Invariant Index Research Articles

Effects of surface reflectance on local second order shape estimation in dynamic scenes

In dynamic scenes, relative motion between the object, the observer, and/or the environment projects as dynamic visual information onto the retina (optic flow) that facilitates 3D shape perception. When the object is diffusely reflective, e.g. a matte painted surface, this optic flow is directly linked to object shape, a property found at the foundations of most traditional shape-from-motion (SfM) schemes. When the object is specular, the corresponding specular flow is related to shape curvature, a regime change that challenges the visual system to determine concurrently both the shape and the distortions of the (sometimes unknown) environment reflected from its surface. While human observers are able to judge the global 3D shape of most specular objects, shape-from-specular-flow (SFSF) is not veridical. In fact, recent studies have also shown systematic biases in the perceived motion of such objects. Here we focus on the perception of local shape from specular flow and compare it to that of matte-textured rotating objects. Observers judged local surface shape by adjusting a rotation and scale invariant shape index probe. Compared to shape judgments of static objects we find that object motion decreases intra-observer variability in local shape estimation. Moreover, object motion introduces systematic changes in perceived shape between matte-textured and specular conditions. Taken together, this study provides a new insight toward the contribution of motion and surface material to local shape perception.

Моделирование рыночного потребительского спроса и анали тические индексы спроса

The paper describes the essence of crisis state of the neoclassical theory of consumer demand and a way to overcome the crisis based on the concept of statistical «assembly» of consumers as an origin of the theory of aggregate market demand. Market demand is modeled via utility maximization problem elaborated in frame of the neoclassical paradigm for an individual consumer. The nonparametric demand analysis is used for testing the adequacy of such a model to the trade statistics. Analytical index numbers of consumers' demand and their variants, invariant and quasi-invariant indices, are presented. The use of nonparametric demand analysis is based on real trade statistics of food products in the Russian Federation, and the quasi-invariant indices are constructed.

Second geometric-arithmetic index and general sum connectivity index of molecule graphs with special structure

Second geometric-arithmetic index and general sum connectivity index as molecular graph invariant topological indices have been studied in recent years for prediction of chemical phenomena. In this paper, we determine the second geometric-arithmetic index and general sum connectivity index of molecular graph with special structures. At last, as supplemental results, we present the general geometric-arithmetic indices of certain molecular graphs.

The pixel rectangle index used in object based building extraction from high resolution images

An improved high resolution object-based building extraction method based on Pixel Rectangle Index is presented in this paper. We use Minimum Span Tree optimal theory to realize object-based high resolution image segmentation. First, we proposed a rotation invariant Pixel Rectangle Index by introducing the principal direction of homogeneous area. Second, we improved the calculation of edge-weight by introducing the band-weight and Pixel Rectangle Index. The QuickBird high resolution images were used to do the building extraction experiment. The experiment result proved that this method can obtain high extraction accuracy and this algorithm can be efficiently used in remote sensing images.

Plausibility Tracking: A method to evaluate anatomical connectivity and microstructural properties along fiber pathways

Diffusion MRI is a non-invasive method that potentially gives insight into the brain's white matter structure regarding the pathway of connections and properties of the axons.Here, we propose a novel global tractography method named Plausibility Tracking that provides the most plausible pathway, modeled as a smooth spline curve, between two locations in the brain. Compared to other tractography methods, plausibility tracking combines the more complete connectivity pattern of probabilistic tractography with smooth tracks that are globally optimized using the fiber orientation density function and hence is relatively robust against local noise and error propagation. It has been tested on phantom and biological data and compared to other methods of tractography. Plausibility tracking provides reliable local directions all along the fiber pathways which makes it especially interesting for tract-based analysis in combination with direction dependent indices of diffusion MRI.In order to demonstrate this potential of plausibility tracking, we propose a framework for the assessment and comparison of diffusion derived tissue properties. This framework comprises atlas-guided parameterization of tract representation and advanced bundle-specific indices describing fiber density, fiber spread and white matter complexity. We explore the new method using real data and show that it allows for a more specific interpretation of the white matter's microstructure compared to rotationally invariant indices derived from the diffusion tensor.

Dynamic base-age invariant site index models for Tectona grandis in peninsular India

Data from 27 remeasured sample plots were used to evaluate dynamic base-age invariant site index models for teak (Tectona grandis) forests in Karnataka, India. The data were obtained in observational field studies covering a wide range of sites in Karnataka and provided up to three interval measurements per plot. All the functions were fitted simultaneously using iterative seemingly unrelated regression and a base-age-invariant method. The model evaluation criteria were bias, root mean square error and the adjusted coefficient of determination. The best results were obtained with the generalised algebraic difference equations derived from the Korf base model. The selected model accounted for 99.8% of the total variance in height–age relationships in dominant trees. The dynamic base-age invariant site index model proved to be effective and accurate in presenting polymorphic site index curves with multiple asymptotes. The new dynamic base-age invariant site index models based on generalised algebraic difference approach (GADA) methodology can be recommended for dominant height prediction and forest site quality evaluations in the teak forests in Karnataka, India.

Dynamic base-age invariant site index models based on generalized algebraic difference approach for mixed Scots pine (Pinus sylvestris L.) and Oriental beech (Fagus orientalis Lipsky) stands

Data from stem analysis of 397 dominant trees (198 Scots pine and 199 Oriental beech) were used to evaluate dynamic base-age invariant site index models derived from Bertalanffy-Richards, Hossfeld, and Lundqvist-Korf functions with the generalized algebraic difference approach (GADA) for mixed Scots pine (Pinus sylvestris L.) and Oriental beech (Fagus orientalis Lipsky) stands. These functions were compared with respect to residuals of these models; specifically, the evaluation criteria were bias (E), root mean square error (RMSE), absolute mean error (AME), adjusted coefficient of determination (R2adj), and Akaike information criterion. The best results were obtained with generalized algebraic difference equations derived from the base models of Bertalanffy-Richards for Oriental beech and Hossfeld for Scots pine. These selected models accounted for 95%-96% of the total variance in height-age relationships in dominant trees with bias of 0.049841 and 0.00171, RMSE of 1.55624 and 1.353736, AME of 0.940128 and 0.884034, and AIC of 723.55 and 1250.78 for Scots pine and Oriental beech, respectively. These dynamic base-age invariant site index models for the 2 tree species presented more effective and accurate polymorphic site index curves with multiple asymptotes than earlier site index models for Oriental beech and Scots pine. The important differences of height growth trend between developed base-age invariant site index models in this study and earlier site curves were determined by graphical comparisons for site index predictions. Therefore, the new dynamic base-age invariant site index models developed based on GADA methodology can be recommended for dominant height prediction and forest site quality evaluations in the mixed stands of these 2 species.

Influence of MODIS-Derived Dynamic Vegetation on VIC-Simulated Soil Moisture in Oklahoma

Abstract Soil moisture–vegetation interactions are an important component of land–atmosphere coupling, especially in semiarid regions such as the North American Great Plains. However, many land surface models parameterize vegetation using an interannually invariant leaf area index (LAI). This study quantifies how utilizing a dynamic vegetation parameter in the variability infiltration capacity (VIC) hydrologic model influences model-simulated soil moisture. Accuracy is assessed using in situ soil moisture observations from 20 stations from the Oklahoma Mesonet. Results show that VIC simulations generated with an interannually variant LAI parameter are not consistently more accurate than those generated with the invariant (static) LAI parameter. However, the static LAI parameter tends to overestimate LAI during anomalously dry periods. This has the greatest influence on the accuracy of the soil moisture simulations in the deeper soil layers. Soil moisture drought, as simulated with the static LAI parameter, tends to be more severe and persist for considerably longer than drought simulated using the interannually variant LAI parameter. Dynamic vegetation parameters can represent interannual variations in vegetation health and growing season length. Therefore, simulations with a dynamic LAI parameter better capture the intensity and duration of drought conditions and are recommended for use in drought monitoring.

Rapidly reconfigurable optically induced photonic crystals in hot rubidium vapor

Through periodic index modulation, we create two different types of photonic structures in a heated rubidium vapor for controlled reflection, transmission and diffraction of light. The modulation is achieved through the use of the AC Stark effect resulting from a standing-wave control field. The periodic intensity structures create translationally invariant index profiles analogous to photonic crystals in spectral regions of steep dispersion. Experimental results are consistent with modeling.

New paradigms for the integration of yaw stability and rollover prevention functions in vehicle stability control

The integration of rollover prevention and yaw stability control objectives in electronic stability control (ESC) has traditionally been done based on a priority calculation. The control system nominally focuses on yaw stability control until a danger of rollover is detected. When a danger of rollover is detected, the control system switches from yaw stability control to rollover prevention. This paper focuses on an integrated ESC system wherein the objectives of yaw stability and rollover prevention are addressed simultaneously, rather than one at a time. First, we show that staying on a desired planar trajectory at a specified speed results in an invariant rollover index. This implies that rollover prevention can be achieved whenever there is a danger of rollover only by reducing vehicle speed, since changing the desired vehicle trajectory is not a desirable option. In this regard, it is shown that a vehicle that reduces its speed before entering a sharp curve performs significantly better than a vehicle that uses differential braking during the turn for yaw stability control. Second, this paper explores how the use of steer-by-wire technology can address the tradeoff between yaw stability, speed, and rollover prevention performance. It is shown that the use of traditional steer-by-wire simply as an additional actuator cannot by itself ameliorate the tradeoff. However, this tradeoff can be eliminated if steer-by-wire is used to invert the direction of the roll angle of the vehicle. A new steer-by-wire algorithm that uses transient countersteering is shown to change the location of the rollover dynamics from the neighborhood of an unstable to a stable equilibrium. In this case, a desired trajectory can indeed be achieved by the vehicle at the same speed with a much smaller danger of rollover. This is a novel and viable approach to integrating the yaw stability and rollover prevention functions and eliminating the inherent tradeoffs in the performance of both.

3-D Curvilinear Structure Detection Filter Via Structure-Ball Analysis

Curvilinear structure detection filters are crucial building blocks in many medical image processing applications, where they are used to detect important structures, such as blood vessels, airways, and other similar fibrous tissues. Unfortunately, most of these filters are plagued by an implicit single structure direction assumption, which results in a loss of signal around bifurcations. This peculiarity limits the performance of all subsequent processes, such as understanding angiography acquisitions, computing an accurate segmentation or tractography, or automatically classifying image voxels. This paper presents a new 3-D curvilinear structure detection filter based on the analysis of the structure ball, a geometric construction representing second order differences sampled in many directions. The structure ball is defined formally, and its computation on a discreet image is discussed. A contrast invariant diffusion index easing voxel analysis and visualization is also introduced, and different structure ball shape descriptors are proposed. A new curvilinear structure detection filter is defined based on the shape descriptors that best characterize curvilinear structures. The new filter produces a vesselness measure that is robust to the presence of X- and Y-junctions along the structure by going beyond the single direction assumption. At the same time, it stays conceptually simple and deterministic, and allows for an intuitive representation of the structure's principal directions. Sample results are provided for synthetic images and for two medical imaging modalities.

Mapping and monitoring the extent of submerged aquatic vegetation in the Laurentian Great Lakes with multi-scale satellite remote sensing

A satellite-based algorithm intended to map submerged aquatic vegetation (SAV), which was mostly the nuisance algae Cladophora, for the Laurentian Great Lakes has been developed and successfully demonstrated in test areas in Lakes Michigan and Ontario. The new Submerged Aquatic Vegetation Mapping Algorithm (SAVMA) first utilizes deep water (opaque) radiance values to correct shallow water values (transparent) so that depth invariant reflectance values for all three visible Landsat bands of the lake bottom can be classified. Combinations of two bands are then used to generate a depth invariant bottom type index. The algorithm then maps the lake bottom into three types: sand, dense SAV, less dense SAV by thresh-holding the depth invariant reflectance values. The SAVMA also generates a biomass estimate by assigning an average dry weight obtained by field sampling to both the dense and less dense SAV areas identified by the algorithm.The algorithm performance was successfully evaluated on Lake Michigan at the Sleeping Bear Dunes National Lakeshore (SBDNL) using Cladophora locations provided by diver survey as well as from an independent National Park Service monitoring. The SAVMA correctly mapped Cladophora to an approximate accuracy of 85%, where the misclassification was a result of mixed pixels due to the resolution of the Landsat data and imprecise atmospheric corrections. The algorithm was also successfully evaluated in Lake Ontario near Pickering, ON. The SAVMA was then used to generate both short and long term time-series analyses of Cladophora extent at SBDNL.

Examining Possible Construct Changes to a Licensure Test by Evaluating Equating Requirements

We demonstrate how to assess the potential changes to a test's score scale necessitated by changes to the test specifications when a field study is not feasible. We used a licensure test, which is currently under revision, as an example. We created two research forms from an actual form of the test. One research form was developed with the current specifications and the other was developed with the redesigned (new) specifications in terms of the proportion (not number) of items in each category. We examined whether the current and redesigned tests measure the same construct and have the same level of reliability. Then we used subpopulation invariance indices to assess the equatability of the redesigned test to the current test using data sets from actual operational administrations of the current test. The results suggest that the change in test specifications might be great enough that the current and redesigned test scores could not be considered exchangeable across the score range. However, the score scales for the two tests appear to coincide in the cut-score region.

Contrast and stability of the axon diameter index from microstructure imaging with diffusion MRI

The ActiveAx technique fits the minimal model of white matter diffusion to diffusion MRI data acquired using optimized protocols that provide orientationally invariant indices of axon diameter and density. We investigated how limitations of the available maximal gradient strength (Gmax) on a scanner influence the sensitivity to a range of axon diameters. Multishell high-angular-diffusion-imaging (HARDI) protocols for Gmax of 60, 140, 200, and 300 mT/m were optimized for the pulsed-gradient-spin-echo (PGSE) sequence. Data were acquired on a fixed monkey brain and Monte-Carlo simulations supported the results. Increasing Gmax reduces within-voxel variation of the axon diameter index and improves contrast beyond what is achievable with higher signal-to-noise ratio. Simulations reveal an upper bound on the axon diameter (∼10 μm) that pulsed-gradient-spin-echo measurements are sensitive to, due to a trade-off between short T2 and the long diffusion time needed to probe larger axon diameters. A lower bound (∼2.5 μm) slightly dependent on Gmax was evident, below which axon diameters are identifiable as small, but impossible to differentiate. These results emphasize the key-role of Gmax for enhancing contrast between axon diameter distributions and are, therefore, relevant in general for microstructure imaging methods and highlight the need for increased Gmax on future commercial systems.

Mapping of distributions of a local b‐matrix cross‐term strength using diffusion tensor MRI in patients with Alzheimerˈs disease

Mapping of the distribution of local susceptibility strength could be very important in understanding the mechanisms of progression in neurodegenerative diseases, due to depositions of iron and iron-containing plaques. The goal of this study is to map the voxelwise distribution of local cross-term b-value (b(c)) effect caused by interactions between the external and internal gradients, in subjects with Alzheimer's disease (AD), mild cognitive impairment (MCI), and cognitively normal (CN) elderly, using a diffusion tensor (DT) MRI. Two DT-MRI experiments were conducted with opposite polarities of the external diffusion-sensitizing gradients, and the authors modeled the 3 × 3 tensor matrix of b(c) maps and drove a rotationally independent mean b(c) (i.e., MB(c)) maps. To test whether AD has higher cross-term gradients than MCI and∕or CN, 15 AD patients, 18 MCI patients, and 16 CN controls were acquired from DT-MRI data, with six diffusion encoding directions, five b-values (0, 160, 360, 640, and 1000 s∕mm(2)), and positively and negatively alternating polarities of the external diffusion-sensitizing gradients. The b(c) and MB(c) maps were calculated and were spatially normalized into a study specific template for all subjects. The differences of MB(c) maps across the three subject groups were investigated with voxelwise one-way ANOVA tests for each b-value. The differences of MB(c) maps, among the four b-values, were also investigated with a voxelwise one-way within-subject ANOVA test for each group. The authors successfully mapped the local cross-term strength, using a DT-MRI data in the three groups. The MB(c) differences between the groups were increased with increasing b-values. Compared with the CN group and the MCI group, MB(c) values in the AD group were significantly increased. However, compared with the CN group, MB(c) values in the MCI group were not significantly different for all the b-values. In order to map the b-matrix cross-term effect, the authors developed a rotationally invariant index of MB(c), and the index was applied in AD, MCI, and CN subjects. In the AD group, compared with the MCI and CN groups, MB(c) values were increased. AD patients may have much more local intrinsic gradients in the brain than those MCI or CN subjects. MB(c) maps may be used to detect the intrinsically susceptible materials in the human brain, such as iron-containing plaques in the brain with AD.

A descriptor of amino acids SVWG and its applications in peptide QSAR

A descriptor, SVWG (principal component scores vector of WHIM (weighted holistic invariant molecular index) descriptors and GETWAY (GEometry, Topology, and Atom‐Weights AssemblY) descriptors), was derived from a principal component analysis of a matrix of two structural variables of coded amino acid. SVWG scales were then applied in three panels of peptide quantitative structure activity relationship (QSAR) that were molded by partial least squares regression. The obtained models with the correlation coefficient () and cross‐validation correlation coefficient () were 0.893 and 0.830 for angiotensin‐converting enzyme inhibitors, 0.990 and 0.968 for antimicrobial peptides, and 0.955 and 0.908 for oxytocin, respectively. Satisfactory results showed that information related to biological activity can be systemically expressed by SVWG scales, which may be a useful structural expression methodology for study on peptide QSAR. Copyright © 2012 John Wiley & Sons, Ltd.

Bessel Fourier Orientation Reconstruction (BFOR): An analytical diffusion propagator reconstruction for hybrid diffusion imaging and computation of q-space indices

The ensemble average propagator (EAP) describes the 3D average diffusion process of water molecules, capturing both its radial and angular contents. The EAP can thus provide richer information about complex tissue microstructure properties than the orientation distribution function (ODF), an angular feature of the EAP. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed, such as diffusion propagator imaging (DPI) and spherical polar Fourier imaging (SPFI). In this study, a new analytical EAP reconstruction method is proposed, called Bessel Fourier Orientation Reconstruction (BFOR), whose solution is based on heat equation estimation of the diffusion signal for each shell acquisition, and is validated on both synthetic and real datasets. A significant portion of the paper is dedicated to comparing BFOR, SPFI, and DPI using hybrid, non-Cartesian sampling for multiple b-value acquisitions. Ways to mitigate the effects of Gibbs ringing on EAP reconstruction are also explored. In addition to analytical EAP reconstruction, the aforementioned modeling bases can be used to obtain rotationally invariant q-space indices of potential clinical value, an avenue which has not yet been thoroughly explored. Three such measures are computed: zero-displacement probability (Po), mean squared displacement (MSD), and generalized fractional anisotropy (GFA).

Science Teachers’ Thinking About the Nature of Science: A New Methodological Approach to Its Assessment

This paper describes Spanish science teachers’ thinking about issues concerning the nature of science (NOS) and the relationships connecting science, technology, and society (STS). The sample consisted of 774 in-service and pre-service teachers. The participants responded to a selection of items from the Questionnaire of Opinions on Science, Technology & Society in a multiple response model. These data were processed to generate the invariant indices that are used as the bases for subsequent quantitative and qualitative analyses. The overall results reflect moderately informed conceptions, and a detailed analysis by items, categories, and positions reveals a range of positive and negative conceptions about the topics of NOS dealt with in the questionnaire items. The implications of the findings for teaching and teacher training on the themes of NOS are discussed.

Determining the Anchor Composition for a Mixed-Format Test: Evaluation of Subpopulation Invariance of Linking Functions

This study examined the appropriateness of the anchor composition in a mixed-format test, which includes both multiple-choice (MC) and constructed-response (CR) items, using subpopulation invariance indices. Linking functions were derived in the nonequivalent groups with anchor test (NEAT) design using two types of anchor sets: (a) MC only and (b) a mix of MC and CR. In each anchor condition, the linking functions were also derived separately for males and females, and those subpopulation functions were compared to the total group function. In the MC-only condition, the difference between the subpopulation functions and the total group function was not trivial in a score region that included cut scores, leading to inconsistent pass/fail decisions for low-performing examinees in particular. Overall, the mixed anchor was a better choice than the MC-only anchor to achieve subpopulation invariance between males and females. The research reinforces subpopulation invariance indices as a means of determining the adequacy of the anchor.

Symmetries and blow-up phenomena for a Dirichlet problem with a large parameter

\noindent For the Dirichlet problem $-\Delta u+\lambda V(x) u=u^p$ in $\Omega \subset \mathbb R^N$, $N\geq 3$, in the regime $\lambda \to +\infty$ we aim to give a description of the blow-up mechanism. For solutions with symmetries an uniform bound on the ``invariant Morse index provides a localization of the blow-up orbits in terms of c.p.'s of a suitable modified potential. The main difficulty here is related to the presence of fixed points for the underlying group action.