Plane-Wave Decomposition of Acoustical Scenes Via Spherical and Cylindrical Microphone Arrays

Spherical and cylindrical microphone arrays offer a number of attractive properties such as direction-independent acoustic behavior and ability to reconstruct the sound field in the vicinity of the array. Beamforming and scene analysis for such arrays is typically done using sound field representation in terms of orthogonal basis functions (spherical/cylindrical harmonics). In this paper, an alternative sound field representation in terms of plane waves is described, and a method for estimating it directly from measurements at microphones is proposed. It is shown that representing a field as a collection of plane waves arriving from various directions simplifies source localization, beamforming, and spatial audio playback. A comparison of the new method with the well-known spherical harmonics based beamforming algorithm is done, and it is shown that both algorithms can be expressed in the same framework but with weights computed differently. It is also shown that the proposed method can be extended to cylindrical arrays. A number of features important for the design and operation of spherical microphone arrays in real applications are revealed. Results indicate that it is possible to reconstruct the sound scene up to order p with p2 microphones spherical array.     

SoftPOSIT: Simultaneous Pose and Correspondence Determination

The problem of pose estimation arises in many areas of computer vision, including object recognition, object tracking, site inspection and updating, and autonomous navigation when scene models are available. We present a new algorithm, called SoftPOSIT, for determining the pose of a 3D object from a single 2D image when correspondences between object points and image points are not known. The algorithm combines the iterative softassign algorithm (Gold and Rangarajan, 1996; Gold et al., 1998) for computing correspondences and the iterative POSIT algorithm (DeMenthon and Davis, 1995) for computing object pose under a full-perspective camera model. Our algorithm, unlike most previous algorithms for pose determination, does not have to hypothesize small sets of matches and then verify the remaining image points. Instead, all possible matches are treated identically throughout the search for an optimal pose. The performance of the algorithm is extensively evaluated in Monte Carlo simulations on synthetic data under a variety of levels of clutter, occlusion, and image noise. These tests show that the algorithm performs well in a variety of difficult scenarios, and empirical evidence suggests that the algorithm has an asymptotic run-time complexity that is better than previous methods by a factor of the number of image points. The algorithm is being applied to a number of practical autonomous vehicle navigation problems including the registration of 3D architectural models of a city to images, and the docking of small robots onto larger robots.     

Computation of singular and hypersingular boundary integrals by Green identity and application to boundary value problems

The problem of computing singular and hypersingular integrals involved in a large class of boundary value problems is considered. The method is based on Green's theorem for calculating the diagonal elements of the resulting discretized matrix using the Nyström discretization method. The method is successfully applied to classical boundary value problems. Convergence of the method is also discussed.