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Hyperspectral image visualization reduces color bands to three, but prevailing linear methods fail to address data characteristics, and nonlinear embeddings are computa- tionally demanding. Qualitative evaluation of embedding is also lacking. We propose faithful stochastic proximity embedding (FSPE), which is a scalable and nonlinear dimensionality re- duction method. FSPE considers the nonlinear characteristics of spectral signatures, yet it avoids the costly computation of geodesic distances that are often required by other nonlinear methods. Furthermore, we employ a pixelwise metric that measures the quality of hyperspectral image visualization at each pixel. FSPE outperforms the state-of-art methods by at least 12% on average and up to 25% in the qualitative measure. An implementation on graphics processing units is two orders of magnitude faster than the baseline. Our method opens the path to high-fidelity and real-time analysis of hyperspectral images.

A new nonlinear dimension reduction (DR) method which is called Trustworthy Stochastic Proximity Embedding (TSPE) is introduced in this paper to visualize different types of data sets. TSPE overcome the main shortcomings of the DR by sending the false neighbour points to the correct locations, and preserving the neighbourhood relation to the true neighbours, which are inside the local neighbourhood. The visualization of our proposed method displays the trustworthy, useful and meaningful colours, where the objects of the image can be easily distinguished. The performances of TSPE and 20 dimension reduction methods are compared, and the efficiency of the proposed method in both visualization accuracy and computational cost is shown. The results showed the ability of our method in preserving neighbourhood relation, where they revealed more interested information. In real data set, the efficiency of the visualization of tensor images data sets by TSPE might help the specialist to make a good decision about a patient’s treatment. The comparison with experimental data set, as three dimensions of curved cylinder, showed the ability of TSPE to unfold this complex data set efficiently whilst preserving most information of the original data set.

Previous empirical studies have shown that information along visual contours is known to be concentrated in regions of high magnitude of curvature, and, for closed contours, segments of negative curvature (i.e., concave segments) carry greater perceptual relevance than corresponding regions of positive curvature (i.e., convex segments). Lately, Feldman and Singh (2005, Psychological Review, 112, 243-252) proposed a mathematical derivation to yield information content as a function of curvature along a contour. Here, we highlight several fundamental errors in their derivation and in its associated implementation, which are problematic in both mathematical and psychological senses. Instead, we propose an alternative mathematical formulation for information measure of contour curvature that addresses these issues. Additionally, unlike in previous work, we extend this approach to 3-dimensional (3D) shape by providing a formal measure of information content for surface curvature and outline a modified version of the minima rule relating to part segmentation using curvature in 3D shape.

This paper investigates the stability of an automatic system for classifying kerogen material from images of sieved rock samples. The system comprises four stages: image acquisition, background removal, segmentation, and classification of the segmented kerogen pieces as either inertinite or vitrinite. Depending upon a segmentation parameter d, called “overlap”, touching pieces of kerogen may be split differently. The aim of this study is to establish how robust the classification result is to variations of the segmentation parameter. There are two issues that pose difficulties in carrying out an experiment. First, even a trained professional may be uncertain when distinguishing between isolated pieces of inertinite and vitrinite, extracted from transmitted-light microscope images. Second, because manual labelling of large amount of data for training the system is an arduous task, we acquired the true labels (ground truth) only for the pieces obtained at overlap d=0.5. To construct ground truth for various values of d we propose here label-inheritance trees. With thus estimated ground truth, an experiment was carried out to evaluate the robustness of the system to changes in the segmentation through varying the overlap value d. The average system accuracy across values of d spanning the range from 0 to 1 was 86.5%, which is only slightly lower than the accuracy of the system at the design value of d=0.5 (89.07%).

A forager in a patchy environment faces two types of uncertainty: ambiguity regarding the quality of the current patch and risk associated with the background opportunities. We argue that the order in which the forager deals with these uncertainties has an impact on the decision whether to stay at the current patch. The order effect is formalised with a context-dependent quantum probabilistic framework. Using Heisenberg's uncertainty principle, we demonstrate the two types of uncertainty cannot be simultaneously minimised, hence putting a formal limit on rationality in decision making. We show the applicability of the contextual decision function with agent-based modelling. The simulations reveal order-dependence. Given that foraging is a universal pattern that goes beyond animal behaviour, the findings help understand similar phenomena in other fields. Sponsorship:This work was partially supported by the European Commission Seventh Framework Programme under Grant Agreement Number FP7-601138 PERICLES. Xavier Rubio-Campillo is supported by the SimulPast Project (CSD2010-00034), funded by the CONSOLIDER-INGENIO2010 program of the Ministry of Science and Innovation -- Spain.

This article presents a new approach for Fourier-based modeling of bone anatomies for compression and smoothing. By treating the bone surface as a level set of a 31) scalar field, we can model topologically complex models such as bones. In particular, we experiment with five different alternatives, and prove that 31) scalar field which allows monotonous continuity around the boundary can be a good choice for volumetric description of the surface. This allows avoiding Gibbs phenomena which previous volume-based methods have suffered from, returning better results in compression and smoothing than other scalar fields. We demonstrate the efficacy of the proposed method by showing results with various bone data.

Classification of organic materials obtained from rock and drill cuttings involves finding multiple objects in the image. This task is usually approached by segmentation. The quality of segmentation is evaluated by matching the whole detected objects to a reference segmentation. We are interested in representing each object by a single reference point called the “centre”. This paper proposes an evaluation measure of image segmentation for such representation. We argue that measures based only on distance between obtained centres and a set of predefined centres are insufficient. The proposed measure is based on a list of desirable properties of the segmentation. The three components of the measure evaluate the under/over segmentation of the objects, the proportion of centres placed in the background rather than in objects, and the distance between the guessed and the true centres. The ability of the measure to distinguish between segmentation results of different quality is illustrated on three sets of examples including an image containing microfossils and pieces of inert material.

Closed-form solutions for lowpass filtering of 3D digital geometry are presented. Conventional signal processing is difficult to apply since 3D digital geometry does not usually satisfy the prerequisites of regular sampling and global parameterisation. Representing digital geometry as a level set of a 3D scalar field fitted with Gaussians and polynomials, derived are closed-form solutions of convolution with Gaussian smoothing kernels and lowpass filtering without the pitfalls of other approaches are analytically achieved.

Convolutional radial basis function (RBF) networks are introduced for smoothing out irregularly sampled signals. The proposed technique involves training an RBF network and then convolving it with a Gaussian smoothing kernel in an analytical manner. Since the convolution results in an analytic form, the computation necessary for numerical convolution is avoided. Convolutional RBF networks need training only once, do not depend on any particular details of the training methods used, and different degrees of smoothing are immediately available.