In this work we present a novel approach to recover objects 3D position and occupancy in a generic scene using only 2D object detections from multiple view images. The method reformulates the problem as the estimation of a quadric (ellipsoid) in 3D given a set of 2D ellipses fitted to the object detection bounding boxes in multiple views. We show that a closed-form solution exists in the dual-space using a minimum of three views while a solution with two views is possible through the use of non-linear optimisation and object constraints on the size of the object shape. In order to make the solution robust toward inaccurate bounding boxes, a likely occurrence in object detection methods, we introduce a data preconditioning technique and a non-linear refinement of the closed form solution based on implicit subspace constraints. Results on synthetic tests and on different real datasets, involving challenging scenarios, demonstrate the applicability and potential of our method in several realistic scenarios.
Frequency-invariant beam patterns are often required by systems using an array of sensors to process broadband signals. If the spatial aperture is shorter than the involved wavelengths, using a superdirective beamforming is essential to get an efficient system. In this context, robustness of array imperfections is a crucial feature. In the literature, only a few approaches have been proposed to design a robust, superdirective, frequency-invariant beamformer based on filter-and-sum architecture; all of them achieve frequency-invariance by imposing a desired beam pattern. However, the choice of a suitable desired beam pattern is critical; an improper choice results in unsatisfactory performance. This paper proposes a new method of array synthesis that allows the design of a robust broadband beamformer with tunable tradeoff between frequency-invariance and directivity, without the need for imposing a desired beam pattern. The latter is defined as a set of variables that do not depend on frequency and are included in the vector of variables to be optimized. To this end, a suitable cost function has been devised whose minimum can be found in closed form. Therefore, the method is analytical and computationally inexpensive. In addition, a technique that allows obtaining a beam pattern with a linear phase over frequency is described. The results show the effectiveness of the proposed method in designing robust superdirective beam patterns for linear arrays receiving far-field signals, with special attention to microphone arrays of limited aperture.Index Terms-Beamforming robustness, broadband beamforming, filter-and-sum beamforming, frequency-invariant beam patterns, microphone arrays, superdirective arrays.
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