{"id":59,"date":"2022-04-29T07:40:27","date_gmt":"2022-04-29T07:40:27","guid":{"rendered":"https:\/\/mscvprojects.ri.cmu.edu\/2022team6\/?page_id=59"},"modified":"2022-04-29T08:18:00","modified_gmt":"2022-04-29T08:18:00","slug":"analysis","status":"publish","type":"page","link":"https:\/\/mscvprojects.ri.cmu.edu\/2022team6\/analysis\/","title":{"rendered":"Analysis"},"content":{"rendered":"\n

Double Sphere Camera Model<\/h2>\n\n\n\n

Due to the extreme distortion that a fisheye lens produces, the pinhole camera model doesn’t apply. There are several models such as the Fisheye Projection Model[1]<\/a><\/sup> and the Kannala-Brandt Camera Model[2]<\/a><\/sup> which could be used. However, the inverse projection (3D point to 2D) either requires solving an optimization problem or expensive trigonometric operations. Enter Double Sphere Camera Model[3]<\/a><\/sup>.<\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

In order to verify that this model worked and to test that the project and inverse projection matched, we performed a small test. By taking a mask similar to a fisheye image, we projected each pixel to 3D space and then reprojected these back to the image plane. Both these operations were performed using the formulae defined by the Double Sphere Camera Model. The resulting pixel locations were compared with the original pixel locations and the projection errors were plotted.<\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

As can be observed, the maximum error was below a pixel separation of 0.0001 which was definitely acceptable. Thus, this camera model would work well for our project.<\/p>\n\n\n\n

Determining Output Size<\/h2>\n\n\n\n

As part of our pipeline, the six fisheye images are stitched together into a panorama image.<\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

The input fisheye size is fixed due to the compute constraints and the requirements of the other modules. \u200b However, the output panorama resolution needs to be determined.\u200b <\/p>\n\n\n\n