Bài giảng Chapter 2: Projective geometry and camera models

Lecture with the content mapping between image and world coordinates, projective geometry vanishing points and lines, pinhole camera model, cameras & lenses, projection matrix.

Chapter – Camera Model 2-1 Chapter Projective Geometry and Camera Models James Hays, Brown University Department of Mechatronics Chapter – Camera Model 2-2 Contents Mapping between image and world coordinates • Projective geometry  Vanishing points and lines • Pinhole camera model • Cameras & lenses • Projection matrix Department of Mechatronics Chapter – Camera Model 2-3 Camera and World Geometry Department of Mechatronics 2-4 Chapter – Camera Model Projection can be tricky… Department of Mechatronics 2-5 Chapter – Camera Model Projection can be tricky… Department of Mechatronics Chapter – Camera Model 2-6 Projective Geometry • What is lost?  Length Department of Mechatronics 2-7 Chapter – Camera Model Length is not preserved Department of Mechatronics Chapter – Camera Model 2-8 Projective Geometry • What is lost?  Length  Angles Department of Mechatronics Chapter – Camera Model 2-9 Projective Geometry • What is preserved?  Straight lines are still straight Department of Mechatronics Chapter – Camera Model 2-10 Vanishing points and lines • Parallel lines in the world intersect in the image at a “vanishing point” Department of Mechatronics Chapter – Camera Model 2-40 Homogeneous coordinates Conversion Converting to homogeneous coordinates homogeneous image coordinates homogeneous scene coordinates Converting from homogeneous coordinates Department of Mechatronics 2-41 Department of Mechatronics Chapter – Camera Model 2-42 Department of Mechatronics Chapter – Camera Model 2-43 Department of Mechatronics Chapter – Camera Model 2-44 Department of Mechatronics Chapter – Camera Model 2-45 Department of Mechatronics Chapter – Camera Model 2-46 Department of Mechatronics Chapter – Camera Model 2-47 Department of Mechatronics Chapter – Camera Model 2-48 Chapter – Camera Model Finally, the camera coordinate system may be skewed due to manufacturing error, so that angle  between two image axes is not equal to 90º Department of Mechatronics 2-49 Department of Mechatronics Chapter – Camera Model 2-50 Department of Mechatronics Chapter – Camera Model 2-51 Department of Mechatronics Chapter – Camera Model 2-52 Department of Mechatronics Chapter – Camera Model 2-53 Department of Mechatronics Chapter – Camera Model 2-54 Department of Mechatronics Chapter – Camera Model ... Mechatronics Chapter – Camera Model Chapter – Camera Model 2-23 Cameras and Lenses • A lens focuses light onto the film Department of Mechatronics Chapter – Camera Model 2-24 Cameras and Lenses... Mechatronics Chapter – Camera Model 2-3 Camera and World Geometry Department of Mechatronics 2-4 Chapter – Camera Model Projection can be tricky… Department of Mechatronics 2-5 Chapter – Camera Model... Mechatronics Chapter – Camera Model 2-6 Projective Geometry • What is lost?  Length Department of Mechatronics 2-7 Chapter – Camera Model Length is not preserved Department of Mechatronics Chapter – Camera