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.

The interaction of luminance and texture amplitude in surface depth perception

Previous studies have suggested separate channels for detection of first-order luminance modulations (LM) and second-order modulations of the local amplitude (AM) of a texture. Mixtures of LM and AM with different phase relationships appear very different: in-phase compounds (LM + AM) look like 3-D corrugated surfaces, while out-of-phase compounds (LM - AM) appear flat and/or transparent. This difference may arise because the in-phase compounds are consistent with multiplicative shading, while the out-of-phase compounds are not. We investigated the role of these modulation components in surface depth perception. We used a textured background with thin bars formed by local changes in luminance and/or texture amplitude. These stimuli appear as embossed surfaces with wide and narrow regions. Keeping the AM modulation depth fixed at a suprathreshold level, we determined the amount of luminance contrast required for observers to correctly indicate the width (narrow or wide) of 'raised' regions in the display. Performance (compared to the LM-only case) was facilitated by the presence of AM, but, unexpectedly, performance for LM - AM was as good as for LM + AM. Thus, these results suggest that there is an interaction between first-order and second-order mechanisms during depth perception based on shading cues, but the phase dependence is not yet understood.

The interaction of luminance and texture amplitude in depth perception

Previous studies have suggested separate channels for the detection of first-order luminance (LM) and second-order modulations of the local amplitude (AM) of a texture (Schofield and Georgeson, 1999 Vision Research 39 2697 - 2716; Georgeson and Schofield, 2002 Spatial Vision 16 59). It has also been shown that LM and AM mixtures with different phase relationships are easily separated in identification tasks, and (informally) appear very different with the in-phase compound (LM + AM), producing the most realistic depth percept. We investigated the role of these LM and AM components in depth perception. Stimuli consisted of a noise texture background with thin bars formed as local increments or decrements in luminance and/or noise amplitude. These stimuli appear as embossed surfaces with wide and narrow regions. When luminance and amplitude changes have the same sign and magnitude (LM + AM) the overall modulation is consistent with multiplicative shading, but this is not so when the two modulations have opposite sign (LM - AM). Keeping the AM modulation depth fixed at a suprathreshold level, we determined the amount of luminance contrast required for observers to correctly indicate the width (narrow or wide) of raised regions in the display. Performance (compared to the LM-only case) was facilitated by the presence of AM, but, unexpectedly, performance for LM - AM was even better than for LM + AM. Further tests suggested that this improvement in performance is not due to an increase in the detectability of luminance in the compound stimuli. Thus, contrary to previous findings, these results suggest the possibility of interaction between first-order and second-order mechanisms in depth perception.

Resistance heating of steel conductors of circular cross-section

The object of this thesis is to develop a method for calculating the losses developed in steel conductors of circular cross-section and at temperatures below 100oC, by the direct passage of a sinusoidally alternating current. Three cases are considered. 1. Isolated solid or tubular conductor. 2. Concentric arrangement of tube and solid return conductor. 3. Concentric arrangement of two tubes. These cases find applications in process temperature maintenance of pipelines, resistance heating of bars and design of bus-bars. The problems associated with the non-linearity of steel are examined. Resistance heating of bars and methods of surface heating of pipelines are briefly described. Magnetic-linear solutions based on Maxwell's equations are critically examined and conditions under which various formulae apply investigated. The conditions under which a tube is electrically equivalent to a solid conductor and to a semi-infinite plate are derived. Existing solutions for the calculation of losses in isolated steel conductors of circular cross-section are reviewed, evaluated and compared. Two methods of solution are developed for the three cases considered. The first is based on the magnetic-linear solutions and offers an alternative to the available methods which are not universal. The second solution extends the existing B/H step-function approximation method to small diameter conductors and to tubes in isolation or in a concentric arrangement. A comprehensive experimental investigation is presented for cases 1 and 2 above which confirms the validity of the proposed methods of solution. These are further supported by experimental results reported in the literature. Good agreement is obtained between measured and calculated loss values for surface field strengths beyond the linear part of the d.c. magnetisation characteristic. It is also shown that there is a difference in the electrical behaviour of a small diameter conductor or thin tube under resistance or induction heating conditions.

Vibrational methods applied to NDT testing and fluid density measurement

A system for the NDI' testing of the integrity of conposite materials and of adhesive bonds has been developed to meet industrial requirements. The vibration techniques used were found to be applicable to the development of fluid measuring transducers. The vibrational spectra of thin rectangular bars were used for the NDT work. A machined cut in a bar had a significant effect on the spectrum but a genuine crack gave an unambiguous response at high amplitudes. This was the generation of fretting crack noise at frequencies far above that of the drive. A specially designed vibrational decrement meter which, in effect, measures mechanical energy loss enabled a numerical classification of material adhesion to be obtained. This was used to study bars which had been flame or plasma sprayed with a variety of materials. It has become a useful tool in optimising coating methods. A direct industrial application was to classify piston rings of high performance I.C. engines. Each consists of a cast iron ring with a channel into which molybdenum, a good bearing surface, is sprayed. The NDT classification agreed quite well with the destructive test normally used. The techniques and equipment used for the NOT work were applied to the development of the tuning fork transducers investigated by Hassan into commercial density and viscosity devices. Using narrowly spaced, large area tines a thin lamina of fluid is trapped between them. It stores a large fraction of the vibrational energy which, acting as an inertia load reduces the frequency. Magnetostrictive and piezoelectric effects together or in combination enable the fork to be operated through a flange. This allows it to be used in pipeline or 'dipstick' applications. Using a different tine geometry the viscosity loading can be predoninant. This as well as the signal decrement of the density transducer makes a practical viscometer.

The control of alkali silica reaction using blended cements

It has been previously established that alkali silica reaction (ASR) in concrete may be controlled by blending Portland cement with suitable hydraulic or pozzolanic materials. The controlling mechanism has been attributed to the dilution of the cement's alkali content and reduced mobility of ions in concrete's pore solution. In this project an attempt has been made to identify the factors which influence the relative importance of each mechanism in the overall suppression of the reaction by the use of blended cements. The relationship between the pore solution alkalinity and ASR was explored by the use of expansive mortar bars submerged in alkaline solutions of varying concentration. This technique enabled the blended cement's control over expansion to be assessed at given `pore solution' alkali concentrations. It was established that the cement blend, the concentration and quantity of alkali present in the pore solution were the factors which determined the rate and extent of ASR. The release of alkalis into solution by Portland cements of various alkali content was studied by analysis of pore solution samples expressed from mature specimens. The specification for avoiding ASR by alkali limitation, both by alkali content of cement and the total quantity of alkali were considered. The effect on the pore solution alkalinity when a range of Portland cements were blended with various replacement materials was measured. It was found that the relationship between the type of replacement material, its alkali content and that of the cement were the factors which primarily determined the extent of the pore solution alkali dilution effect. It was confirmed that salts of alkali metals of the kinds found as common concrete contaminants were able to increase the pore solution hydroxyl ion concentration significantly. The increase was limited by the finite anion complexing ability of the cement.

Chloride resistance and durability of cement paste and concrete containing metakaolin

Metakaolin (MK), a calcined clay, was included as a partial cement replacement material, at up to 20% by weight of binder, in cement pastes and concrete, and its influence on the resistance to chloride ingress investigated. Reductions in effective chloride diffusion coefficients through hardened cement paste were obtained for binary blends and by combining OPC, MK and a second cement replacement material of pulverised fuel ash or ground granulated blast furnace slag. Steady state oxygen diffusion measurements through hardened cement pastes measured using an electrochemical cell showed that the interaction between charged species and the pore surfaces is a major factor in determining chloride diffusion rate. Rheology of the binder, particularly at high MK replacement levels, was found to have a dramatic influence on the diffusion performance of cement pastes. It was concluded that plasticising admixtures are essential for adequate dispersion of MK in cement pastes. Chloride concentration profile analysis of the concrete cylinders, exposed to sodium chloride solution for one year, was employed to obtain apparent chloride diffusion coefficients for concrete specimens. MK was found to reduce the depth of chloride penetration into concrete when compared with that of unblended mixes. Corrosion rate and corrosion potential measurements were taken on steel bars embedded in concrete exposed to a saline environment under conditions of cyclic wetting and drying. The initiation time for corrosion was found to be significantly longer for MK blended mixes than for plain OPC systems. The aggregate-paste interfacial zone of MK blended systems was investigated by steady state diffusion of chloride ions through mortar containing glass beads as model aggregate. For the model aggregate specimens tested the work confirmed the hypothesis that properties of the bulk paste are the controlling factors in ionic diffusion through mortar.

Corrosion inhibitors for the rehabilitation of reinforced concrete

Four corrosion inhibitors namely sodium nitrite, sodium monofluorophosphate, ethanolamine and an alkanolamine-based mixture were studied by immersing mild steel bars for 42 days in model electrolytes of varied pH and chloride concentration which were intended to simulate the pore solution phase present within carbonated and/or chloride-contaminated concrete. Site trials were carried out on sodium monofluorophosphate and the alkanolamine-based inhibitor to study their depth of penetration into concrete. The influence of various carbonating atmospheres on the pore solution chemistry and microstructure of hydrated cement paste was investigated. Physical realkalisation of carbonated cement paste and a calcium nitrite-based corrosion rehabilitation system for chloride-contaminated cement paste were investigated by monitoring ionic transport within the pore solution phase of laboratory specimens. The main findings were as follows: 1,Sodium nitrite, sodium monofluorophosphate, ethanolamine and the alkanolamine-based mixture all behaved as passivating anodic inhibitors of steel corrosion in air-saturated aqueous solutions of varied pH and chloride concentration. 2,Sodium monofluorophosphate failed to penetrate significantly into partially carbonated site concrete when applied as recommended by the supplier. Phosphate and fluoride penetrated 5mm into partially carbonated site concrete treated with sodium monofluorophosphate. 3,The ethanolamine component of the alkanolamine-based inhibitor was found to have penetrated significant depths into partially carbonated site concrete. 4,Carbonating hydrated cement paste over saturated solutions of sodium nitrite resulted in significant concentrations of nitrite in the pore solution of the carbonated paste. Saturated solutions of sodium chloride, ammonium nitrate, magnesium nitrate and sodium dichromate were investigated and identified as alternatives for controlling the relative humidity of the carbonating environment. 5,Hardened carbonated cement paste can by physically realkalised to a limited extent due to the diffusion of hydroxyl ions under saturated conditions. A substantial proportion of the hydroxyl ions that diffused into the carbonated cement paste however, became bound into the cement matrix. Hydroxyl ion concentrations remained below 5mmol/l within the pore solution of the realkalised cement paste. 6, Nitrite ions penetrated significant distances by diffusion within the pore solution of saturated uncarbonated hydrated cement paste.

The strength of column-to-foundation joints in reinforced concrete

This thesis is concerned with the experimental and theoretical investigation into the compression bond of column longitudinal reinforcement in the transference of axial load from a reinforced concrete column to a base. Experimental work includes twelve tests with square twisted bars and twenty four tests with ribbed bars. The effects of bar size, anchorage length in the base, plan area of the base, provision of bae tensile reinforcement, links around the column bars in the base, plan area of column and concrete compressive strength were investigated in the tests. The tests indicated that the strength of the compression anchorage of deformed reinforcing steel in the concrete was primarily dependent on the concrete strength and the resistance to bursting, which may be available within the anchorage . It was shown in the tests without concreted columns that due to a large containment over the bars in the foundation, failure occurred due to the breakdown of bond followed by the slip of the column bars along the anchorage length. The experimental work showed that the bar size , the stress in the bar, the anchorage length, provision of the transverse steel and the concrete compressive strength significantly affect the bond stress at failure. The ultimate bond stress decreases as the anchorage length is increased, while the ultimate bond stress increases with increasing each of the remainder parameters. Tests with concreted columns also indicated that a section of the column contributed to the bond length in the foundation by acting as an extra anchorage length. The theoretical work is based on the Mindlin equation( 3), an analytical method used in conjunction with finite difference calculus. The theory is used to plot the distribution of bond stress in the elastic and the elastic-plastic stage of behaviour. The theory is also used to plot the load-vertical displacement relationship of the column bars in the anchorage length, and also to determine the theoretical failure load of foundation. The theoretical solutions are in good agreement with the experimental results and the distribution of bond stress is shown to be significantly influenced by the bar stiffness factor K. A comparison of the experimental results with the current codes shows that the bond stresses currently used are low and in particular, CPIlO(56) specifies very conservative design bond stresses .

Effect of poor curing conditions and remedies on the durability of steel in concrete

An investigation was undertaken to study the effect of poor curing simulating hot climatic conditions and remedies on the durability of steel in concrete. Three different curing environments were used i.e. (1) Saturated Ca(OH)2 solution at 20°C, (2) Saturated Ca(OH)2 solution at 50°C and (3) Air at 50°C at 30% relative humidity. The third curing condition corresponding to the temperature and relative humidity typical of Middle Eastern Countries. The nature of the hardened cement paste matrix, cured under the above conditions was studied by means of Mercury Intrusion Porosimetry for measuring pore size distribution. The results were represented as total pore volume and initial pore entry diameter. The Scanning Electron Microscope was used to look at morphological changes during hydration, which were compared to the Mercury Intrusion Porosimetry results. X-ray defraction and Differential Thermal Analysis techniques were also employed for looking at any phase transformations. Polymer impregnation was used to reduce the porosity of the hardened cement pastes, especially in the case of the poorly cured samples. Carbonation rates of unimpregnated and impregnated cements were determined. Chloride diffusion studies were also undertaken to establish the effect of polymer impregnation and blending of the cements. Finally the corrosion behaviour of embedded steel bars was determined by the technique of Linear Polarisation. The steel was embedded in both untreated and polymer impregnated hardened cement pastes placed in either a solution containing NaCl or an environmental cabinet which provided carbonation at 40°C and 50% relative humidity.

Control of soundness and mechanical properties in aluminium-silicon-magnesium alloys

Previously, specifications for mechanical properties of casting alloys were based on separately cast test bars. This practice provided consistently reproducible results; thus, any change in conditions was reflected in changes in the mechanical properties of the test coupons. These test specimens, however, did not necessarily reflect the actual mechanical properties of the castings they were supposed to represent'. Factors such as section thickness and casting configuration affect the solidification rate and soundness of the casting thereby raising or lowering its mechanical properties in comparison with separately cast test specimens. In the work now reported, casting shapes were developed to investigate the variations of section thickness, chemical analysis and heat treatment on the mechanical properties of a high strength Aluminium alloy under varying chilling conditions. In addition, an insight was sought into the behaviour of chills under more practical conditions. Finally, it was demonstrated that additional information could be derived from the radiographs which form an essential part of the quality control of premium quality castings. As a result of the work, it is now possible to select analysis and chilling conditions to optimize the as cast and the heat treated mechanical properties of Aluminum 7% Silicon 0.3% Magnesium alloy.

Vibration in electromagnetically heated steel

When a ferromagnetic steel billet was heated by induction a large increase in the amplitude of longitudinal vibration frequently occurred as a result of resonance. This happened when a natural frequency of the bar coincided with twice the heating frequency or multiples thereof. The temperature at which resonance occurred depended on a number of factors including billet length and heating power. Resonance was most often observed when the surface temperature of the billet reached the Curie point. It is well established that magnetostrictive vibrations occur in a ferromagnetic material subjected to an alternating electromagnetic field, but existing data suggests that linear magnetostriction decreases towards the Curie point. Linear magnetostriction was measured in a sample of mild steel up to 800ºC using a high temperature strain gauge. The magnetostriction constant 100 was calculated assuming an average grain orientation in mild steel. The data was found to be comparable to that published for single crystals of iron. It was discovered that linear magnetostriction was responsible for resonance below 600ºC but not for temperatures near the Curie point. Other possible causes of resonance such as forces produced by the interaction between eddy currents and the alternating electromagnetic field, the alpha to gamma phase transformation and the existence of a thin ferromagnetic layer were investigated. None were found to account for resonance in bars of mild steel heated by induction. Experimental work relating to the induction heating of steel is compared to previous work on the subject of electromagnetic generation of ultrasound where a similar increase of the amplitude of longitudinal waves in steel is reported at the Curie point. It is concluded that the two phenomena are related as they show strong similarities.

Wear of high aluminium zinc-based alloys in plain bearing applications

Two zinc-based alloys of high aluminium content, Super Cosmal alloy containing 60% Al, 6% Si, 1% Cu, 0.3% Mn and HAZCA alloy containing 60% Al, 8% Si, 2% Cu, 0.06% Mg were produced by sand casting. Foundry characteristics in particular, fluidity, mode of solidification and feeding ability were examined. Metallographic analysis of structures was carried out using optical and scanning electron microscopy and their mechanical properties were determined using standard techniques. Dry wear characteristics were determined using a pin-on-disc test, and boundary-lubricated wear was studied using full bearing tests. Results from casting experiments were evaluated and compared with the behaviour of a standard ZA-27 alloy and those from tribological tests with both ZA-27 alloy and a leaded tin-bronze (SAE660) under the same testing conditions. The presence of silicon was beneficial, reducing the temperature range of solidification, improving feeding efficiency and reducing gravity segregation of phases. Use of chills and melt degassing was found necessary to achieve soundness and enhanced mechanical properties. Dry wear tests were performed against a steel counterface for sliding speeds of 0.25, 0.5, 1.0 and 2 m/s and for a range of loads up to 15 kgf. The high aluminium alloys showed wear rates as low as those of ZA-27 at speeds of 0.25 and 0.5 m/s for the whole range of applied loads. ZA-27 performed better at higher speeds. The build up of a surface film on the wearing surface of the test pins was found to be responsible for the mild type of wear of the zinc based alloys. The constitution of the surface film was determined as a complex mixture of aluminium, zinc and iron oxides and metallic elements derived from both sliding materials. For full bearing tests, bushes were machined from sand cast bars and were tested against a steel shaft in the presence of a light spindle oil as the lubricant. Results showed that all zinc based alloys run-in more rapidly than bronze, and that wear in Super Cosmal and HAZCA alloys after prolonged running were similar to those in ZA-27 bearings and significantly smaller than those of the bronze.

Low level feature detection in human vision

Influential models of edge detection have generally supposed that an edge is detected at peaks in the 1st derivative of the luminance profile, or at zero-crossings in the 2nd derivative. However, when presented with blurred triangle-wave images, observers consistently marked edges not at these locations, but at peaks in the 3rd derivative. This new phenomenon, termed ‘Mach edges’ persisted when a luminance ramp was added to the blurred triangle-wave. Modelling of these Mach edge detection data required the addition of a physiologically plausible filter, prior to the 3rd derivative computation. A viable alternative model was examined, on the basis of data obtained with short-duration, high spatial-frequency stimuli. Detection and feature-making methods were used to examine the perception of Mach bands in an image set that spanned a range of Mach band detectabilities. A scale-space model that computed edge and bar features in parallel provided a better fit to the data than 4 competing models that combined information across scale in a different manner, or computed edge or bar features at a single scale. The perception of luminance bars was examined in 2 experiments. Data for one image-set suggested a simple rule for perception of a small Gaussian bar on a larger inverted Gaussian bar background. In previous research, discriminability (d’) has typically been reported to be a power function of contrast, where the exponent (p) is 2 to 3. However, using bar, grating, and Gaussian edge stimuli, with several methodologies, values of p were obtained that ranged from 1 to 1.7 across 6 experiments. This novel finding was explained by appealing to low stimulus uncertainty, or a near-linear transducer.

The slope of the psychometric function and non-stationarity of thresholds in spatiotemporal contrast vision

The slope of the two-interval, forced-choice psychometric function (e.g. the Weibull parameter, ß) provides valuable information about the relationship between contrast sensitivity and signal strength. However, little is known about how or whether ß varies with stimulus parameters such as spatiotemporal frequency and stimulus size and shape. A second unresolved issue concerns the best way to estimate the slope of the psychometric function. For example, if an observer is non-stationary (e.g. their threshold drifts between experimental sessions), ß will be underestimated if curve fitting is performed after collapsing the data across experimental sessions. We measured psychometric functions for 2 experienced observers for 14 different spatiotemporal configurations of pulsed or flickering grating patches and bars on each of 8 days. We found ß ˜ 3 to be fairly constant across almost all conditions, consistent with a fixed nonlinear contrast transducer and/or a constant level of intrinsic stimulus uncertainty (e.g. a square law transducer and a low level of intrinsic uncertainty). Our analysis showed that estimating a single ß from results averaged over several experimental sessions was slightly more accurate than averaging multiple estimates from several experimental sessions. However, the small levels of non-stationarity (SD ˜ 0.8 dB) meant that the difference between the estimates was, in practice, negligible.