Projective geometry is an incidence geometry of colinearity preserving transformations. Its use is widespread in computer graphics, computer vision, image registration, photography, among others. Homogeneous coordinates are commonly used to represent objects (point, lines, planes etc.) in real projective geometry. These are well-known to represent translation, rotation and perspective transformation simply as matrix-vector multiplication.
Questions tagged [projective-geometry]
94 questions
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Compute homography given rotation and translation between two cameras
I know that one can compute the homography matrix by using at least four correpondence points.
I was wondering if and how can I obtain a homography matrix if I already know the rotation and translation between two cameras, including the camera…
rfn123
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Rectify perspective image of planar structure given the normal vector of the plane and viewing direction of the camera
I have taken images of the facade of a building under multiple view points. Then I use bundler to reconstruct the 3D point cloud of the building. Then I use a RANSAC method to find the plane of the facade in the point cloud.
This gives me the…
user473453
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3D Camera coordinates to world coordinates (change of basis?)
Suppose I have the coordinates X, Y, Z and orientation Rx, Ry, Rz of an object with respect to a camera.
In addition, I have the coordinates U, V, W and orientation Ru, Rv, Rw of this camera in the world.
How do I transform the position (location…
Goosebumps
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Calculate square bounds on Earth with given radius for center point
I'm trying to calculate bounds for square with particular radius and when center of square is known(longitude, latitude). But I'm getting into troubles with it.
I've tried to use haversine formula from here :
But I'm getting into troubles when…
hades
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How can I transform an image using matrices R and T (extrinsic parameters matrices) in opencv?
I have a rotation-translation matrix [R T] (3x4).
Is there a function in opencv that performs the rotation-translation described by [R T]?
Carlo Pane
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Need some help to understanding the formula
This is pinhole camera model:
(I don't get, is there [R t], or (R, t))
This formula is translating the 3d coordinates of the point, to the 2d coordinates of a picture, which is obtained by pinhole camera.
Projection drawing:
Tilde over vector,…
Userr
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Finding Projection and z distance
I have an image that represents a projection. I am going to explain the problem with an example:
In the screen, there is a line from one point E(100,200) to another point
H (150,100). A represent one point
that in the real world is at 200 cm…
manuz
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Normals from projective depth
I want to compute a normal map N(i,j) from a depth map D(i,j), where (i,j) describes 2D pixel location. A basic case of this problem is discussed here: Calculate surface normals from depth image using neighboring pixels cross product
In my case,…
ASML
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How to get rotation angles of Image Plane relative to the World Plane?
So we have such situation:
In this illustration, the first quadrilateral is shown on the Image Plane and the second quadrilateral is shown on the World Plane. [1]
In my particular case the Image Plane has 3 quadrilaterals - projections of real…
Rella
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3D reconstruction using the projection matrices from the trifocal tensor
I have computed the trifocal tensor and corresponding projection matrices P_0, P_1 and P_2 from line correspondences over 3 views, according to 'Multiple View Geometry by Hartley & Zisserman, 2nd edition', Chapter 16. The computed matrices are:
P_0…
takahashi
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Projection matrix + world plane ~> Homography from image plane to world plane
I think I have my wires crossed on this, it should be quite easy.
I have a projection matrix from world coordinates to image coordinates (4D homogeneous to 3D homgeneous), and therefore I also have the inverse projection matrix from image…
B3ret
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Uncalibrated multi-view reconstruction depth estimation
I'm trying to make a 3D reconstruction from a set of uncalibrated photographs in MATLAB. I use SIFT to detect feature points and matches between images. I want to make a projective reconstruction first and then update this to a metric one using…
Hera
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How to compute Aspect angle
I have many 3D planes. The thing that I need to know is the way of computing aspect angle.
I hope, I can compute the aspect angle by using the projected normal vector of each plane (my plane equation is ax+by-z+c=0; so normal vector of this plane…
niro
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Projective or Euclidean 3D- Reconstruction?
I have problems understanding if I get an euclidean reconstruction result or just a projective one. So at first let me tell you what I've done:
I have two stereo images. The images are SEM images and are eucentrically tilted. The difference of tilt…
Miau
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Homographic image transformation issue for sattelite images
I want to apply homography to the satellite images. I found this post quite helpful. So I decided to use the same Matlab code.
im = imread('cameraman.tif');
n = [0;0;-1];
d = Inf
theta = 60*pi/180;
R = [ 1 0 0 ;
…
Addee
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