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Abstract: A new model for describing a three-dimensional (3D) trajectory is proposed in this paper. The studied trajectory is viewed as a linear combination of rotatable 3D patterns. The resulting model is thus 3D rotation invariant (3DRI). Moreover, the temporal patterns are considered as shift-invariant. This paper is divided into two parts based on this model. On the one hand, the 3DRI decomposition estimates the active patterns, their coefficients, their rotations and their shift parameters. Based on sparse approximation, this is carried out by two non-convex optimizations: 3DRI matching pursuit (3DRI-MP) and 3DRI orthogonal matching pursuit (3DRI-OMP). On the other hand, a 3DRI learning method learns the characteristic patterns of a database through a 3DRI dictionary learning algorithm (3DRI-DLA). The proposed algorithms are first applied to simulation data to evaluate their performances and to compare them to other algorithms. Then, they are applied to real motion data of cued speech, to learn the 3D trajectory patterns characteristic of this gestural language. [Copyright &y& Elsevier]

Abstract: We developed a scheme to compute the depths of four idealized magnetized sources, viz., a monopole, a line of monopoles, a dipole and a line of dipoles from the Walsh spectra of the total-field magnetic anomalies. The sequency numbers, l max corresponding to the peaks of the differential energy density spectra over these sources are practically independent of the shape of the observed anomaly and are linearly dependent on the source depths. For each model, we derived a quantitative relation between the depth and the sequency number l max. Analyses of simulated data over idealized isolated sources reveal that (i) a profile length of about 8 times the source depth provides accurate value in computed depth; (ii) data spacing of less than one-fourth the source depth has no significant error in depth computation and (iii) the technique is capable of tolerating random error to the tune of 10% of the peak amplitude of the simulated anomaly. We compared the results of depth estimations from Walsh and Fourier spectra. Analysis of total-field magnetic anomalies over a buried water supply pipe has demonstrated the applicability of the proposed method. [Copyright &y& Elsevier]