ABSTRACT
To obtain geometric insight into the structure of defined in R ¯ ( t ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429489211/b92fa297-e1f1-48d1-8b2a-eb0fa6ba8aab/content/inline291_1.tif"/> and x ¯ f ( t ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429489211/b92fa297-e1f1-48d1-8b2a-eb0fa6ba8aab/content/inline291_2.tif"/> defined in (13.2) can be obtained from Figure 9.1 by placing a fictitious camera that has a frame https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429489211/b92fa297-e1f1-48d1-8b2a-eb0fa6ba8aab/content/i.tif"/> attached to its center such that https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429489211/b92fa297-e1f1-48d1-8b2a-eb0fa6ba8aab/content/i.tif"/> initially coincides with https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429489211/b92fa297-e1f1-48d1-8b2a-eb0fa6ba8aab/content/i.tif"/> . Since https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429489211/b92fa297-e1f1-48d1-8b2a-eb0fa6ba8aab/content/i.tif"/> and https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429489211/b92fa297-e1f1-48d1-8b2a-eb0fa6ba8aab/content/i.tif"/> coincide, the relationship between https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429489211/b92fa297-e1f1-48d1-8b2a-eb0fa6ba8aab/content/i.tif"/> and https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429489211/b92fa297-e1f1-48d1-8b2a-eb0fa6ba8aab/content/fs.tif"/> can be denoted by rotational and translational parameters ( x f * , R * ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429489211/b92fa297-e1f1-48d1-8b2a-eb0fa6ba8aab/content/inline291_3.tif"/> as is evident from Figure 9.1. Without relative translational or rotational motion between https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429489211/b92fa297-e1f1-48d1-8b2a-eb0fa6ba8aab/content/i.tif"/> and https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429489211/b92fa297-e1f1-48d1-8b2a-eb0fa6ba8aab/content/fs.tif"/>, the two coordinate frames are moved until https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429489211/b92fa297-e1f1-48d1-8b2a-eb0fa6ba8aab/content/fs.tif"/> aligns with https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429489211/b92fa297-e1f1-48d1-8b2a-eb0fa6ba8aab/content/f.tif"/>, resulting in Figure B.1. It is now evident that the fixed camera problem reduces to a stereo vision problem with the parameters ( x f − R ( R * ) T ) x f * , R ( R * ) T https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429489211/b92fa297-e1f1-48d1-8b2a-eb0fa6ba8aab/content/inline291_4.tif"/> denoting the translation and rotation between https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429489211/b92fa297-e1f1-48d1-8b2a-eb0fa6ba8aab/content/i.tif"/> and https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429489211/b92fa297-e1f1-48d1-8b2a-eb0fa6ba8aab/content/i.tif"/>.
