A multi-firearm, multi-orientation audio dataset of gunshots.

Early detection of firearm discharge has become increasingly critical for situational awareness in both civilian and military domains. The ability to determine the location and model of a discharged firearm is vital, as this can inform effective response plans. To this end, several gunshot audio datasets have been released that aim to facilitate gunshot detection and classification of a discharged firearm based on acoustic signatures. However, these datasets often suffer from a lack of variety in the orientations of recording devices around the source of the gunshot. Additionally, these datasets often suffer from the absence of proper time synchronization, which prevents the usage of these datasets for determining the Direction of Arrival (DoA) of the sound. In this paper, we present a multi-firearm, multi-orientation time-synchronized audio dataset collected in a semi-controlled real-world setting - providing us a degree of supervision - using several edge devices positioned in and around an outdoor firing range.

Transversality Conditions for Geodesics on the Statistical Manifold of Multivariate Gaussian Distributions.

We consider the problem of finding the closest multivariate Gaussian distribution on a constraint surface of all Gaussian distributions to a given distribution. Previous research regarding geodesics on the multivariate Gaussian manifold has focused on finding closed-form, shortest-path distances between two fixed distributions on the manifold, often restricting the parameters to obtain the desired solution. We demonstrate how to employ the techniques of the calculus of variations with a variable endpoint to search for the closest distribution from a family of distributions generated via a constraint set on the parameter manifold. Furthermore, we examine the intermediate distributions along the learned geodesics which provide insight into uncertainty evolution along the paths. Empirical results elucidate our formulations, with visual illustrations concretely exhibiting dynamics of 1D and 2D Gaussian distributions.

A Grassmannian Graph Approach to Affine Invariant Feature Matching.

In this work, we present a novel, theoretical approach to address one of the longstanding problems in computer vision: 2D and 3D affine invariant feature matching. Our proposed Grassmannian Graph (GrassGraph) framework employs a two stage procedure that is capable of robustly recovering correspondences between two unorganized, affinely related feature (point) sets. In the ideal case, the first stage maps the feature sets to an affine invariant Grassmannian representation, where the features are mapped into the same subspace. It turns out that coordinate representations extracted from the Grassmannian differ by an arbitrary orthonormal matrix. In the second stage, by approximating the Laplace-Beltrami operator (LBO) on these coordinates, this extra orthonormal factor is nullified, providing true affine invariant coordinates which we then utilize to recover correspondences via simple mutual nearest neighbor relations. Our validation benchmarks use large number of experimental trials performed on 2D and 3D datasets. Experimental results show that the proposed GrassGraph method successfully recovers large affine transformations.

CASAIR: Content and Shape-Aware Image Retargeting and Its Applications.

This paper proposes a novel image-retargeting algorithm that can retarget images to a large family of non-rectangular shapes. Specifically, we study image retargeting from a broader perspective that includes the content as well as the shape of an image, and the proposed content and shape-aware image-retargeting (CASAIR) algorithm is driven by the dual objectives of image content preservation and image domain transformation, with the latter defined by an application-specific target shape. The algorithm is based on the idea of seam segment carving that successively removes low-cost seam segments from the image to simultaneously achieve the two objectives, with the selection of seam segments determined by a cost function incorporating inputs from image content and target shape. To provide a complete characterization of shapes that can be obtained using CASAIR, we introduce the notion of bhv-convex shapes, and we show that bhv-convex shapes are precisely the family of shapes that can be retargeted to by CASAIR. The proposed algorithm is simple in both its design and implementation, and in practice, it offers an efficient and effective retargeting platform that provides its users with considerable flexibility in choosing target shapes. To demonstrate the potential of CASAIR for broadening the application scope of image retargeting, this paper also proposes a smart camera-projector system that incorporates CASAIR. In the context of ubiquitous display, CASAIR equips the camera-projector system with the capability of retargeting images online in order to maximize the quality and fidelity of the displayed images whenever the situation demands.

Information geometry for landmark shape analysis: unifying shape representation and deformation.

Shape matching plays a prominent role in the comparison of similar structures. We present a unifying framework for shape matching that uses mixture models to couple both the shape representation and deformation. The theoretical foundation is drawn from information geometry wherein information matrices are used to establish intrinsic distances between parametric densities. When a parameterized probability density function is used to represent a landmark-based shape, the modes of deformation are automatically established through the information matrix of the density. We first show that given two shapes parameterized by Gaussian mixture models (GMMs), the well-known Fisher information matrix of the mixture model is also a Riemannian metric (actually, the Fisher-Rao Riemannian metric) and can therefore be used for computing shape geodesics. The Fisher-Rao metric has the advantage of being an intrinsic metric and invariant to reparameterization. The geodesicâcomputed using this metricâestablishes an intrinsic deformation between the shapes, thus unifying both shape representation and deformation. A fundamental drawback of the Fisher-Rao metric is that it is not available in closed form for the GMM. Consequently, shape comparisons are computationally very expensive. To address this, we develop a new Riemannian metric based on generalized \phi-entropy measures. In sharp contrast to the Fisher-Rao metric, the new metric is available in closed form. Geodesic computations using the new metric are considerably more efficient. We validate the performance and discriminative capabilities of these new information geometry-based metrics by pairwise matching of corpus callosum shapes. We also study the deformations of fish shapes that have various topological properties. A comprehensive comparative analysis is also provided using other landmark-based distances, including the Hausdorff distance, the Procrustes metric, landmark-based diffeomorphisms, and the bending energies of the thin-plate (TPS) and Wendland splines.