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Questions tagged [projective-geometry]

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.

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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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Are homogeneous coordinates represented by appending image coordinates with a 1 in camera imaging

In camera imaging, there are several terms for point coordinates. World coordinates: [X, Y, Z] in physical unit Image coordinates: [u, v] in pixel. Do these coordinates become homogeneous coordinates by appending with a 1? Sometimes in books and…
Jogging Song
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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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Trouble understanding the alignment of epipoles with an axe

This question arose when I was reading this paper. The goal is the estimation of the relative pose of two cameras C1 and C2, given five point correspondences. The projective planes are considered as unit spheres, and the global coordinate system is…
Ash
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Computing a projective transformation to texture an arbitrary quad

I would like to compute a projective transformation to texture an arbitrary quad in webgl (with three.js and shaders if possible/necessary). This is what I want to obtain, taken from this answer. Everything is well described in the post, so I…
arthur.sw
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What is projective geometry and cross ratio in computer vision?

Please explain a layman's way. I was reading this tutorial http://lear.inrialpes.fr/people/triggs/pubs/isprs96/node27.html but i am not able to understand.
nowonder
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Cropping out Extreme Distortion from a Homography

I have a picture of a checkerboard taken from an arbitrary camera angle. I find the two vanishing points corresponding to the two sets of lines that form the checkerboard grid. From these two vanishing points, I compute a homography from the…
user2397833
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2d to 3d - how to wrap a drawing around a cylinder

I have drawings (arrays of points with x and y coordinates) that are rotated in 3d space: http://www.motiondraw.com/md/as_samples/Testing/_mindreader/main.html As it is now, the drawing looks as if wrapped around a cube, with a nasty 90° degree in…
Andreas Weber
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Projective transformation by dragging handles

We would like to implement this kind of transformation: Screenshot-73.png This image is taken from Gimp, using the Unified Transform Tool. You simply drag the corners and the rectangle is transformed freely. I believe this is called a projective…
Gazihan Alankus
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How to deduce l' = Ex or l' = Fx using the epipolar constraint?

How to deduce l' = Ex using the epipolar constraint? Where l' is the epipolar line, E is the essential matrix and x is the projected point in the image plane. I understood that according to the epipolar constraint (all 3 vectors lie on the same…
Hangon
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Point projection using cross-ratios goes completely wrong after certain threshold

I'm trying for a computer vision project to determine the projection transformation occurring in a football image. I detect the vanishing points, get 2 point matches, and calculate the projection from model field points to image points based on…
Jacco.Oosterhuis
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Reconstructing a non-planar polygon in 3D given a 2d projection and known polygon dimensions

I have a non-planar object with 9 points with known dimensions in 3D i.e. length of all sides is known. Now given a 2D projection of this shape, I want to reconstruct the 3D model of it. I basically want to retrieve the shape of this object in the…
Shivam Mangla
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Find Focal Length with DLT Algorithm, Matlab Paper Implementation

I'm trying to implement this paper in matlab: Geometry-Based Camera Calibration Using Five-Point Correspondences From a Single Image Now, I think I have correctly found the camera position, while I'm still doubtful on the Rotation Matrix and can't…
Brokenp17
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Detecting moving objects in Images with trifocal tensor and trilinear constraints

I want to use trifocal tensor to detect moving objects. but I have a problem. I already know what is the 3 camera projection matrixes(P matrixes) in 3 image frames. I assume that 3 P matrixes are [I|0], [I|-1; 0; 0], [I|-2; 0; 0]. A 3D point X is…
chungjae
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