Tham khảo tài liệu 'innovations in intelligent machines 1 - javaan singh chahl et al (eds) part 13', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 234 J. Gaspar et al. expression for F 4. Re-arranging Eq. 7 results in the following second order polynomial equation F 2 2aF - 1 0 8 where a is a function of the mirror shape t F and of an arbitrary 3D point r z _ - z - F F r - t t a z - F t r - t F 9 We call a the mirror Shaping Function since it ultimately determines the mirror shape by expressing the relationship that should be observed between 3D coordinates r z and those on the image plane determined by t F. In the next section we will show that the mirror shaping functions allow us to bring the desired linear projection properties into the design procedure. Concluding to obtain the mirror profile first we specify the shaping function Eq. 9 and then solve Eq. 8 or simply integrate F -a ựa2 1 10 where we choose the in order to have positive slopes for the mirror shape F . Setting Constant Resolution Properties Our goal is to design a mirror profile to match the sensor s resolution in order to meet in terms of desired image properties the application constraints. As shown in the previous section the shaping function defines the mirror profile and here we show how to set it accordingly to the design goal. For constant resolution mirrors we want some world distances D to be linearly mapped to pixel distances p measured in the image sensor . D a0 .p b0 for some values of a0 and b0 which mainly determine the visual field. When considering conventional cameras pixel distances are obtained by scaling metric distances in the image plane p. In addition knowing that those distances relate to the slope t F of the ray of light intersecting the image plane as p f. F. The linear constraint may be conveniently rewritten in terms of the mirror shape as D F b 11 Notice that the parameters a and b can easily be scaled to account for a desired focal length thus justifying the choice f 1. We now specify which 3D distances D t F should be mapped linearly to pixel coordinates in order to preserve different image invariants .
