GauCho: Gaussian Distributions with Cholesky Decomposition for Oriented Object Detection

Motivation & Goals • Oriented object detection (OOD) is an essential application of computer vision that extends horizontal (HBB) object detection by considering the orientation of objects in images. • Oriented Bounding Boxes (OBBs) are typically represented as (x, y, w, h, θ), but the parametrization is not unique: Long Edge (LE), OpenCV (OC) present the boundary discontinuity problem • Gaussian representations are unique, but the mapping from OBB to Gaussian still generates training ambiguities. • In this work, we propose a new paradigm for OOD by regressing the parameters of a Gaussian distribution directly from the network, avoiding the intermediate use of OBBs that theoretically mitigates the boundary discontinuity problem -To avoid a constrained optimization imposed by positive-definiteness of the covariance matrix, we explore the Cholesky Decomposition to develop the GauCho head. • We show a one-to-one mapping between GauCho and Oriented Ellipses (OEs), and advocate their use as an alternative representation for oriented object detection. Mathematical Background Gaussian Bounding Boxes • Represent an OBB with center (x, y), dimensions (w, h) and orientation θ ∈ [-90 • , 90 • ) as a Gaussian distribution with mean µ and covariance matrix C.