Perceiving edge blur: Gaussian-derivative filtering and a rectifying nonlinearity

We studied the visual mechanisms that encode edge blur in images. Our previous work suggested that the visual system spatially differentiates the luminance profile twice to create the `signature' of the edge, and then evaluates the spatial scale of this signature profile by applying Gaussian derivative templates of different sizes. The scale of the best-fitting template indicates the blur of the edge. In blur-matching experiments, a staircase procedure was used to adjust the blur of a comparison edge (40% contrast, 0.3 s duration) until it appeared to match the blur of test edges at different contrasts (5% - 40%) and blurs (6 - 32 min of arc). Results showed that lower-contrast edges looked progressively sharper. We also added a linear luminance gradient to blurred test edges. When the added gradient was of opposite polarity to the edge gradient, it made the edge look progressively sharper. Both effects can be explained quantitatively by the action of a half-wave rectifying nonlinearity that sits between the first and second (linear) differentiating stages. This rectifier was introduced to account for a range of other effects on perceived blur (Barbieri-Hesse and Georgeson, 2002 Perception 31 Supplement, 54), but it readily predicts the influence of the negative ramp. The effect of contrast arises because the rectifier has a threshold: it not only suppresses negative values but also small positive values. At low contrasts, more of the gradient profile falls below threshold and its effective spatial scale shrinks in size, leading to perceived sharpening.

The primal sketch revisited: locating and representing edges in human vision via Gaussian-derivative filtering

Marr's work offered guidelines on how to investigate vision (the theory - algorithm - implementation distinction), as well as specific proposals on how vision is done. Many of the latter have inevitably been superseded, but the approach was inspirational and remains so. Marr saw the computational study of vision as tightly linked to psychophysics and neurophysiology, but the last twenty years have seen some weakening of that integration. Because feature detection is a key stage in early human vision, we have returned to basic questions about representation of edges at coarse and fine scales. We describe an explicit model in the spirit of the primal sketch, but tightly constrained by psychophysical data. Results from two tasks (location-marking and blur-matching) point strongly to the central role played by second-derivative operators, as proposed by Marr and Hildreth. Edge location and blur are evaluated by finding the location and scale of the Gaussian-derivative `template' that best matches the second-derivative profile (`signature') of the edge. The system is scale-invariant, and accurately predicts blur-matching data for a wide variety of 1-D and 2-D images. By finding the best-fitting scale, it implements a form of local scale selection and circumvents the knotty problem of integrating filter outputs across scales. [Supported by BBSRC and the Wellcome Trust]

The interrogation and multiplexing of long period grating curvature sensors using a Bragg grating based, derivative spectroscopy technique

A long period grating is interrogated with a fibre Bragg grating using a derivative spectroscopy technique. A quasi-linear relationship between the output of the sensing scheme and the curvature experienced by the long period grating is demonstrated, with a sensitivity of 5.05 m and with an average curvature resolution of 2.9 × 10-2 m-1. In addition, the feasibility of multiplexing an in-line series of long period gratings with this interrogation scheme is demonstrated with two pairs of fibre Bragg gratings and long period gratings. With this arrangement the cross-talk error between channels was less than ± 2.4 × 10-3 m-1.

Mach bands and multiscale models of spatial vision:the role of first, second, and third derivative operators in encoding bars and edges

Ernst Mach observed that light or dark bands could be seen at abrupt changes of luminance gradient in the absence of peaks or troughs in luminance. Many models of feature detection share the idea that bars, lines, and Mach bands are found at peaks and troughs in the output of even-symmetric spatial filters. Our experiments assessed the appearance of Mach bands (position and width) and the probability of seeing them on a novel set of generalized Gaussian edges. Mach band probability was mainly determined by the shape of the luminance profile and increased with the sharpness of its corners, controlled by a single parameter (n). Doubling or halving the size of the images had no significant effect. Variations in contrast (20%-80%) and duration (50-300 ms) had relatively minor effects. These results rule out the idea that Mach bands depend simply on the amplitude of the second derivative, but a multiscale model, based on Gaussian-smoothed first- and second-derivative filtering, can account accurately for the probability and perceived spatial layout of the bands. A key idea is that Mach band visibility depends on the ratio of second- to first-derivative responses at peaks in the second-derivative scale-space map. This ratio is approximately scale-invariant and increases with the sharpness of the corners of the luminance ramp, as observed. The edges of Mach bands pose a surprisingly difficult challenge for models of edge detection, but a nonlinear third-derivative operation is shown to predict the locations of Mach band edges strikingly well. Mach bands thus shed new light on the role of multiscale filtering systems in feature coding. © 2012 ARVO.

The interrogation and multiplexing of long period grating curvature sensors using a Bragg grating based, derivative spectroscopy technique

A long period grating is interrogated with a fibre Bragg grating using a derivative spectroscopy technique. A quasi-linear relationship between the output of the sensing scheme and the curvature experienced by the long period grating is demonstrated, with a sensitivity of 5.05 m and with an average curvature resolution of 2.9 × 10-2 m-1. In addition, the feasibility of multiplexing an in-line series of long period gratings with this interrogation scheme is demonstrated with two pairs of fibre Bragg gratings and long period gratings. With this arrangement the cross-talk error between channels was less than ± 2.4 × 10-3 m-1.

The nitric oxide-donating pravastatin derivative, NCX 6550 [(1S-[1α(βS*, δS*), 2α, 6α, 8β-(R*), 8aα]]-1,2,6,7,8,8a-hexahydro-β, δ, 6-trihydroxy-2-methyl-8-(2-methyl-1-oxobutoxy)-1-naphtalene-heptanoic acid 4-(nitrooxy)butyl ester)], reduces splenocyte adhesion and reactive oxygen species generation in normal and atherosclerotic mice

Statins possess anti-inflammatory effects that may contribute to their ability to slow atherogenesis, whereas nitric oxide (NO) also influences inflammatory cell adhesion. This study aimed to determine whether a novel NO-donating pravastatin derivative, NCX 6550 [(1S-[1∝(ßS*,dS*),2∝,6a∝,8ß-(R*),8a∝]]-1,2,6,7,8,8a-hexahydro-ß,δ,6-trihydroxy-2-methyl-8-(2-methyl-1-oxobutoxy)-1-naphthalene-heptanoic acid 4-(nitrooxy)butyl ester)], has greater anti-inflammatory properties compared with pravastatin in normal and atherosclerotic apolipoprotein E receptor knockout (ApoE-/-) mice. C57BL/6 and ApoE-/- mice were administered pravastatin (40 mg/kg), NCX 6550 (48.5 mg/kg), or vehicle orally for 5 days. Ex vivo studies assessed splenocyte adhesion to arterial segments and splenocyte reactive oxygen species (ROS) generation. NCX 6550 significantly reduced splenocyte adhesion to artery segments in both C57BL/6 (8.8 ± 1.9% versus 16.6 ± 6.7% adhesion; P < 0.05) and ApoE-/- mice (9.3 ± 2.9% versus 23.4 ± 4.6% adhesion; P < 0.05) concomitant with an inhibition of endothelial intercellular adhesion molecule-1 expression. NCX 6550 also significantly reduced phorbol 12-myristate 13-acetate-induced ROS production that was enhanced in isolated ApoE-/- splenocytes. Conversely, pravastatin had no significant effects on adhesion in normal or ApoE-/- mice but reduced the enhanced ROS production from ApoE-/- splenocytes. In separate groups of ApoE-/- mice, NCX 6550 significantly enhanced endothelium-dependent relaxation to carbachol in aortic segments precon-tracted with phenylephrine (-logEC50, 6.37 ± 0.37) compared with both vehicle-treated (-logEC50, 5.81 ± 0.15; P < 0.001) and pravastatin-treated (-logEC50, 5.57 ± 0.45; P < 0.05) mice. NCX 6550 also significantly reduced plasma monocyte chemoattractant protein-1 levels (648.8 pg/ml) compared with both vehicle (1191.1 pg/ml; P < 0.001) and pravastatin (847 ± 71.0 pg/ml; P < 0.05) treatment. These data show that NCX 6550 exerts superior anti-inflammatory actions compared with pravastatin, possibly through NO-related mechanisms.

Thermal degradation of a brominated bisphenol a derivative

The thermal degradation of 2,6,2',6'-tetrabromo-4,4-pm-isoproylidene-di phenol (tetrabromobisphenol A) (TBBPA) has been investigated and a mechanism for its thermal degradation is suggested. TBBPA is a comonomer widely used in epoxy and in unsaturated polyester resins to impart fire retardance. These resins find a common use in electric and electronic equipment. The presence of bromine atoms is the key factor in fire retardant activity, while on the other hand it represents an ecological problem when pyrolytic recycling is programmed at the end of the useful life of such items. However, pyrolysis is the more advantageous recycling system for thermosetting resins and thus efforts should be made to control the pyrolysis in order to avoid or minimize the development of toxics. Homolytic scission of the aromatic bromine and condensation of aromatic bromine with phenolic hydroxyl are the main processes occuring in the range 270-340°C. A large amount of charred residue is left as a consequence of condensation reactions. HBr and brominated phenols and bisphenols are the main volatile products formed. Brominated dibenzodioxins structures are included in the charred residue and not evolved in the volatile phases.

Existence and Uniqueness of Solutions for Partial Differential-Functional Equations of the First Order with Deviating Argument of the Derivative of Unknown Function

We consider the existence and uniqueness problem for partial differential-functional equations of the first order with the initial condition for which the right-hand side depends on the derivative of unknown function with deviating argument.

Cauchy Problem for Differential Equation with Caputo Derivative

The paper is devoted to the study of the Cauchy problem for a nonlinear differential equation of complex order with the Caputo fractional derivative. The equivalence of this problem and a nonlinear Volterra integral equation in the space of continuously differentiable functions is established. On the basis of this result, the existence and uniqueness of the solution of the considered Cauchy problem is proved. The approximate-iterative method by Dzjadyk is used to obtain the approximate solution of this problem. Two numerical examples are given.

Cauchy-Type Problem for Diffusion-Wave Equation with the Riemann-Liouville Partial Derivative

2000 Mathematics Subject Classification: 35A15, 44A15, 26A33

Nonexistence Results of Solutions of Semilinear Differential Inequalities with Temperal Fractional Derivative on the Heinsenberg Group

2000 Mathematics Subject Classification: 26A33, 33C60, 44A15, 35K55

Impulsive Fractional Differential Inclusions Involving the Caputo Fractional Derivative

Mathematics Subject Classification: 26A33, 34A37.

Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative

2000 Math. Subject Classification: 26A33; 33E12, 33E30, 44A15, 45J05