In order to realize autonomous robot navigation, we propose a method for detecting the boundary between a floor and a wall by extracting an ellipse projected from a robot-mounted projector. We note that a circular cone of light projected onto the region where the floor and the wall meet produces two intersecting ellipses in the image. We detect the two ellipses from the image and estimate the line that separates them, which we regard as the floor-wall boundary. We also propose a new method for fitting an ellipse to an edge point sequence which may contain outliers, i.e., non-elliptic arcs. Using real images, we show that our proposed method can detect the floor-wall boundary even when the detected edge point sequence contains outliers that have complicated forms.