---

CS4670/5670: Computer Vision, Spring 2015

Project 4:  Single View Modeling

To Do

---

These are the routines that you'll write:

svmmath.cpp:

• BestFitIntersect(const std::list &lines)
  Compute the best intersection point of 3 or more lines in a least squares sense. Here is a write-up for a recommended method that extends the cross-product method discussed in class to return the best intersection point of 3 or more lines in a least squared sense.
• ComputeHomography(double H[3][3], double Hinv[3][3], const vector<SVMPoint> &points, vector<Vec3d> &basisPts, bool isRefPlane)
  Compute the homography H from the plane specified by points to the image plane, as well as Hinv, the inverse of H. This is used to compute the homography for the reference plane, as well as the polygonal patches you create. In case of an arbitrary polygonal patch in 3D space, you need to convert the coordinate system first. See this document for a more detailed explanation.
• ConvertToPlaneCoordinate(const vector& points, vector& basisPts, double &uScale, double &vSvale)
  Convert the coordinate of points on the designated plane to the plane coordinate system, as described in above mentioned document. This is called from ComputeHomography to compute homographies from polygonal patches you defined in the scene. Save the final scales you apply to the u and v dimensions to the output parameters uScale and vScale.

ImgView.inl (part of ImgView.cpp to be filled in, in a separate file):

• ImgView::sameXY()
  Compute the 3D position of a new point that is directly above another point whose 3D position is already known. See the slides for measuring height (Projective Geometry slides 15, 16). Also, your work on the written part of this project should inform what you do here.
• ImgView::sameZPlane()
  Compute the 3D position of a new point that is on the same plane as another point whose 3D position is already known. A special case of this is a point on the reference plane. In this case, the reference homography H can be used to compute its 3D position. You should be able to use your work from the written part of this project to inform what you do here.   More generally, see the man on the box slide from lecture (Projective Geometry slide 16), where the given reference point is t₁, the new point is m₀, and you want to compute the point b₀ (once you have b₀, you can compute its X and Y positions using H).  Note that the man is not used here, we're only interested in a point on the box.  You may use v_z instead of t₀ to help find b₀. While you're not given the image position of b₁, you can compute it from its 3D coordinates (knowing it has the same X-Y coords as t₁ and is on the ground), using H^-1.

ImgViewBox.cpp:

• solveForOppositeCorners(double u0, double v0, double u2, double v2, double &u1, double &v1, double &u3, double &v3)
  Given the 2D position of corners 0 and 2 on an XZ rectangle, compute the 2D positions of the other two corners (with indices 1 and 3). You'll need to use the vanishing points and construct various lines to find the points. The indexing of the corners is shown here:
  
• solveForOppositeFace(SVMSweep *sweep, double imgX, double imgY, Vec3d &p4_out, Vec3d &p5_out, Vec3d &p6_out, Vec3d &p7_out)
  Given the 2D positions of corners 0,1,2, and 3 on a box, compute the 2D positions of the other four corners (with indices 4, 5, 6, and 7). Again, you'll need to use the vanishing points and construct various lines to find the points. The indexing of the corners is shown here:
  
• find3DPositionsBox(SVMPoint *points[8])
  Given the 2D position of all eight corners of a box (indexed according to the previous image), and the 3D position of the anchor (point 0), compute the 3D coordinates of all points. You will want to first implement the sameXY and sameZPlane routines.

camera.cpp:

• computeCameraParameters()
  Compute the position and projection matrix for the camera, assuming the reference homography and reference height have already been specified. See the main project page for more information.
• invertScene(double zScale)
  Invert the scene in order to create a reverse perspective image. You'll need to compute a transformation for inverting the scene, as described on the main project page. The parameter zScale controls how deep the inverted scene will be. Before inverting the scene, you first need to compute the camera parameters.

---

Last modified April 7, 2015