Transformation

1. Transformation

=> Transformation Groups

  -> Group의 결성조건 : 3D data가 3D를 벗어나지 않고 Group 안에 닫혀있어야 한다.

  -> Group의 특성

    -> 1. Operator *에 닫혀있음[AㅌG and BㅌG -> A*BㅌG]

    -> 2. 독립적인 element I가 존재함[A*I = I*A = A]

    -> 3. Inverse가 존재함[A^(-1) * A = A * A^(-1) = I]

  -> Example

    -> A*(B*C) = (A*B)*C

    ->

? = T1^(-1) * T2^(-1)

 

 

=> Transformations

 ->

    -> Translation[이동] / Euclidean[회전] / affine[찌그러짐] / projective[양방향 찌그러짐] / similarity[크기변형]

  -> 1. Scale

Scale

 

    -> Scale은 항상 기준이 필요하며, Sx Sy가 다르더라도 Scale에 속함

 

  -> 2. Rotation[DOF = 1 / 3D DOF = 3]

Rotation

 

    -> 세타 방향으로 Rotation

 

  -> 3. Euclidean[DOF = 3 / 3D DOF = 6]

Euclidean

 

    -> Rotation+Translation

 

  -> 4. Similarity[DOF = 4 / 3D DOF = 7]

similarity

 

    -> Translate + Rotate + Scaling

 

  -> 5. Affine[DOF = 6]

Affine

 

  -> 6. Projective[DOF = 8]

Projective

 

 

2. Camera model

=> World(u,v,w) -> Camera(x,y,z) -> Film(x,y) -> Pixel(u,v)

 

  -> World to Camera Transformation[P_c = M_ext x P_w]

 Pc = R(Pw-C)

  -> Camera to Film(3D-to-2D projection)[p = M_int x P_c]

  -> Film to Pixel(Affine Transformation)[u = M_int x P_c = M_aff x M_proj x Pc]

o(translation) / s(좌/우 차이 조정)