This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Assignment 3 By Assignment 3 Honor Pledge: I pledge on my honor that I have not given or received any unauthorized assistance on this assignment/examination. 1. Question 1 Let us assume the rotation matrix and translation matrix has the following form R = r 11 r 12 r 13 r 21 r 22 r 23 r 31 r 32 r 33 T = t 1 t 2 t 3 Hence, we have 12 parameters to estimate in total. For any given 3D point coordinate with respect to the world coordinate, C = X Y Z , and the corresponding coordinate with respect to camera coordinate system is c = x y z . The transformation between C and c is x y z = R X Y Z + T To be more explict, x = r 11 X + r 12 Y + r 13 Z + t 1 y = r 21 X + r 22 Y + r 23 Z + t 2 z = r 31 X + r 32 Y + r 33 Z + t 2 We do not know the exact coordinate ( x,y,z ) , but we have the 2D coordinate ( x ,y ) after projection in the image plane. x f = x z y f = y z Hence, x f = r 11 X + r 12 Y + r 13 Z + t 1 r 31 X + r 32 Y + r 33 Z + t 3 y f = r 21 X + r 22 Y + r 23 Z + t 2 r 31 X + r 32 Y + r 33 Z + t 3 Therefore, for every calibration point, we could be able to construct two equations. However, due to the orthonormality properties of the rotation matrix, i.e., R T = R 1 and det R = 1 , we have another 4 equations. Therefore, we need at least four calibration points to determine the transformation....
View
Full
Document
This note was uploaded on 01/12/2012 for the course CMSC 733 taught by Professor Staff during the Spring '08 term at Maryland.
 Spring '08
 staff

Click to edit the document details