  G i b b s ensemble, Julesz ensemble, texture modeling, texture synthesis, M a r k o v chain M o n t e C a r l o . Song C h u n Z h u a n d X i u W e n L i u are w i t h the Department of C o m p u t e r a n d Informa- t i o n Sciences, T h e O h i o State University, C o l u m b u s , O H 43210. Y i n g N i a n W u is w i t h the Department of Statistics, U n i v e r s i t y of C a l i f o r n i a , Los Angeles, C A 90095.
Effective Bayesian inference by data-driven Markov chain Monte Carlo for object recognition and image segmentation

This article presents a mathematical paradigm called Data Driven Markov Chain Monte Carlo (DDMCMC) for effective stochastic inference in the Bayesian framework. We apply the DDMCMC paradigm to two typical problems in image analysis: object recognition and image segmentation. In both problems, the solution spaces are not only high dimensional but heterogeneously-structured in the sense that they are composed of many subspaces of varying dimensions. Each of the subspace is product of what we called the object spaces. The latter is further decomposed into the so-called atomic spaces. The DDMCMC paradigm simulates Markov chains for exploring the solution spaces using both jump and diffusion dynamics. Unlike traditional MCMC algorithms, the DDMCMC paradigm utilizes data driven (or bottom-up) techniques, such as Hough transform, edge detection, and color clustering, to design effective transition probabilities for Markov chain dynamics. This drastically improves the effectiveness of traditional MCMC algorithms in terms of two standard metrics: 'burn-in' period and 'mixing' rate. The article proceeds in three steps. Firstly, we analyze the structures of the solution space (Omega) for the two tasks. Secondly, we study how data-driven techniques are utilized to compute importance proposal probabilities in the solution spaces, the object spaces and atomic spaces. These proposal probabilities are expressed in non-parametric form using weighted samples or particles. Thirdly, we design Markov chains to travel in such heterogeneous structured solution space as an ergodic and reversible process. The paper first review the DDMCMC theory using a simple object recognition problem -- the (psi) -- world reported in , then we briefly introduce the results on image segmentation.
Embedding Gestalt Laws in Markov Random Fields

The goal of this paper is to study a mathematical framework of 2D object shape modeling and learning for middle level vision problems, such as image segmentation and perceptual organization. For this purpose, we pursue generic shape models which characterize the most common features of 2D object shapes. In this paper, shape models are learned from observed natural shapes based on a minimax entropy learning theory. The learned shape models are Gibbs distributions defined on Markov random fields (MRFs). The neighborhood structures of these MRFs correspond to Gestalt laws-colinearity, cocircularity, proximity, parallelism, and symmetry. Thus, both contour-based and region-based features are accounted for. Stochastic Markov chain Monte Carlo (MCMC) algorithms are proposed for learning and model verification. Furthermore, this paper provides a quantitative measure for the so-called nonaccidental statistics and, thus, justifies some empirical observations of Gestalt psychology by information theory. Our experiments also demonstrate that global shape properties can arise from interactions of local features.
Stochastic Jump-Diffusion Process for Computing Medial Axes in Markov Random Fields

Proposes a statistical framework for computing medial axes of 2D shapes. In the paper, the computation of medial axes is posed as a statistical inference problem not as a mathematical transform. The paper contributes to three aspects in computing medial axes. 1) Prior knowledge is adopted for axes and junctions so that axes around junctions are regularized. 2) Multiple interpretations of axes are possible, each being assigned a probability. 3) A stochastic jump-diffusion process is proposed for estimating both axes and junctions in Markov random fields. We argue that the stochastic algorithm for computing medial axes is compatible with existing algorithms for image segmentation, such as region growing, snake, and region competition. Thus, our method provides a new direction for computing medial axes from texture images. Experiments are demonstrated on both synthetic and real 2D shapes.
Equivalence of Julesz and Gibbs texture ensembles

Research on texture has been pursued along two different lines. The first line of research, pioneered by Julesz (1962), seeks the essential ingredients in terms of features and statistics in human texture perception. This leads us to a mathematical definition of texture as a Julesz ensemble. A Julesz ensemble is the maximum set of images that share the same value of some basic feature statistics as the image lattice /spl Lambda//spl rarr/Z/sup 2/, or equivalently it is a uniform distribution on this set. The second line of research studies statistical models, in particular, Markov random field (MRF) and FRAME models (Zhu et al., 1997), to characterize texture patterns locally. In this article, we bridge the two lines by the fundamental principle of equivalence of ensembles in statistical mechanics (Gibbs, 1902). We prove that 1) the conditional probability of an arbitrary image patch given its environment, under the Julesz ensemble or the uniform model, is inevitably a FRAME (MRF) model, and 2) the limit of the FRAME (MRF) model, which we called the Gibbs ensemble, is equivalent to a Julesz ensemble as /spl Lambda//spl rarr/Z/sup 2/. Thus the advantages of the two methodologies can be fully utilized.
Stochastic computation of medial axis in Markov random fields

In this paper the computation of medial axis is posed as a statistical inference problem not as a mathematical transform. This method provides answers to two essential problems in computing the medial axis representation. I) Prior knowledge are adopted for axes and junctions so that the axes around junctions become well defined. II) A stochastic jump-diffusion process is proposed for estimating medial axis in a Markov random field. We argue that the stochastic algorithm for computing medial axis is compatible with existing algorithms for image segmentation, such as snake and region competition. Thus it provides a new direction for computing medial axis from real textured images. Experiments ale demonstrated on both synthetic and real shapes.
Filters, Random Fields and Maximum Entropy (FRAME): Towards a Unified Theory for Texture Modeling

This article presents a statistical theory for texture modeling. This theory combines filtering theory and Markov random field modeling through the maximum entropy principle, and interprets and clarifies many previous concepts and methods for texture analysis and synthesis from a unified point of view. Our theory characterizes the ensemble of images I with the same texture appearance by a probability distribution f (I) on a random field, and the objective of texture modeling is to make inference about f (I), given a set of observed texture examples. In our theory, texture modeling consists of two steps. (1) A set of filters is selected from a general filter bank to capture features of the texture, these filters are applied to observed texture images, and the histograms of the filtered images are extracted. These histograms are estimates of the marginal distributions of f (I). This step is called feature extraction. (2) The maximum entropy principle is employed to derive a distribution p(I), which is restricted to have the same marginal distributions as those in (1). This p(I) is considered as an estimate of f (I). This step is called feature fusion. A stepwise algorithm is proposed to choose filters from a general filter bank. The resulting model, called FRAME (Filters, Random fields And Maximum Entropy), is a Markov random field (MRF) model, but with a much enriched vocabulary and hence much stronger descriptive ability than the previous MRF models used for texture modeling. Gibbs sampler is adopted to synthesize texture images by drawing typical samples from p(I), thus the model is verified by seeing whether the synthesized texture images have similar visual appearances to the texture images being modeled. Experiments on a variety of 1D and 2D textures are described to illustrate our theory and to show the performance of our algorithms. These experiments demonstrate that many textures which are previously considered as from different categories can be modeled and synthesized in a common framework.
GRADE: Gibbs reaction and diffusion equations

Recently there have been increasing interests in using nonlinear PDEs for applications in computer vision and image processing. In this paper, we propose a general statistical framework for designing a new class of PDEs. For a given application, a Markov random field model p(I) is learned according to the minimax entropy principle so that p(I) should characterize the ensemble of images in our application. P(I) is a Gibbs distribution whose energy terms can be divided into two categories. Subsequently the partial differential equations given by gradient descent on the Gibbs potential are essentially reaction-diffusion equations, where the energy terms in one category produce anisotropic diffusion while the inverted energy terms in the second category produce reaction associated with pattern formation. We call this new class of PDEs the Gibbs Reaction And Diffusion Equations-GRADE and we demonstrate experiments where GRADE are used for texture pattern formation, denoising, image enhancement, and clutter removal.
Prior Learning and Gibbs Reaction-Diffusion

This article addresses two important themes in early visual computation: it presents a novel theory for learning the universal statistics of natural images, and, it proposes a general framework of designing reaction-diffusion equations for image processing. We studied the statistics of natural images including the scale invariant properties, then generic prior models were learned to duplicate the observed statistics, based on minimax entropy theory. The resulting Gibbs distributions have potentials of the form U(I; /spl Lambda/, S)=/spl Sigma//sub /spl alpha/=1//sup k//spl Sigma//sub x,y//spl lambda//sup (/spl alpha/)/((F/sup (/spl alpha/)/*I)(x,y)) with S={F/sup (1)/, F/sup (2)/,...,F/sup (K)/} being a set of filters and /spl Lambda/={/spl lambda//sup (1)/(),/spl lambda//sup (2)/(),...,/spl lambda//sup (K)/()} the potential functions. The learned Gibbs distributions confirm and improve the form of existing prior models such as line-process, but, in contrast to all previous models, inverted potentials were found to be necessary. We find that the partial differential equations given by gradient descent on U(I; /spl Lambda/, S) are essentially reaction-diffusion equations, where the usual energy terms produce anisotropic diffusion, while the inverted energy terms produce reaction associated with pattern formation, enhancing preferred image features. We illustrate how these models can be used for texture pattern rendering, denoising, image enhancement, and clutter removal by careful choice of both prior and data models of this type, incorporating the appropriate features.
Modeling images and textures by minimax entropy

This article proposes a general theory and methodology, called the minimax entropy principle, for building statistical models for images (or signals) in a variety of applications. This principle consists of two parts. (1) Maximum entropy principle for feature binding (or fusion): for a given set of observed feature statistics, a distribution can be built to bind these feature statistics together by maximizing the entropy over all distributions that reproduce these feature statistics. The second part is the minimum entropy principle for feature selection: among all plausible sets of feature statistics, we choose the set whose maximum entropy distribution has the minimum entropy. Computational and inferential issues in both parts are addressed. The minimax entropy principle is then corrected by considering the sample variation in the observed feature statistics, and a novel information criterion is derived for feature selection. The minimax entropy principle is applied to texture modeling. Relationship between our theory and the mechanisms of neural computation is also discussed.
Learning generic prior models for visual computation

This paper presents a novel theory for learning generic prior models from a set of observed natural images based on a minimax entropy theory that the authors studied in modeling textures. We start by studying the statistics of natural images including the scale invariant properties, then generic prior models were learnt to duplicate the observed statistics. The learned Gibbs distributions confirm and improve the forms of existing prior models. More interestingly inverted potentials are found to be necessary, and such potentials form patterns and enhance preferred image features. The learned model is compared with existing prior models in experiments of image restoration.
Minimax Entropy Principle and Its Application to Texture Modeling

This article proposes a general theory and methodology, called the minimax entropy principle, for building statistical models for images (or signals) in a variety of applications. This principle consists of two parts. The first is the maximum entropy principle for feature binding (or fusion): for a given set of observed feature statistics, a distribution can be built to bind these feature statistics together by maximizing the entropy over all distributions that reproduce them. The second part is the minimum entropy principle for feature selection: among all plausible sets of feature statistics, we choose the set whose maximum entropy distribution has the minimum entropy. Computational and inferential issues in both parts are addressed; in particular, a feature pursuit procedure is proposed for approximately selecting the optimal set of features. The minimax entropy principle is then corrected by considering the sample variation in the observed feature statistics, and an information criterion for feature pursuit is derived. The minimax entropy principle is applied to texture modeling, where a novel Markov random field (MRF) model, called FRAME (filter, random field, and minimax entropy), is derived, and encouraging results are obtained in experiments on a variety of texture images. The relationship between our theory and the mechanisms of neural computation is also discussed.
The role of V1 in shape representation

The analysis of higher level global visual attributes such as geometric shapes is thought to be a function of specialist modules in the extrastriate cortices. However, V1 is unique because only in this area can one find cells tuned to orientation and other local features with the spatial precision needed for representing high resolution and geometric aspects of an image. Geometric computation that demands such resolution may need to involve V1 via feedback. V1 neurons are known to exhibit very different types of responses in the short latency (40–80 milliseconds post-stimulus time window) versus longer latencies (80–200 milliseconds)1–5 Here we report that the later part of V1 neurons’ responses is sensitive to geometric attributes of globally defined shapes. We propose a computational interpretation of these results.
Statistical and computational theories for image segmentation, texture modeling and object recognition

Presented in this thesis are the statistical theories and computational schemes for three fundamental problems in computational vision: image segmentation, texture modeling, and two dimensional object recognition. Though these problems can be studied separately, they, like many other vision problems, depend on each other, therefore if our objective is to build a consistent and sophisticated vision system, the solutions to these problems should obey a common theory. The first chapter of this thesis proposes a general unified theory and a computational framework for solving vision problems. Lying at the core of this unified theory is a pyramidal description scheme, where various visual concepts are described by random variables, continuous or discrete, in a hierarchic structure. Visual computation is then posed as a statistical inference problem according to the Bayesian theory. It suggests that given the observed images, we should be able to infer the random variables of various levels all together. This computational scheme automatically incorporates concepts like the multiple intermediate solutions and the top-down/bottom-up loop. Guided by this unified theory, an algorithm for image segmentation, called region competition, is proposed in chapter 2, This algorithm is derived by minimizing a generalized Bayes/MDL criterion using the variational principle. It combines the most attractive features of the existing algorithms such as snakes/balloons and region growing, and is also related to edge detection using filters. Hence addresses the existing 4 kinds of approaches to image segmentation as different aspect of the same problem. Then in chapter 3, a unified theory called FRAME (filters, random fields and maximum entropy) is proposed for texture modeling, and it combines filtering theory and random field modeling through the maximum entropy principle. It interprets many previous concepts and methods for texture analysis and synthesis from a unified point of view. A novel strategy for filter pursuit and probability approximation is also proposed in chapter 3. Chapter 4 reports a flexible object recognition and modeling system (FORMS) which represents and recognizes objects from their contours. This consists of a forward model for generating the shapes of animate objects which gives a formalism for solving the inverse problem-object recognition in a topdown/bottom-up loop. In FORMS, the forward model includes principal component analysis for shape deformation and stochastic grammar for shape generation. The inverse process includes a novel method for skeleton extraction and part segmentation.
FRAME: filters, random fields, and minimax entropy towards a unified theory for texture modeling

In this paper, a minimax entropy principle is studied, based on which a novel theory, called FRAME (Filters, Random fields And Minimax Entropy) is proposed for texture modeling. FRAME combines attractive aspects of two important themes in texture modeling: multi-channel filtering and Markov random field (MRF) modeling. It incorporates the responses of a set of well selected filters into the distribution over a random field and hence has a much stronger descriptive ability than the traditional MRF models. Furthermore, it interprets and clarifies many previous concepts and methods for texture analysis and synthesis from a unified point of view. Algorithms are proposed for probability inference, stochastic simulation and filter selection. Experiments on a variety of textures are described to illustrate our theory and to show the performance of our algorithms. These experiments demonstrate that many textures previously considered as different categories can be modeled and synthesized in a common framework.
Modelling Uncertainty in the Game of Go

Go is an ancient oriental game whose complexity has defeated attempts to automate it. We suggest using probability in a Bayesian sense to model the uncertainty arising from the vast complexity of the game tree. We present a simple conditional Markov random field model for predicting the pointwise territory outcome of a game. The topology of the model reflects the spatial structure of the Go board. We describe a version of the Swendsen-Wang process for sampling from the model during learning and apply loopy belief propagation for rapid inference and prediction. The model is trained on several hundred records of professional games. Our experimental results indicate that the model successfully learns to predict territory despite its simplicity.