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.

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.

From filters to features:Scale-space analysis of edge and blur coding in human vision

To make vision possible, the visual nervous system must represent the most informative features in the light pattern captured by the eye. Here we use Gaussian scale-space theory to derive a multiscale model for edge analysis and we test it in perceptual experiments. At all scales there are two stages of spatial filtering. An odd-symmetric, Gaussian first derivative filter provides the input to a Gaussian second derivative filter. Crucially, the output at each stage is half-wave rectified before feeding forward to the next. This creates nonlinear channels selectively responsive to one edge polarity while suppressing spurious or "phantom" edges. The two stages have properties analogous to simple and complex cells in the visual cortex. Edges are found as peaks in a scale-space response map that is the output of the second stage. The position and scale of the peak response identify the location and blur of the edge. The model predicts remarkably accurately our results on human perception of edge location and blur for a wide range of luminance profiles, including the surprising finding that blurred edges look sharper when their length is made shorter. The model enhances our understanding of early vision by integrating computational, physiological, and psychophysical approaches. © ARVO.

Perceiving edge contrast

We have shown previously that a template model for edge perception successfully predicts perceived blur for a variety of edge profiles (Georgeson, 2001 Journal of Vision 1 438a; Barbieri-Hesse and Georgeson, 2002 Perception 31 Supplement, 54). This study concerns the perceived contrast of edges. Our model spatially differentiates the luminance profile, half-wave rectifies this first derivative, and then differentiates again to create the edge's 'signature'. The spatial scale of the signature is evaluated by filtering it with a set of Gaussian derivative operators. This process finds the correlation between the signature and each operator kernel at each position. These kernels therefore act as templates, and the position and scale of the best-fitting template indicate the position and blur of the edge. Our previous finding, that reducing edge contrast reduces perceived blur, can be explained by replacing the half-wave rectifier with a smooth, biased rectifier function (May and Georgeson, 2003 Perception 32 388; May and Georgeson, 2003 Perception 32 Supplement, 46). With the half-wave rectifier, the peak template response R to a Gaussian edge with contrast C and scale s is given by: R=Cp-1/4s-3/2. Hence, edge contrast can be estimated from response magnitude and blur: C=Rp1/4s3/2. Use of this equation with the modified rectifier predicts that perceived contrast will decrease with increasing blur, particularly at low contrasts. Contrast-matching experiments supported this prediction. In addition, the model correctly predicts the perceived contrast of Gaussian edges modified either by spatial truncation or by the addition of a ramp.

Template model for blur coding: the role of early nonlinearity in edge segmentation

We describe a template model for perception of edge blur and identify a crucial early nonlinearity in this process. The main principle is to spatially filter the edge image to produce a 'signature', and then find which of a set of templates best fits that signature. Psychophysical blur-matching data strongly support the use of a second-derivative signature, coupled to Gaussian first-derivative templates. The spatial scale of the best-fitting template signals the edge blur. This model predicts blur-matching data accurately for a wide variety of Gaussian and non-Gaussian edges, but it suffers a bias when edges of opposite sign come close together in sine-wave gratings and other periodic images. This anomaly suggests a second general principle: the region of an image that 'belongs' to a given edge should have a consistent sign or direction of luminance gradient. Segmentation of the gradient profile into regions of common sign is achieved by implementing the second-derivative 'signature' operator as two first-derivative operators separated by a half-wave rectifier. This multiscale system of nonlinear filters predicts perceived blur accurately for periodic and aperiodic waveforms. We also outline its extension to 2-D images and infer the 2-D shape of the receptive fields.

Immunological and biochemical techniques in the analysis of tear proteins

This study is concerned with the analysis of tear proteins, paying particular attention to the state of the tears (e.g. non-stimulated, reflex, closed), created during sampling, and to assess their interactions with hydrogel contact lenses. The work has involved the use of a variety of biochemical and immunological analytical techniques for the measurement of proteins, (a), in tears, (b), on the contact lens, and (c), in the eluate of extracted lenses. Although a diverse range of tear components may contribute to contact lens spoilation, proteins were of particular interest in this study because of their theoretical potential for producing immunological reactions. Although normal host proteins in their natural state are generally not treated as dangerous or non-self, those which undergo denaturation or suffer a conformational change may provoke an excessive and unnecessary immune response. A novel on-lens cell based assay has been developed and exploited in order to study the role of the ubiquitous cell adhesion glycoprotein, vitronectin, in tears and contact lens wear under various parameters. Vitronectin, whose levels are known to increase in the closed eye environment and shown here to increase during contact lens wear, is an important immunoregulatory protein and may be a prominent marker of inflammatory activity. Immunodiffusion assays were developed and optimised for use in tear analysis, and in a series of subsequent studies used for example in the measurement of albumin, lactoferrin, IgA and IgG. The immunodiffusion assays were then applied in the estimation of the closed eye environment; an environment which has been described as sustaining a state of sub-clinical inflammation. The role and presence of a lesser understood and investigated protein, kininogen, was also estimated, in particular, in relation to contact lens wear. Difficulties arise when attempting to extract proteins from the contact lens in order to examine the individual nature of the proteins involved. These problems were partly alleviated with the use of the on-lens cell assay and a UV spectrophotometry assay, which can analyse the lens surface and bulk respectively, the latter yielding only total protein values. Various lens extraction methods were investigated to remove protein from the lens and the most efficient was employed in the analysis of lens extracts. Counter immunoelectrophoresis, an immunodiffusion assay, was then applied to the analysis of albumin, lactoferrin, IgA and IgG in the resultant eluates.

Synthesis of S6-(2,4-dinitrophenyl)-6-thioguanosine phosphoramidite and its incorporation into oligoribonucleotides

The preparation of N2-phenoxylacetyl-S 6-(2,4-dinitrophenyl)-6-thioguanosine phosphoramidite and its subsequent incorporation into oligoribonucleotides is described. The identity of the oligonucleotides was confirmed by UV spectrophotometry and nucleoside composition analysis. © 2003 Elsevier Ltd. All rights reserved.

UV femtosecond laser inscribes a 300 nm period nanostructure in a pure fused silica

We report on the first recording of a periodic structure of ∼150 nm pitch in a permanently moving sample of a pure fused silica using the tightly focused, 82 nJ, 267 nm, 300 fs, 1 kHz laser pulses. © 2007 IOP Publishing Ltd.

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.

Writing and characterisation methods for UV-photosensitivity based devices and their applications

The underlying work to this thesis focused on the exploitation and investigation of photosensitivity mechanisms in optical fibres and planar waveguides for the fabrication of advanced integrated optical devices for telecoms and sensing applications. One major scope is the improvement of grating fabrication specifications by introducing new writing techniques and the use of advanced characterisation methods for grating testing. For the first time the polarisation control method for advanced grating fabrication has successfully been converted to apodised planar waveguide fabrication and the development of a holographic method for the inscription of chirped gratings at arbitrary wavelength is presented. The latter resulted in the fabrication of gratings for pulse-width suppression and wavelength selection in diode lasers. In co-operation with research partners a number of samples were tested using optical frequency domain and optical low coherence reflectometry for a better insight into the limitations of grating writing techniques. Using a variety of different fabrication methods, custom apodised and chirped fibre Bragg gratings were written for the use as filter elements for multiplexer-demultiplexer devices, as well as for short pulse generation and wavelength selection in telecommunication transmission systems. Long period grating based devices in standard, speciality and tapered fibres are presented, showing great potential for multi-parameter sensing. One particular scope is the development of vectorial curvature and refractive index sensors with potential for medical, chemical and biological sensing. In addition the design of an optically tunable Mach-Zehnder based multiwavelength filter is introduced. The discovery of a Type IA grating type through overexposure of hydrogen loaded standard and Boron-Germanium co-doped fibres strengthened the assumption of UV-photosensitivity being a highly non-linear process. Gratings of this type show a significantly lower thermal sensitivity compared to standard gratings, which makes them useful for sensing applications. An Oxford Lasers copper-vapour laser operating at 255 nm in pulsed mode was used for their inscription, in contrast to previous work using CW-Argon-Ion lasers and contributing to differences in the processes of the photorefractive index change

Water diffusion into UV inscripted long period grating in microstructured polymer fibre

A long period grating was photoinscribed step-by-step in microstructured poly(methyl methacrylate) fiber for the first time using a continuous wave HeCd laser at 325 nm, irradiating the fiber with a power of 1 mW. The grating had a length of 2 cm and a period of 1 mm. A series of cladding mode coupling resonances were observed throughout the spectral region studied of 600 to 1100 nm. The resonance wavelengths were shown to be sensitive to the diffusion of water into the fiber.

UV femtosecond laser inscribes a 300 nm period nanostructure in a pure fused silica

We report on the first recording of a periodic structure of ~150 nm pitch in a permanently moving sample of a pure fused silica using the tightly focused, 82 nJ, 267 nm, 300 fs, 1 kHz laser pulses.

UV-inscription, polarization-dependant loss characteristics and applications of 45° tilted fiber gratings

We have UV-inscribed and theoretically and experimentally analyzed fiber gratings with the structure tilted at 45° and implemented this type of devices as an in-fiber polarizer. A systematic investigation has been carried out on the characterization of 45° tilted fiber gratings (45° TFGs) in terms of the polarization-dependant loss (PDL) and thermal response. The detailed theoretical modeling has revealed a linear correlation between the grating length and the PDL, which has been proved by the experimental results. For the first time, we have examined the UV beam diffraction from a tilted phase mask and designed the UV-inscription system to suit the 45° TFG fabrication. Experimentally, a 24 mm long 45° TFG UV-inscribed in standard telecom single-mode fiber exhibited around 25 dB PDL at 1530 nm and an over ~300 nm bandwidth of PDL spectrum. By the concatenation method, a 44 mm long grating showed a PDL as high as 40 dB that is close to the high polarization extinction ratio of commercial products. Moreover, we have revealed that the PDL of 45° TFGs has low thermal influence, which is desirable for real application devices. Finally, we experimentally demonstrated an all-fiber twist sensor system based on a 45° and an 81° TFG.

UV-inscription, polarization-dependant loss characteristics and applications of 45° tilted fiber gratings

We have UV-inscribed and theoretically and experimentally analyzed fiber gratings with the structure tilted at 45° and implemented this type of devices as an in-fiber polarizer. A systematic investigation has been carried out on the characterization of 45° tilted fiber gratings (45° TFGs) in terms of the polarization-dependant loss (PDL) and thermal response. The detailed theoretical modeling has revealed a linear correlation between the grating length and the PDL, which has been proved by the experimental results. For the first time, we have examined the UV beam diffraction from a tilted phase mask and designed the UV-inscription system to suit the 45° TFG fabrication. Experimentally, a 24 mm long 45° TFG UV-inscribed in standard telecom single-mode fiber exhibited around 25 dB PDL at 1530 nm and an over ~300 nm bandwidth of PDL spectrum. By the concatenation method, a 44 mm long grating showed a PDL as high as 40 dB that is close to the high polarization extinction ratio of commercial products. Moreover, we have revealed that the PDL of 45° TFGs has low thermal influence, which is desirable for real application devices. Finally, we experimentally demonstrated an all-fiber twist sensor system based on a 45° and an 81° TFG.

Increase of the photosensitivity of undoped poly(methylmethacrylate) under UV radiation at 325 nm

In this paper we report, for the first time to our knowledge, an increase of the photosensitivity of a microstructured polymer optical fibre (mPOF) made of undoped PMMA due to applied strain during the fabrication of the gratings. In the work, fibre Bragg gratings (FBGs) have been fabricated in undoped PMMA mPOFs with a hexagonal structure of three rings in the inner cladding. Two sets of FBGs were inscribed at two different resonant wavelengths (827 nm and 1562 nm) at different strains using an UV He-Cd laser at 325 nm focused by a lens and scanned over the fibre. We observed an increase of the reflection of the fibre Bragg gratings when the fabrication strain is higher. The photosensitivity mechanism is discussed in the paper along with the chemical reactions that could underlie the mechanism. Furthermore, the resolution limit of the material was investigated. © 2014 Copyright SPIE.