Spectrum of Functions for the Dunkl Transform on R^d

Mathematics Subject Classification: 42B10

On the Uniform Convergence of Partial Dunkl Integrals in Besov-Dunkl Spaces

2000 Mathematics Subject Classification: 44A15, 44A35, 46E30

Herz-Type Hardy Spaces for the Dunkl Operator on the Real Line

2000 Mathematics Subject Classification: Primary 46F12, Secondary 44A15, 44A35

An Analogue of Beurling-Hörmander’s Theorem for the Dunkl-Bessel Transform

Mathematics Subject Classification: Primary 35R10, Secondary 44A15

Towards automatic power line detection for a UAV surveillance system using pulse coupled neural filter and an improved Hough transform

Spatial information captured from optical remote sensors on board unmanned aerial vehicles (UAVs) has great potential in automatic surveillance of electrical infrastructure. For an automatic vision-based power line inspection system, detecting power lines from a cluttered background is one of the most important and challenging tasks. In this paper, a novel method is proposed, specifically for power line detection from aerial images. A pulse coupled neural filter is developed to remove background noise and generate an edge map prior to the Hough transform being employed to detect straight lines. An improved Hough transform is used by performing knowledge-based line clustering in Hough space to refine the detection results. The experiment on real image data captured from a UAV platform demonstrates that the proposed approach is effective for automatic power line detection.

Classification of Airborne LIDAR Intensity Data Using Statistical Analysis and Hough Transform with Application to Power Line Corridors

Light Detection and Ranging (LIDAR) has great potential to assist vegetation management in power line corridors by providing more accurate geometric information of the power line assets and vegetation along the corridors. However, the development of algorithms for the automatic processing of LIDAR point cloud data, in particular for feature extraction and classification of raw point cloud data, is in still in its infancy. In this paper, we take advantage of LIDAR intensity and try to classify ground and non-ground points by statistically analyzing the skewness and kurtosis of the intensity data. Moreover, the Hough transform is employed to detected power lines from the filtered object points. The experimental results show the effectiveness of our methods and indicate that better results were obtained by using LIDAR intensity data than elevation data.

Chemical functionalities of high and low sulfur Australian coals : a case study using micro attenuated total reflectance–fourier transform infrared (ATR–FTIR) spectrometry

The macerals in bituminous coals with varying organic sulfur content from the Early Permian Greta Coal Measures at three locations (Southland Colliery, Drayton Colliery and the Cranky Corner Basin), in and around the Sydney Basin (Australia), have been studied using light-element electron microprobe (EMP) analysis and micro-ATR–FTIR. Electron microprobe analysis of individual macerals reveals that the vitrinite in both the Cranky Corner Basin and Drayton Colliery (Puxtrees seam) samples have similar carbon contents (ca. 78% C in telocollinite), suggesting that they are of equivalent rank. However, the Cranky Corner coals have anomalously low vitrinite reflectance (down to 0.45%) vs. the Drayton materials (ca. 0.7%). They also have very high organic S content (3–6.5%) and lower O content (ca. 10%) than the equivalent macerals in the Drayton sample (0.7% S and 15.6% O). A study was carried out to investigate the impacts of the high organic S on the functional groups of the macerals in these two otherwise iso-rank, stratigraphically-equivalent seams. An iso-rank low-S coal from the overlying Wittingham Coal Measures near Muswellbrook and coals of slightly higher rank from the Greta Coal Measures at Southland Colliery near Cessnock were also evaluated using the same techniques to extend the data set. Although the telocollinite in the Drayton and Cranky Corner coals have very similar carbon content (ca.78% C), the ATR–FTIR spectra of the vitrinite and inertinite macerals in these respectively low S and high S coals show some distinct differences in IR absorbance from various aliphatic and aromatic functional groups. The differences in absorbance of the aliphatic stretching bands (2800–3000 cm−1) and the aromatic carbon (CC) peak at 1606 cm−1 are very obvious. Compared to that of the Drayton sample (0.7% S and 15% O), the telocollinite of the Cranky Corner coal (6% S and 10% O) clearly shows: (i) less absorbance from OH groups, represented by a broad region around 3553 cm−1, (ii) much stronger aliphatic C–H absorbance (stretching modes around 3000–2800 cm−1 and bending modes around 1442 cm−1) and (iii) less absorbance from aromatic carbon functional groups (peaking at 1606 cm−1). Evaluation of the iso-rank Drayton and Cranky Corner coals shows that: (i) the aliphatic C–H absorbances decrease with increasing oxygen content but increase with increasing organic S content and (ii) the aromatic H to aliphatic H ratio (Har/Hali) for the telocollinite increases with (organic) O%, but decreases progressively with increasing organic S. The high organic S content in the maceral appears to be accompanied by a greater proportion of aliphatic functional groups, possibly as a result of some of the O within maceral ring structures in the high S coal samples being replaced.

Fingerprint analysis using wavelet transform with application to compression and feature extraction

The main goal of this research is to design an efficient compression al~ gorithm for fingerprint images. The wavelet transform technique is the principal tool used to reduce interpixel redundancies and to obtain a parsimonious representation for these images. A specific fixed decomposition structure is designed to be used by the wavelet packet in order to save on the computation, transmission, and storage costs. This decomposition structure is based on analysis of information packing performance of several decompositions, two-dimensional power spectral density, effect of each frequency band on the reconstructed image, and the human visual sensitivities. This fixed structure is found to provide the "most" suitable representation for fingerprints, according to the chosen criteria. Different compression techniques are used for different subbands, based on their observed statistics. The decision is based on the effect of each subband on the reconstructed image according to the mean square criteria as well as the sensitivities in human vision. To design an efficient quantization algorithm, a precise model for distribution of the wavelet coefficients is developed. The model is based on the generalized Gaussian distribution. A least squares algorithm on a nonlinear function of the distribution model shape parameter is formulated to estimate the model parameters. A noise shaping bit allocation procedure is then used to assign the bit rate among subbands. To obtain high compression ratios, vector quantization is used. In this work, the lattice vector quantization (LVQ) is chosen because of its superior performance over other types of vector quantizers. The structure of a lattice quantizer is determined by its parameters known as truncation level and scaling factor. In lattice-based compression algorithms reported in the literature the lattice structure is commonly predetermined leading to a nonoptimized quantization approach. In this research, a new technique for determining the lattice parameters is proposed. In the lattice structure design, no assumption about the lattice parameters is made and no training and multi-quantizing is required. The design is based on minimizing the quantization distortion by adapting to the statistical characteristics of the source in each subimage. 11 Abstract Abstract Since LVQ is a multidimensional generalization of uniform quantizers, it produces minimum distortion for inputs with uniform distributions. In order to take advantage of the properties of LVQ and its fast implementation, while considering the i.i.d. nonuniform distribution of wavelet coefficients, the piecewise-uniform pyramid LVQ algorithm is proposed. The proposed algorithm quantizes almost all of source vectors without the need to project these on the lattice outermost shell, while it properly maintains a small codebook size. It also resolves the wedge region problem commonly encountered with sharply distributed random sources. These represent some of the drawbacks of the algorithm proposed by Barlaud [26). The proposed algorithm handles all types of lattices, not only the cubic lattices, as opposed to the algorithms developed by Fischer [29) and Jeong [42). Furthermore, no training and multiquantizing (to determine lattice parameters) is required, as opposed to Powell's algorithm [78). For coefficients with high-frequency content, the positive-negative mean algorithm is proposed to improve the resolution of reconstructed images. For coefficients with low-frequency content, a lossless predictive compression scheme is used to preserve the quality of reconstructed images. A method to reduce bit requirements of necessary side information is also introduced. Lossless entropy coding techniques are subsequently used to remove coding redundancy. The algorithms result in high quality reconstructed images with better compression ratios than other available algorithms. To evaluate the proposed algorithms their objective and subjective performance comparisons with other available techniques are presented. The quality of the reconstructed images is important for a reliable identification. Enhancement and feature extraction on the reconstructed images are also investigated in this research. A structural-based feature extraction algorithm is proposed in which the unique properties of fingerprint textures are used to enhance the images and improve the fidelity of their characteristic features. The ridges are extracted from enhanced grey-level foreground areas based on the local ridge dominant directions. The proposed ridge extraction algorithm, properly preserves the natural shape of grey-level ridges as well as precise locations of the features, as opposed to the ridge extraction algorithm in [81). Furthermore, it is fast and operates only on foreground regions, as opposed to the adaptive floating average thresholding process in [68). Spurious features are subsequently eliminated using the proposed post-processing scheme.

Reliability analysis of transform-based stereo matching techniques, and a new matching constraint

Stereo vision is a method of depth perception, in which depth information is inferred from two (or more) images of a scene, taken from different perspectives. Practical applications for stereo vision include aerial photogrammetry, autonomous vehicle guidance, robotics and industrial automation. The initial motivation behind this work was to produce a stereo vision sensor for mining automation applications. For such applications, the input stereo images would consist of close range scenes of rocks. A fundamental problem faced by matching algorithms is the matching or correspondence problem. This problem involves locating corresponding points or features in two images. For this application, speed, reliability, and the ability to produce a dense depth map are of foremost importance. This work implemented a number of areabased matching algorithms to assess their suitability for this application. Area-based techniques were investigated because of their potential to yield dense depth maps, their amenability to fast hardware implementation, and their suitability to textured scenes such as rocks. In addition, two non-parametric transforms, the rank and census, were also compared. Both the rank and the census transforms were found to result in improved reliability of matching in the presence of radiometric distortion - significant since radiometric distortion is a problem which commonly arises in practice. In addition, they have low computational complexity, making them amenable to fast hardware implementation. Therefore, it was decided that matching algorithms using these transforms would be the subject of the remainder of the thesis. An analytic expression for the process of matching using the rank transform was derived from first principles. This work resulted in a number of important contributions. Firstly, the derivation process resulted in one constraint which must be satisfied for a correct match. This was termed the rank constraint. The theoretical derivation of this constraint is in contrast to the existing matching constraints which have little theoretical basis. Experimental work with actual and contrived stereo pairs has shown that the new constraint is capable of resolving ambiguous matches, thereby improving match reliability. Secondly, a novel matching algorithm incorporating the rank constraint has been proposed. This algorithm was tested using a number of stereo pairs. In all cases, the modified algorithm consistently resulted in an increased proportion of correct matches. Finally, the rank constraint was used to devise a new method for identifying regions of an image where the rank transform, and hence matching, are more susceptible to noise. The rank constraint was also incorporated into a new hybrid matching algorithm, where it was combined a number of other ideas. These included the use of an image pyramid for match prediction, and a method of edge localisation to improve match accuracy in the vicinity of edges. Experimental results obtained from the new algorithm showed that the algorithm is able to remove a large proportion of invalid matches, and improve match accuracy.