A Stochastic Grammar of Images

This exploratory paper quests for a stochastic and context sensitive grammar of images. The grammar should achieve the following four objectives and thus serves as a unified framework of representation, learning, and recognition for a large number of object categories. (i) The grammar represents both the hierarchical decompositions from scenes, to objects, parts, primitives and pixels by terminal and non-terminal nodes and the contexts for spatial and functional relations by horizontal links between the nodes. It formulates each object category as the set of all possible valid configurations produced by the grammar. (ii) The grammar is embodied in a simple And-Or graph representation where each Or-node points to alternative sub-configurations and an And-node is decomposed into a number of components. This representation supports recursive top-down/bottom-up procedures for image parsing under the Bayesian framework and make it convenient to scale up in complexity. Given an input image, the image parsing task constructs a most probable parse graph on-the-fly as the output interpretation and this parse graph is a subgraph of the And-Or graph after making choice on the Or-nodes. (iii) A probabilistic model is defined on this And-Or graph representation to account for the natural occurrence frequency of objects and parts as well as their relations. This model is learned from a relatively small training set per category and then sampled to synthesize a large number of configurations to cover novel object instances in the test set. This generalization capability is mostly missing in discriminative machine learning methods and can largely improve recognition performance in experiments. (iv) To fill the well-known semantic gap between symbols and raw signals, the grammar includes a series of visual dictionaries and organizes them through graph composition. At the bottom-level the dictionary is a set of image primitives each having a number of anchor points with open bonds to link with other primitives. These primitives can be combined to form larger and larger graph structures for parts and objects. The ambiguities in inferring local primitives shall be resolved through top-down computation using larger structures. Finally these primitives forms a primal sketch representation which will generate the input image with every pixels explained. The proposal grammar integrates three prominent representations in the literature: stochastic grammars for composition, Markov (or graphical) models for contexts, and sparse coding with primitives (wavelets). It also combines the structure-based and appearance based methods in the vision literature. Finally the paper presents three case studies to illustrate the proposed grammar.Mathematic

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; Λ, S)=Σα=1kΣx,yλ (α)((F(α)*I)(x,y)) with S={F(1) , F(2),...,F(K)} being a set of filters and Λ={λ(1)(),λ(2)(),...,λ (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; Λ, 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 featuresMathematic

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.Mathematic

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.Mathematic

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.Mathematic

PHOTOCHEMISTRY OF PHYCOBILIPROTEINS

Native PEC from the cyanobacterium, Mastigocladus laminosus, and its isolated α-subunit show photoreversibly photochromic reactions with difference-maxima around 502 and 570 nm in the spectral region of the α-84 phycoviolobilin chromophore. (b) Native PEC and its β-subunit show little if any reversible photochemistry in the 600–620 nm region, where the phycocyanobilin chromophores on the β-subunit absorb maximally, (c) Reversible photochemistry is retained in ureadenatured PEC at pH = 7.0 or pH ≤ 3. The difference maxima are shifted to 510 and 600 nm, and the amplitudes are decreased. An irreversible absorbance increase occurs around 670 nm (pH ≤ 3). (d) The amplitude of the reversible photoreaction difference spectrum is maximum in the presence of 4–5 M urea or 1 M KSCN, conditions known to dissociate phycobiliprotein aggregates into monomers. At the same time, the phycocyanobilin chromophore(s) are bleached irreversibly, (e) The amplitude becomes very small in high aggregates, e.g. in phycobilisomes. (f) In a reciprocal manner, the phototransformation of native PEC leads to a reversible shift of its aggregation equilibrium between trimer and monomer. The latter is favored by orange, the former by green light, (g) It is concluded that the phycoviolobilin chromophore of PEC is responsible for reversible photochemistry in PEC, and that there is not only an influence of aggregation state on photochemistry, but also vice versa an effect of the status of the chromophore on aggregation state. This could constitute a primary signal in the putative function as sensory pigment, either directly, or indirectly via the release of other polypeptides, via photodynamic effects, or the like

Influence of chromophores on quarternary structure of phycobiliproteins from the cyanobacterium, Mastigocladus laminosus

Chromophores of C-phycocyanin and phycoerythrο-cyanin have been chemically modified by reduction to rubins , bleaching , photoisomerization , or perturbation with bulky substituents. Pigments containing modified chromophores, or hybrids containing modified and unmodified chromophores in individual protomers have been prepared. All modifications inhibit the association of the (aß)-protomers of these pigments to higher aggregates. The results demonstrate a pronounced effect of the state of the chromophores on biliprotein quaternary structure. It may be important in phycobi1isome assembly , and also in the dual function of biliproteins as (i) antenna pigments for photosynthesis and (ii) reaction centers for photomor-phogenesis

Gluteus maximus transfer for hip abductor deficiency

Hip abductor deficiency resulting from gluteus medius and minimus pathology is increasingly recognized as a generator of lateral-sided hip pain. In the setting of a failed gluteus medius repair or in patients with irreparable tears, transfer of the anterior portion of the gluteus maximus muscle can be performed to treat gluteal abductor deficiency. The classic description of the gluteus maximus transfer technique relies solely on bone tunnel fixation. This article describes a reproducible technique that incorporates the addition of a distal row to the tendon transfer, which may improve fixation by both compressing the tendon transfer to the greater trochanter and providing improved biomechanical strength to the transfer

A Note on Encodings of Phylogenetic Networks of Bounded Level

Driven by the need for better models that allow one to shed light into the question how life's diversity has evolved, phylogenetic networks have now joined phylogenetic trees in the center of phylogenetics research. Like phylogenetic trees, such networks canonically induce collections of phylogenetic trees, clusters, and triplets, respectively. Thus it is not surprising that many network approaches aim to reconstruct a phylogenetic network from such collections. Related to the well-studied perfect phylogeny problem, the following question is of fundamental importance in this context: When does one of the above collections encode (i.e. uniquely describe) the network that induces it? In this note, we present a complete answer to this question for the special case of a level-1 (phylogenetic) network by characterizing those level-1 networks for which an encoding in terms of one (or equivalently all) of the above collections exists. Given that this type of network forms the first layer of the rich hierarchy of level-k networks, k a non-negative integer, it is natural to wonder whether our arguments could be extended to members of that hierarchy for higher values for k. By giving examples, we show that this is not the case