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].

EM optimization of latent-variable density models

There is currently considerable interest in developing general non-linear density models based on latent, or hidden, variables. Such models have the ability to discover the presence of a relatively small number of underlying `causes' which, acting in combination, give rise to the apparent complexity of the observed data set. Unfortunately, to train such models generally requires large computational effort. In this paper we introduce a novel latent variable algorithm which retains the general non-linear capabilities of previous models but which uses a training procedure based on the EM algorithm. We demonstrate the performance of the model on a toy problem and on data from flow diagnostics for a multi-phase oil pipeline.

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.

Fabrication and applications of fibre Bragg gratings

The consequences of fabricating Bragg gratings in various fibres, with or without hydrogen loading, and with varying laser power levels are explored. Three new techniques for fabricating chirped gratings are presented. Beams with dissimilar wavefront curvatures are interfered to give chirped gratings. With the same aim techniques of writing gratings on tapered fibres and on deformed fibres are also covered. With these techniques, a wide variety of gratings has been fabricated from the 'superbroad' (with bandwidths of up to 180 nm), small to medium bandwidth gratings with linear chirp profiles and quadratic chirped gratings. It is demonstrated that chirped grating can be concatenated to form all-fibre Fabry-Perot and Moiré resonators. These are further concatenated with chirped gratings to produce filters with narrow passbands and very broad stopbands. A number of other applications are also addressed. The use of chirped fibre gratings for dispersion compensation and femtosecond chirped pulse amplification is demonstrated. Chirped gratings are used as dispersive elements in modelocked fibre lasers producing ultrashort pulses. A chirped fibre grating Fabry-Perot transmission filter is used in a continuous wave laser that exhibits eleven simultaneously lasing wavelengths. Finally, the use of grating-coupler devices as variable reflectivity mirrors for laser optimisation and gain clamping is considered.

Statnote 19: non-linear regression: fitting an exponential curve to data

Non-linear relationships are common in microbiological research and often necessitate the use of the statistical techniques of non-linear regression or curve fitting. In some circumstances, the investigator may wish to fit an exponential model to the data, i.e., to test the hypothesis that a quantity Y either increases or decays exponentially with increasing X. This type of model is straight forward to fit as taking logarithms of the Y variable linearises the relationship which can then be treated by the methods of linear regression.

Data analysis methods in optometry Part 7: multiple linear regression

Multiple regression analysis is a complex statistical method with many potential uses. It has also become one of the most abused of all statistical procedures since anyone with a data base and suitable software can carry it out. An investigator should always have a clear hypothesis in mind before carrying out such a procedure and knowledge of the limitations of each aspect of the analysis. In addition, multiple regression is probably best used in an exploratory context, identifying variables that might profitably be examined by more detailed studies. Where there are many variables potentially influencing Y, they are likely to be intercorrelated and to account for relatively small amounts of the variance. Any analysis in which R squared is less than 50% should be suspect as probably not indicating the presence of significant variables. A further problem relates to sample size. It is often stated that the number of subjects or patients must be at least 5-10 times the number of variables included in the study.5 This advice should be taken only as a rough guide but it does indicate that the variables included should be selected with great care as inclusion of an obviously unimportant variable may have a significant impact on the sample size required.

All-fiber polarization interference filters based on 45°-tilted fiber gratings

We report all-fiber polarization interference filters, known as Lyot and Lyot-Ohman filters, based on alternative concatenation of UV-inscribed fiber gratings with structure tilted at 45° and polarization maintaining (PM) fiber cavities. Such filters generate comb-like transmission of linear polarization output. The free spectral range (FSR) of a single-stage (Lyot) filter is PM fiber cavity length dependent, as a 20 cm long cavity showed a 26.6 nm FSR while the 40 cm one exhibited a 14.8 nm FSR. Furthermore, we have theoretically and experimentally demonstrated all-fiber 2-stage and 3-stage Lyot-Ohman filters, giving more freedom in tailoring the transmission characteristics.

Non-linear hierarchical visualisation

This thesis applies a hierarchical latent trait model system to a large quantity of data. The motivation for it was lack of viable approaches to analyse High Throughput Screening datasets which maybe include thousands of data points with high dimensions. High Throughput Screening (HTS) is an important tool in the pharmaceutical industry for discovering leads which can be optimised and further developed into candidate drugs. Since the development of new robotic technologies, the ability to test the activities of compounds has considerably increased in recent years. Traditional methods, looking at tables and graphical plots for analysing relationships between measured activities and the structure of compounds, have not been feasible when facing a large HTS dataset. Instead, data visualisation provides a method for analysing such large datasets, especially with high dimensions. So far, a few visualisation techniques for drug design have been developed, but most of them just cope with several properties of compounds at one time. We believe that a latent variable model (LTM) with a non-linear mapping from the latent space to the data space is a preferred choice for visualising a complex high-dimensional data set. As a type of latent variable model, the latent trait model can deal with either continuous data or discrete data, which makes it particularly useful in this domain. In addition, with the aid of differential geometry, we can imagine the distribution of data from magnification factor and curvature plots. Rather than obtaining the useful information just from a single plot, a hierarchical LTM arranges a set of LTMs and their corresponding plots in a tree structure. We model the whole data set with a LTM at the top level, which is broken down into clusters at deeper levels of t.he hierarchy. In this manner, the refined visualisation plots can be displayed in deeper levels and sub-clusters may be found. Hierarchy of LTMs is trained using expectation-maximisation (EM) algorithm to maximise its likelihood with respect to the data sample. Training proceeds interactively in a recursive fashion (top-down). The user subjectively identifies interesting regions on the visualisation plot that they would like to model in a greater detail. At each stage of hierarchical LTM construction, the EM algorithm alternates between the E- and M-step. Another problem that can occur when visualising a large data set is that there may be significant overlaps of data clusters. It is very difficult for the user to judge where centres of regions of interest should be put. We address this problem by employing the minimum message length technique, which can help the user to decide the optimal structure of the model. In this thesis we also demonstrate the applicability of the hierarchy of latent trait models in the field of document data mining.

Cortical activity during rotational and linear transformations

Neuroimaging studies of cortical activation during image transformation tasks have shown that mental rotation may rely on similar brain regions as those underlying visual perceptual mechanisms. The V5 complex, which is specialised for visual motion, is one region that has been implicated. We used functional magnetic resonance imaging (fMRI) to investigate rotational and linear transformation of stimuli. Areas of significant brain activation were identified for each of the primary mental transformation tasks in contrast to its own perceptual reference task which was cognitively matched in all respects except for the variable of interest. Analysis of group data for perception of rotational and linear motion showed activation in areas corresponding to V5 as defined in earlier studies. Both rotational and linear mental transformations activated Brodman Area (BA) 19 but did not activate V5. An area within the inferior temporal gyrus, representing an inferior satellite area of V5, was activated by both the rotational perception and rotational transformation tasks, but showed no activation in response to linear motion perception or transformation. The findings demonstrate the extent to which neural substrates for image transformation and perception overlap and are distinct as well as revealing functional specialisation within perception and transformation processing systems.