By Henry Chalfant
Indicates examples of graffiti from all over the world and stocks the reviews of graffiti artists approximately their paintings.
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I) Quasi-perspective projection matrix has nine degrees of freedom, and the parallelism along X and Y directions in world system are preserved in images. (ii) Quasi-fundamental matrix can be simplified to a special form with only six degrees of freedom. The fundamental matrix is invariant to any non-singular projective transformation. (iii) Plane induced homography under quasi-perspective model can be simplified to a special form defined by six degrees of freedom. The quasi-homography may be recovered from two pairs of corresponding points with known fundamental matrix.
4] analyzed a general form of symmetric affine camera model to mimic G. J. 1007/978-0-85729-046-5_2, © Springer-Verlag London Limited 2011 29 30 2 2 Simplified Camera Projection Models perspective projection and provided the minimal requirements for orthographic, weak perspective, and para-perspective simplification. The model contains two free variables that can be determined through self-calibration. Affine assumption is widely adopted for the study of structure from motion due to its simplicity.
Proof In projective geometry, parallel lines in 3D space appear to intersect at a point at infinity, which is also called ideal point in P3 . The intersection of the parallel lines along X and Y directions can be written in canonical form as Vx = [1, 0, 0, 0]T , Vy = [0, 1, 0, 0]T . 5) Obviously, both vx and vy locate at infinity, thus the parallelism is preserved along the X and Y directions. In a similar way, we can verify that parallel lines on the O − XY coordinate plane or any other parallel planes also project to parallel lines in the image.