Curvature-based perceptual singularities and texture saliency with early vision mechanisms

Recent work has shown that salient perceptual singularities occur in visual textures even in the absence of feature gradients. In smoothly varying orientation-defined textures, these striking non-smooth percepts can be predicted from two texture curvatures, one tangential and one normal [Proc. Natl. Acad. Sci. USA103, 15704 (2006)]. We address the issue of detecting these perceptual singularities in a biologically plausible manner and present three different models to compute the tangential and normal curvatures using early cortical mechanisms. The first model relies on the response summation of similarly scaled even-symmetric simple cells at different positions by utilizing intercolumnar interactions in the primary visual cortex (V1). The second model is based on intracolumnar interactions in a two-layer mechanism of simple cells having the same orientation tuning but significantly different scales. Our third model uses a three-layer circuit in which both even-symmetric and odd-symmetric receptive fields (RFs) are used to compute all possible directional derivatives of the dominant orientation, from which the tangential and normal curvatures at each spatial position are selected using nonlinear shunting inhibition. We show experimental results of all three models, we outline an extension to oriented textures with multiple dominant orientations at each point, and we discuss how our results may be relevant to the processing of general textures.     

Stability and model selection in k-means clustering

Clustering stability methods are a family of widely used model selection techniques for data clustering. Their unifying theme is that an appropriate model should result in a clustering which is robust with respect to various kinds of perturbations. Despite their relative success, not much is known theoretically on why or when do they work, or even what kind of assumptions they make in choosing an ‘appropriate’ model. Moreover, recent theoretical work has shown that they might ‘break down’ for large enough samples. In this paper, we focus on the behavior of clustering stability using k-means clustering. Our main technical result is an exact characterization of the distribution to which suitably scaled measures of instability converge, based on a sample drawn from any distribution in ? ⁿ satisfying mild regularity conditions. From this, we can show that clustering stability does not ‘break down’ even for arbitrarily large samples, at least for the k-means framework. Moreover, it allows us to identify the factors which eventually determine the behavior of clustering stability. This leads to some basic observations about what kind of assumptions are made when using these methods. While often reasonable, these assumptions might also lead to unexpected consequences.     

General Geometric Good Continuation: From Taylor to Laplace via Level Sets

Good continuation is the Gestalt observation that parts often group in particular ways to form coherent wholes. Perceptual integration of edges, for example, involves orientation good continuation, a property which has been exploited computationally very extensively. But more general local-global relationships, such as for shading or color, have been elusive. While Taylor’s Theorem suggests certain modeling and smoothness criteria, the consideration of level set geometry indicates a different approach. Using such first principles we derive, for the first time, a generalization of good continuation to all those visual structures that can be abstracted as scalar functions over the image plane. Based on second order differential constraints that reflect good continuation, our analysis leads to a unique class of harmonic models and a cooperative algorithm for structure inference. Among the different applications of good continuation, here we apply these results to the denoising of shading and intensity distributions and demonstrate how our approach eliminates spurious measurements while preserving both singularities and regular structure, a property that facilitates higher level processes which depend so critically on both of these classes of visual structures.     

[18F]PRIMATX,a New Positron Emission Tomography Tracer for Imaging of Autotaxin in Lung Tissue and Tumor-Bearing Mice

Autotaxin (ATX) is a secreted enzyme with tissue levels associated with tissue injury, which increase during wound healing and chronic fibrotic diseases. We selected [¹⁸F](R,E)-3-(4-chloro-2-((5-methyl-2H-tetrazol-2-yl)methyl)phenyl)-1-(4-((5-(2-fluoroethoxy)pyridin-2-yl)methyl)-2-methylpiperazin-1-yl)prop-2-en-1-one ([¹⁸F]PRIMATX, [¹⁸F] 2 ), a tracer for positron emission tomography, to image ATX expression in vivo. It successfully differentiates expression levels in lung tissue samples from idiopathic pulmonary fibrosis patients, and allows the detection of ATX-expressing tumors in living mice, confirming its potential for development as a clinical imaging agent.     

Physical, chemical and palynological characterization of avocado (Persea americana Mill.) honey in Israel

Various methods were used to characterize avocado honey in Israel. Perseitol, a unique sugar present only in avocado honey, served as an indicator for the degree of purity of avocado honey. Low avocado pollen counts made the common melissopalynology method ineffective at predicting the contribution of avocado nectar to honey. It was also found that the levels of fructose, sucrose and glucose do not uniquely characterize avocado honey. Potassium content and eight other minerals were linearly highly correlated to perseitol content. Moreover, pH level, absorbance and degree of darkness were significantly correlated to perseitol content, and can therefore be used to characterize avocado honey.     

Secure reliable multicast protocols in a WAN

Summary. A secure reliable multicast protocol enables a process to send a message to a group of recipients such that all correct destinations receive the same message, despite the malicious efforts of fewer than a third of the total number of processes, including the sender. This has been shown to be a useful tool in building secure distributed services, albeit with a cost that typically grows linearly with the size of the system. For very large networks, for which this is prohibitive, we present two approaches for reducing the cost: First, we show a protocol whose cost is on the order of the number of tolerated failures. Secondly, we show how relaxing the consistency requirement to a probabilistic guarantee can reduce the associated cost, effectively to a constant. Received: August 1997 / Accepted: July 1999     

Using AVL trees for fault-tolerant group key management

In this paper we describe an efficient algorithm for the management of group keys for group communication systems. Our algorithm is based on the notion of key graphs, previously used for managing keys in large Internet-protocol multicast groups. The standard protocol requires a centralized key server that has knowledge of the full key graph. Our protocol does not delegate this role to any one process. Rather, members enlist in a collaborative effort to create the group key graph. The key graph contains n keys, of which each member learns log₂n of them. We show how to balance the key graph, a result that is applicable to the centralized protocol. We also show how to optimize our distributed protocol, and provide a performance study of its capabilities. Published online: 26 October 2001     

Geometrically superresolved lensless imaging using a spatial light modulator

In this paper we introduce an imaging system based on a reflective phase-only spatial light modulator (SLM) in order to perform imaging with improved geometric resolution. By using the SLM, we combine the realization of two main abilities: a lens with a tunable focus and a phase function that, after proper free-space propagation, is projected as an amplitude distribution on top of the inspected object. The first ability is related to the realization of a lens function combined with a tunable prism that yields a microscanning of the inspected object. This by itself improves the spatial sampling density. The second ability is related to a projection of a phase function that is computed using an iterative beam-shaping Gerchberg-Saxton algorithm. After the free-space propagation from the SLM toward the inspected object, an amplitude pattern is generated on top of the object. This projected pattern and a set of low-resolution images with relative shift are interlaced and, after applying the proper regularization method, a geometrically superresolved image is reconstructed.     

Representation of graphs

Summary Given a formulation of a problem, a compact representation is required both for theoretical purposes — measuring the complexity of algorithms, and for practical purposes — data compression.The adjacency lists method for representing graphs is compared to the information theoretic lower bounds, and it is shown to be optimal in many instances. For n-vertex labeled planar graphs the adjacency lists method requires 3nlogn + O(n) bits, a linear algorithm is presented to obtain a 3/2nlogn + O(n) representation while nlogn + O(n) is shown to be the minimum.