Projectors have become a widespread tool to share information in Human-Robot Interaction with large groups of people in a comfortable way. Finding a suitable vertical surface becomes a problem when the projector changes positions when a mobile robot is looking for suitable surfaces to project. Two problems must be addressed to achieve a correct undistorted image: (i) finding the biggest suitable surface free from obstacles and (ii) adapting the output image to correct the distortion due to the angle between the robot and a nonorthogonal surface. We propose a RANSAC-based method that detects a vertical plane inside a point cloud. Then, inside this plane, we apply a rectangle-fitting algorithm over the region in which the projector can work. Finally, the algorithm checks the surface looking for imperfections and occlusions and transforms the original image using a homography matrix to display it over the area detected. The proposed solution can detect projection areas in real-time using a single Kinect camera, which makes it suitable for applications where a robot interacts with other people in unknown environments. Our Projection Surfaces Detector and the Image Correction module allow a mobile robot to find the right surface and display images without deformation, improving its ability to interact with people.