Local feature analysis using higher-order Riesz transforms

Marchant, Ross Glenn Raymond (2016) Local feature analysis using higher-order Riesz transforms. PhD thesis, James Cook University.

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View at Publisher Website: https://doi.org/10.25903/qm8m-sm40


Rich descriptions of local image structures are important for higher-level understanding of images in computer vision. Phase-based representations allow the discrimination of symmetric features, such as lines, and anti-symmetric features, such as edges, independent of their strength. Methods to obtain phase information include quadrature filters using the Hilbert transform, spherical quadrature filters using the Riesz transform, and 2D analytic signals such as the monogenic signal and signal multi-vector.

This thesis develops a new local image descriptor, called the circular harmonic vector, consisting of the higher-order Riesz transforms of an image. The circular harmonic vector describes the symmetries of the local image structure. It extends previous analytic signals, and is formulated in the context of 2D steerable wavelet frames. Methods are introduced to solve for the parameters of a general signal model by splitting the circular harmonic vector into model and residual components. In particular, the super-resolution method, normally used for the resolving of spike trains, can be applied.

The methods are applied to estimating the parameters of sinusoidal, multi-sinusoidal and half-sinusoidal phase-based image models. The sinusoidal model describes lines and edges in terms of amplitude, phase and orientation. Using higher-order Riesz transforms in the circular harmonic vector gives better parameter estimates, and the residual component is used to develop a new detection measure for junctions and corners. The multi-sinusoidal model is applied to coral core x-ray analysis, from which separate reconstruction of features is possible as a result of the wavelet basis. The half-sinusoidal model is used to obtain the amplitudes and orientations of the line and edge segments in junctions and corners, with phase discriminating their type.

Finally, a new representation of local image structure through scale is introduced. It describes the continuous response of the circular harmonic vector response shifted though scale in the form of a quaternion-valued matrix. The matrix is derived from the higher-order Riesz transforms of an isotropic wavelet frame given by Fourier series basis functions in the logarithmic frequency domain. New measures for scale selection are developed, along with a continuous version of phase congruency that is combined with previous image models to detect and discriminate image features in an illumination invariant way.

Item ID: 46047
Item Type: Thesis (PhD)
Keywords: feature analysis; image analysis; image processing; Riesz spaces; Riesz transform; vector spaces
Date Deposited: 13 Oct 2016 04:47
FoR Codes: 08 INFORMATION AND COMPUTING SCIENCES > 0801 Artificial Intelligence and Image Processing > 080106 Image Processing @ 50%
01 MATHEMATICAL SCIENCES > 0199 Other Mathematical Sciences > 019999 Mathematical Sciences not elsewhere classified @ 50%
SEO Codes: 97 EXPANDING KNOWLEDGE > 970101 Expanding Knowledge in the Mathematical Sciences @ 50%
97 EXPANDING KNOWLEDGE > 970108 Expanding Knowledge in the Information and Computing Sciences @ 50%
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