Supplementary Material for Inferring 3D Layout of Building Facades from a Single Image

In Section 4.1 of the main paper, we describe the quadrilateral-based sampling algorithm. Here, we further show in Figure 1 an example of how a quadrillateral is sampled from vanishing lines. First, from all the detected horizontal vanishing directions, we randomly select one of them; and among all the vanishing lines belonging to the selected horizontal vanishing direction, we randomly select a pair of them, such as the line segments in magenta in Figure 1. Also, from all the vanishing lines belonging to the unique vertical vanishing direction, we randomly select a pair of them, such as the line segments in red in Figure 1. (Note that vanishing lines located within the region occupied by already-selected quads are not sampled.) The four line segments delineate a quadrilateral as is shown by the yellow shape in Figure 1. The orientation nsi of this quad is equal to the cross-product of the horizontal vanishing direction represented by the magenta line segments, and the vertical vanishing direction represented by the red line segments. Figure 1 also shows the hybrid score of the quadrilateral.