GauCho: Gaussian Distributions with Cholesky Decomposition for Oriented Object Detection

TL;DR

GauCho introduces a Gaussian-based regression head for oriented object detection that regresses the parameters of a 2D Gaussian via a unique Cholesky factor, $C=LL^T$, enabling seamless use with Gaussian loss functions and addressing angular boundary discontinuities. By linking Gaussian parameters to OBBs and Oriented Ellipses (OEs), GauCho supports both anchor-free and anchor-based detectors, with well-defined bounds on the Cholesky coefficients and explicit decoding into OBBs or OEs. Empirically, GauCho achieves competitive performance with traditional OBB heads across detectors and datasets, while yielding smaller angular errors (e.g., orientation error on HRSC improves from $1.36^{\circ}$ to $1.11^{\circ}$ average) and beneficial effects on DOTA with multiscale training/testing. The work also highlights the advantages of OEs for reducing encoding ambiguity in circular/near-circular objects and provides theoretical and empirical analyses to support the proposed representation and decoding strategies.

Abstract

Oriented Object Detection (OOD) has received increased attention in the past years, being a suitable solution for detecting elongated objects in remote sensing analysis. In particular, using regression loss functions based on Gaussian distributions has become attractive since they yield simple and differentiable terms. However, existing solutions are still based on regression heads that produce Oriented Bounding Boxes (OBBs), and the known problem of angular boundary discontinuity persists. In this work, we propose a regression head for OOD that directly produces Gaussian distributions based on the Cholesky matrix decomposition. The proposed head, named GauCho, theoretically mitigates the boundary discontinuity problem and is fully compatible with recent Gaussian-based regression loss functions. Furthermore, we advocate using Oriented Ellipses (OEs) to represent oriented objects, which relates to GauCho through a bijective function and alleviates the encoding ambiguity problem for circular objects. Our experimental results show that GauCho can be a viable alternative to the traditional OBB head, achieving results comparable to or better than state-of-the-art detectors for the challenging dataset DOTA

Figures (10)

• Figure 1: Examples of different parameterizations for OOD. (a) Long-Edge (LE) for OBBs. (b) Gaussian (covariance matrix).
• Figure 2: Encoding ambiguity problem for circular objects: any rotated square (red) is a viable choice. Oriented Ellipses (OEs, in green) induced by Gaussian representations mitigate the problem.
• Figure 3: Examples of object representations using OEs and OBBs for different categories overlaid with the RGB image (top) and annotated segmentation mask (bottom). (a) Geometrically oriented objects. (b) Semantically oriented objects. (c) Ill-oriented objects. (d) Circular objects.
• Figure 4: Orientation Error for different GT orientation bins using FCOS with OBB and GauCho heads in HRSC.
• Figure 5: When regressing angular information from a Gaussian-based loss, the global angular minimum (red, $\theta = 89^\circ$) might be close to the discontinuous counterpart (green, $\theta = -90^\circ$).

Theorems & Definitions (5)

• Proposition 3.1: Bounds on the elements of the covariance matrix
• proof
• Proposition 3.2: Bounds on the elements of the Cholesky matrix
• proof
• proof