Mach edges: local features predicted by 3rd derivative spatial filtering

Edges are key points of information in visual scenes. One important class of models supposes that edges correspond to the steepest parts of the luminance profile, implying that they can be found as peaks and troughs in the response of a gradient (1st derivative) filter, or as zero-crossings in the 2nd derivative (ZCs). We tested those ideas using a stimulus that has no local peaks of gradient and no ZCs, at any scale. The stimulus profile is analogous to the Mach ramp, but it is the luminance gradient (not the absolute luminance) that increases as a linear ramp between two plateaux; the luminance profile is a blurred triangle-wave. For all image-blurs tested, observers marked edges at or close to the corner points in the gradient profile, even though these were not gradient maxima. These Mach edges correspond to peaks and troughs in the 3rd derivative. Thus Mach edges are inconsistent with many standard edge-detection schemes, but are nicely predicted by a recent model that finds edge points with a 2-stage sequence of 1st then 2nd derivative operators, each followed by a half-wave rectifier.

Mach edges: a critical test of the nonlinear 3rd derivative model for edge-detection

Feature detection is a crucial stage of visual processing. In previous feature-marking experiments we found that peaks in the 3rd derivative of the luminance profile can signify edges where there are no 1st derivative peaks nor 2nd derivative zero-crossings (Wallis and George 'Mach edges' (the edges of Mach bands) were nicely predicted by a new nonlinear model based on 3rd derivative filtering. As a critical test of the model, we now use a new class of stimuli, formed by adding a linear luminance ramp to the blurred triangle waves used previously. The ramp has no effect on the second or higher derivatives, but the nonlinear model predicts a shift from seeing two edges to seeing only one edge as the added ramp gradient increases. In experiment 1, subjects judged whether one or two edges were visible on each trial. In experiment 2, subjects used a cursor to mark perceived edges and bars. The position and polarity of the marked edges were close to model predictions. Both experiments produced the predicted shift from two to one Mach edge, but the shift was less complete than predicted. We conclude that the model is a useful predictor of edge perception, but needs some modification.

Third-derivative filters predict edge locations in spatial vision

Edge detection is crucial in visual processing. Previous computational and psychophysical models have often used peaks in the gradient or zero-crossings in the 2nd derivative to signal edges. We tested these approaches using a stimulus that has no such features. Its luminance profile was a triangle wave, blurred by a rectangular function. Subjects marked the position and polarity of perceived edges. For all blur widths tested, observers marked edges at or near 3rd derivative maxima, even though these were not 1st derivative maxima or 2nd derivative zero-crossings, at any scale. These results are predicted by a new nonlinear model based on 3rd derivative filtering. As a critical test, we added a ramp of variable slope to the blurred triangle-wave luminance profile. The ramp has no effect on the (linear) 2nd or higher derivatives, but the nonlinear model predicts a shift from seeing two edges to seeing one edge as the ramp gradient increases. Results of two experiments confirmed such a shift, thus supporting the new model. [Supported by the Engineering and Physical Sciences Research Council].

Added luminance ramp alters perceived edge blur and contrast:A critical test for derivative-based models of edge coding

In many models of edge analysis in biological vision, the initial stage is a linear 2nd derivative operation. Such models predict that adding a linear luminance ramp to an edge will have no effect on the edge's appearance, since the ramp has no effect on the 2nd derivative. Our experiments did not support this prediction: adding a negative-going ramp to a positive-going edge (or vice-versa) greatly reduced the perceived blur and contrast of the edge. The effects on a fairly sharp edge were accurately predicted by a nonlinear multi-scale model of edge processing [Georgeson, M. A., May, K. A., Freeman, T. C. A., & Hesse, G. S. (in press). From filters to features: Scale-space analysis of edge and blur coding in human vision. Journal of Vision], in which a half-wave rectifier comes after the 1st derivative filter. But we also found that the ramp affected perceived blur more profoundly when the edge blur was large, and this greater effect was not predicted by the existing model. The model's fit to these data was much improved when the simple half-wave rectifier was replaced by a threshold-like transducer [May, K. A. & Georgeson, M. A. (2007). Blurred edges look faint, and faint edges look sharp: The effect of a gradient threshold in a multi-scale edge coding model. Vision Research, 47, 1705-1720.]. This modified model correctly predicted that the interaction between ramp gradient and edge scale would be much larger for blur perception than for contrast perception. In our model, the ramp narrows an internal representation of the gradient profile, leading to a reduction in perceived blur. This in turn reduces perceived contrast because estimated blur plays a role in the model's estimation of contrast. Interestingly, the model predicts that analogous effects should occur when the width of the window containing the edge is made narrower. This has already been confirmed for blur perception; here, we further support the model by showing a similar effect for contrast perception. © 2007 Elsevier Ltd. All rights reserved.

Mach edges: a key role for 3rd derivative filters in spatial vision

Edges are key points of information in visual scenes. One important class of models supposes that edges correspond to the steepest parts of the luminance profile, implying that they can be found as peaks and troughs in the response of a gradient (first-derivative) filter, or as zero-crossings (ZCs) in the second-derivative. A variety of multi-scale models are based on this idea. We tested this approach by devising a stimulus that has no local peaks of gradient and no ZCs, at any scale. Our stimulus profile is analogous to the classic Mach-band stimulus, but it is the local luminance gradient (not the absolute luminance) that increases as a linear ramp between two plateaux. The luminance profile is a smoothed triangle wave and is obtained by integrating the gradient profile. Subjects used a cursor to mark the position and polarity of perceived edges. For all the ramp-widths tested, observers marked edges at or close to the corner points in the gradient profile, even though these were not gradient maxima. These new Mach edges correspond to peaks and troughs in the third-derivative. They are analogous to Mach bands - light and dark bars are seen where there are no luminance peaks but there are peaks in the second derivative. Here, peaks in the third derivative were seen as light-to-dark edges, troughs as dark-to-light edges. Thus Mach edges are inconsistent with many standard edge detectors, but are nicely predicted by a new model that uses a (nonlinear) third-derivative operator to find edge points.

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.

Base modified peptidic nucleic acids: synthesis and crystallographic analysis of intermediates

Peptidic Nucleic Acids (PNAs) are achiral, uncharged nucleic add mimetics, with a novel backbone composed of N-(2-aminoethyl)glycine units attached to the DNA bases through carboxymethylene linkers. With the aim of extending and improving upon the molecular recognition properties of PNAs, the aim of this work was to synthesjse PNA building block intermediates containing a series of substituted purine bases for subsequent use in automated PNA synthesis. Four purine bases: 2,6~diaminopurine (D), isoGuanine (isoG), xanthine (X) and hypoxanthine (H) were identified for incorporation into PNAs targeted to DNA, with the promise of increased hybrid stability over extended pH ranges together with improvements over the use of adenine (A) in duplex formation, and cytosine (C) in triplex formation. A reliable, high-yielding synthesis of the PNA backbone component N -('2- butyloxycarbonyl-aminoethyl)glycinate ethyl ester was establishecl. The precursor N~(2-butyloxycarbonyl)amino acetonitrile was crystallised and analysed by X-ray crystallography for the first time. An excellent refinement (R = 0.0276) was attained for this structure, allowing comparisons with known analogues. Although chemical synthesis of pure, fully-characterised PNA monomers was not achieved, chemical synthesis of PNA building blocks composed of diaminopurine, xanthine and hypoxanthine was completely successful. In parallel, a second objective of this work was to characterise and evaluate novel crystalline intermediates, which formed a new series of substituted purine bases, generated by attaching alkyl substituents at the N9 or N7 sites of purine bases. Crystallographic analysis was undertaken to probe the regiochemistry of isomers, and to reveal interesting structural features of the new series of similarly-substituted purine bases. The attainment of the versatile synthetic intermediate 2,6-dichloro~9- (carboxymethyl)purine ethyl ester, and its homologous regioisomers 6-chloro~9- (carboxymethyl)purine ethyl ester and 6-chloro-7-(carboxymethyl)purine ethyl ester, necessitated the use of X-ray crystallographic analysis for unambiguous structural assignment. Successful refinement of the disordered 2,6-diamino-9-(carboxymethyl) purine ethyl ester allowed comparison with the reported structure of the adenine analogue, ethyl adenin-9-yl acetate. Replacement of the chloro moieties with amino, azido and methoxy groups expanded the internal angles at their point of attachment to the purine ring. Crystallographic analysis played a pivotal role towards confirming the identity of the peralkylated hypoxanthine derivative diethyl 6-oxo-6,7-dihydro-3H-purlne~3,7~djacetate, where two ethyl side chains were found to attach at N3 and N7,

Chemical synthesis of isotopically labelled (M+4) purine nucleosides and their incorporation into DNA oligomers

Development of accurate and sensitive analytical methods to measure the level of biomarkers, such as 8-oxo-guanine or its corresponding nucleoside, 8-oxo-2’-deoxyguanosine, has become imperative in the study of DNA oxidative damage in vivo. Of the most promising techniques, HPLC-MS/MS, has many attractive advantages. Like any method that employs the MS technique, its accuracy depends on the use of multiply, isotopically-labelled internal standards. This project is aimed at making available such internal standards. The first task was to synthesise the multiply, isotopically-labelled bases (M+4) guanine and (M+4) 8-oxo-guanine. Synthetic routes for both (M+4) guanine and (M+4) 8-oxo-guanine were designed and validated using the unlabelled compounds. The reaction conditions were also optimized during the “dry runs”. The amination of the 4-hydroxy-2,6-dichloropyrimidine, appeared to be very sensitive to the purity of the commercial [15]N benzylamine reagent. Having failed, after several attempts, to obtain the pure reagent from commercial suppliers, [15]N benzylamine was successfully synthesised in our laboratory and used in the first synthesis of (M+4) guanine. Although (M+4) bases can be, and indeed have been used as internal standards in the quantitative analysis of oxidative damage, they can not account for the errors that may occur during the early sample preparation stages. Therefore, internal standards in the form of nucleosides and DNA oligomers are more desirable. After evaluating a number of methods, an enzymatic transglycolization technique was adopted for the transfer of the labelled bases to give their corresponding nucleosides. Both (M+4) 2-deoxyguanosine and (M+4) 8-oxo-2’-deoxyguanosine can be purified on micro scale by HPLC. The challenge came from the purification of larger scale (>50 mg) synthesis of nucleosides. A gel filtration method was successfully developed, which resulted in excellent separation of (M+4) 2’-deoxyguanosine from the incubation mixture. The (M+4) 2’-deoxyguanosine was then fully protected in three steps and successfully incorporated, by solid supported synthesis, into a DNA oligomer containing 18 residues. Thus, synthesis of 8-oxo-deoxyguanosine on a bigger scale for its future incorporation into DNA oligomers is now a possibility resulting from this thesis work. We believe that these internal standards can be used to develop procedures that can make the measurement of oxidative DNA damage more accurate and sensitive.

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.