The following is a list of my conference papers published to date

#### Modelling Line and Edge Features Using Higher-Order Riesz Transforms

ACIVS2013

The 2D-complex Riesz transform is an extension of the Hilbert transform to images. It can be used to model local image structure as a superposition of sinusoids, and to construct 2D steerable wavelets. In this paper we propose to model local image structure as the superposition of a 2D steerable wavelet at multiple amplitudes and orientations. These parameters are estimated by applying recent developments in super-resolution theory. Using 2D steerable wavelets corresponding to line or edge segments then allows for the underlying structure of image features such as junctions and edges to be determined.

[gpp_toggle title=”Errata”]The test above equation 4 should read: The 2D steerable wavelet, s_f(z), whose *normalised* RT vector is the same as

the signal at z = 0, i.e. (R^N s_f(0)) / ||(R^N s_f(0))|| = f^N(0) / ||f^N(0)||, and has same value at the origin, i.e. s_f(0) = f(0) is[/gpp_toggle]

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#### Using Super-Resolution Methods to Solve a Novel Multi-Sinusoidal Signal Model

DICTA2013

Sinusoidal signal models are a useful representation of local image structure, as sinusoid phase describes symmetry separately from strength and orientation. Existing models consist of one or two oriented sinusoids, calculated using the 0th to 3rd order Riesz transforms. We propose an expanded signal model consisting of a larger number of oriented sinusoids. The model parameters are estimated using higher-order Riesz transforms and a novel application of super-resolution theory. Image features consisting of multiple lines or edges can be analysed using the method, which compares favourably to existing approaches.

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#### Local feature analysis using a sinusoidal signal model derived from higher-order Riesz transforms

ICIP2013

The monogenic signal consists of an image and its first-order Riesz transform. It describes signal structure as a sinusoid with a particular amplitude, phase and orientation; however, the orientation estimate is poor around certain phase values. We describe a novel method of estimating this sinusoidal signal model using higher-order Riesz transforms, such that amplitude, phase and orientation estimates are improved under noise conditions. Furthermore, the method leads to novel intrinsically-1D (line and edge) and intrinsically-2D (corner and junction) detectors.

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#### Feature Detection from the Maximal Response to a Spherical Quadrature Filter Set

DICTA2012

In this paper we describe a novel method of feature detection and classification using the maximal response of a set of spherical quadrature filters to either a line-segment or wedge-segment signal type. This is achieved via a rotation and illumination invariant distance function. The development of the method is described, and some experimental results are provided to demonstrate the usefulness of the technique.

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#### Generalised Hilbert Transforms for the Estimation of Growth Direction in Coral Cores

DICTA2011

Measuring coral growth rate is essential for monitoring coral reef health, and part of the process involves directional analysis of x-ray images of coral sections. The monogenic signal is useful for this application as it represents an image in terms of intrinsically-1D feature type (phase), strength (amplitude) and orientation. At certain locations the monogenic signal may give orientation errors, however these can be resolved using higher order generalised Hilbert transforms. We follow this approach, but combine components using a double angle representation as well as the sign of the phase. The improved algorithm is then applied to estimation of growth direction in coral x-ray images. An objective estimation of major growth axis, growth band location, and off axis extension compensation is now possible, and shows the usefulness of 2D analytic signal based image analysis.

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