San Francisco World: Leveraging Structural Regularities of Slope for 3-DoF Visual Compass

We propose the San Francisco world (SFW) model, a novel structural model inspired by San Francisco's hilly terrain, enabling 3D inter-floor navigation in urban areas rather than being limited to 2D intra-floor navigation of various robotics platforms. Our SFW consists of a single vertical dominant direction (VDD), two horizontal dominant directions (HDDs), and four sloping dominant directions (SDDs) sharing a common inclination angle. Although SFW is a more general model than the Manhattan world (MW), it is a more compact model than the mixture of Manhattan world (MMW). Leveraging the structural regularities of SFW, such as uniform inclination angle and geometric patterns of the four SDDs, we design an efficient and robust DD/vanishing point estimation method by aggregating sloping line normals on the Gaussian sphere. We further utilize the structural patterns of SFW for the 3-DoF visual compass, the rotational motion tracking from a single line and plane, which corresponds to the theoretical minimal sampling for 3-DoF rotation estimation. Our method demonstrates enhanced adaptability in more challenging inter-floor scenes in urban areas and the highest rotational tracking accuracy compared to state-of-the-art methods. We release the first dataset of sequential RGB-D images captured in San Francisco world (SFW) and open source codes at: <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://SanFranciscoWorld.github.io/</uri>.