# Image Projection with Homography Estimation in R: Computer Vision Concepts

(Sandipan Dey, 17 August 2016)

• In this article, the concepts of projective geometry and homographies will be used to project an image onto a scene in a natural way that respects perspective.
• To demonstrate this, first the UMBC logo will be projected onto the goal during a football match (this appeared as an assignment in the Coursera Course Robotics Perception by the University of Pennsyvania). The images were extracted from a video sequence of a football match, as well as the corners of the goal in each image and an image of the UMBC logo are provided.
• For each image in the video sequence, the homography is computed between the UMBC logo and the goal, and the goal points are then warpped onto the ones in the UMBC logo to generate a projection of the logo onto the video frame.
• Homography Estimation: To project one image patch onto another, the homography between the two image patches are needed to be calculated. This homography is a 3×3 matrix that satisfies the equation x_logoH_xvideo.
• Inverse Warping: first the logo image is projected onto the video frames and then every point in the video frame x_video is replaced with the corresponding point in the logo x_logo. The corresponding math equations needed are shown below:
• The original movie for the football match is shown below.
• The next movie shows the projected image of the UMBC logo on the goal post of the original movie using Homography.
• The next animations show the projected logo / face image of the image of the UMBC buildings, as the proportion of projection varies from 0 to 1.