Hierarchical Uncertainty-Aware Salient Object Detection for $360 ^{\circ }$ Images via Bi-Projection Collaborative Learning

<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$360^{\circ }$</tex-math></inline-formula> salient object detection has recently received much attention for 3D scene perception owing to its omnidirectional field of view (FoV). The capability of recognizing salient objects of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$360^{\circ }$</tex-math></inline-formula> images remains technically challenging due to severe spherical distortion. In this paper, we develop a hierarchical uncertainty-aware <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$360^{\circ }$</tex-math></inline-formula> image salient object detection methodology that explicitly explores the geometric and spatial complementary coherence of Tangent projection (TP) and Equirectangular projection (ERP) by a collaborative learning strategy. Concretely, to mitigate spherical distortion, we first intend to learn saliency-related features from less-distorted tangent images, in which a deformation-aware attention block is introduced to mitigate the geometric distortion caused by projecting a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$360^{\circ }$</tex-math></inline-formula> image onto a 2D plane. However, the discrepancies among tangent images pose a new challenge to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$360^{\circ }$</tex-math></inline-formula> image salient object detection. To tackle this issue and achieve accurate localization for salient objects of all sizes, we design a spatial-frequency saliency feature aggregation module to leverage fast Fourier convolution to capture global contextual information from ERP images, such that obtaining more representative saliency features. Moreover, a hierarchical uncertainty-aware bi-projection consistency learning module with strong local-global information embedding capabilities is constructed, which learns the geometric and spatial correlations between tangent images and ERP images via a collaborative learning strategy. Ultimately, salient object maps are produced for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$360^{\circ }$</tex-math></inline-formula> images on the basis of the merged saliency features driven by the uncertainty. Extensive experiments show that our developed method improves <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathrm{F}}_\beta ^{\sigma }$</tex-math></inline-formula> by an average of 31.67% compared to twenty existing advanced methods on the publicly available 360-SOD dataset.