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Consider a room with world coordinate system U-V-W as shown. Two cameras are mounted in the room, forming a stereo pair. The world coordinate origin is in one corner of the room, with UV-W axes shown. The "Left" camera Cl is located at world coordinates (10,1,3) and it's xl-yl-zl axes are oriented as shown. The "Right" camera Cr is located at world coordinates (7.1.2) and its xr-yr-zr axes are oriented as shown. Both cameras have a focal length of 1. (1) What is the 3x4 matrix that maps 3D points in world coordinates into 2D points in film plane coordinates (when points are represented as homogeneous coordinates), for the left camera CI? (2) What is the 3x3 essential matrix for the two cameras, treating them as a stereo pair where Cl is the "left camera" and Cr is the "right" camera?

Consider a room with world coordinate system U-V-W as shown. Two cameras are mounted in the room, forming a stereo pair. The world coordinate origin is in one corner of the room, with UV-W axes shown. The "Left" camera Cl is located at world coordinates (10,1,3) and it's xl-yl-zl axes are oriented as shown. The "Right" camera Cr is located at world coordinates (7.1.2) and its xr-yr-zr axes are oriented as shown. Both cameras have a focal length of 1. (1) What is the 3x4 matrix that maps 3D points in world coordinates into 2D points in film plane coordinates (when points are represented as homogeneous coordinates), for the left camera CI? (2) What is the 3x3 essential matrix for the two cameras, treating them as a stereo pair where Cl is the "left camera" and Cr is the "right" camera?

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Consider a room with world coordinate system U-V-W as shown. Two cameras are mounted in the room, forming a stereo pair. The world coordinate origin is in one corner of the room, with UV-W axes shown. The "Left" camera Cl is located at world coordinates (10,1,3) and it's xl-yl-zl axes are oriented as shown. The "Right" camera Cr is located at world coordinates (7.1,2) and its xr-yr-zr axes are oriented as shown. Both cameras have a focal length of 1. U (1) What is the 3x4 matrix that maps 3D points in world coordinates into 2D points in film plane coordinates (when points are represented as homogeneous coordinates), for the left camera CI? (2) What is the 3x3 essential matrix for the two cameras, treating them as a stereo pair where Cl is the "left camera" and Cr is the "right" camera?
Transcribed Image Text:Consider a room with world coordinate system U-V-W as shown. Two cameras are mounted in the room, forming a stereo pair. The world coordinate origin is in one corner of the room, with UV-W axes shown. The "Left" camera Cl is located at world coordinates (10,1,3) and it's xl-yl-zl axes are oriented as shown. The "Right" camera Cr is located at world coordinates (7.1,2) and its xr-yr-zr axes are oriented as shown. Both cameras have a focal length of 1. U (1) What is the 3x4 matrix that maps 3D points in world coordinates into 2D points in film plane coordinates (when points are represented as homogeneous coordinates), for the left camera CI? (2) What is the 3x3 essential matrix for the two cameras, treating them as a stereo pair where Cl is the "left camera" and Cr is the "right" camera?
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