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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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proportions of a perspective-deformed rectangle

Given a 2d picture of a rectangle distorted by perspective: I know that the shape was originally a rectangle, but I do not know its original size. If I know the pixel coordinates of the corners in this picture, how can I calculate the original…
HugoRune
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What is the difference between the fundamental, essential and homography matrices?

I have two images that are taken from different positions. The 2nd camera is located to the right, up and backward with respect to 1st camera. So I think there is a perspective transformation between the two views and not just an affine transform…
Karthik Murugan
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Extract projective homography from two Kinect depth maps

Given two consecutive 3D point clouds 1 and 2 (not the whole cloud, say 100 points selected from the cloud with OpenCV's GoodFeaturesToMatch), obtained from a Kinect depthmap, I want to compute camera's homography from 1 to 2. I understand that this…
smirkingman
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Warping an image using control points

I want to convert an image using control points according to this scheme extracted from here: A and B contains the coordinates of the source an target vertices. I am computing the transformation matrix as: A = [51 228; 51 127; 191 127; 191 228]; B…
Freeman
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Is there an algorithm for solving such projection reconstruction geometric problem?

We have a grid with red squares on it. Meaning we have an array of 3 squares (with angles == 90 deg) which as we know have same size, lying on the same plane and with same rotation relative to the plane they are lying on, and are not situated on…
Rella
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Normal Vector of Three Points

Hey math geeks, I've got a problem that's been stumping me for a while now. It's for a personal project. I've got three dots: red, green, and blue. They're positioned on a cardboard slip such that the red dot is in the lower left (0,0), the blue dot…
mattbasta
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Howto project a planar polygon on a plane in 3d-space

I want to project my Polygon along a vector to a plane in 3d Space. I would preferably use a single transformation matrix to do this, but I don't know how to build a matrix of this kind. Given the plane's parameters (ax+by+cz+d), the world…
sum1stolemyname
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Describing nonlinear transformation between two images, using homography

A one to one point matching has already been established between the blue dots on the two images. The image2 is the distorted version of the image1. The distortion model seems to be eyefish lens distortion. The question is: Is there any way to…
C graphics
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How can I project an arbitrary plane identified by 4 points onto a 2d plane?

The issue we are trying to solve the issue of locating a point in two different representations of a plane. The first plane we have is rotated to create perspective; the second is a 2d view of that same plane. We have 4 points on each of the plans…
Scott
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Need help for proper rectilinear projection of equirectangular panoramic image

With the algorithm below, when the projection plane is tangent to the equator (the center line of the equirectangular image), projected image looks rectilinear. But when the projection plane is tilted, (py0 != panorama.height/2), lines are…
Panoramidal
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back-projecting a 2D point to 3D Plucker line

I'm trying to build a tracker (hand tracking personal project), and for this reason I need to back-project a 2d point to a 3d line, using Plucker coordinates. (like ray tracing) As an input, I have the 2d coordinates of a point and the projection…
dim_tz
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Computing a matrix which transforms a quadrangle to another quadrangle in 2D

In the figure below the goal is to compute the homography matrix H which transforms the points a1 a2 a3 a4 to their counterparts b1 b2 b3 b4. That is: [b1 b2 b3 b4] = H * [a1 a2 a3 a4] What way would you suggest to be the best way to calculate…
C graphics
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How is the reprojection error calculated in Matlab's triangulate function? Sadly, the documentation gives no mathematical formula

How is the reprojection error calculated in Matlab's triangulate function? Sadly, the documentation gives no mathematical formula. It only says: The vector contains the average reprojection error for each M world point. What is the procedure/Matlab…
jhegedus
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Multiple-View Geometry

I've two images captured from two cameras of same make placed some distance apart, capturing the same scene. I want to calculate the real world rotation and translation among the two cameras. In order to achieve this, I first extracted the SIFT…
Aarambh
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Different fundamental matrix from the same projection matrices

I use two projection matrices P1 and P2 (for example I'm using dinosaur dataset) and I need to compute the fundamental matrix F. So I use two Matlab functions: Peter Kovesi's function:…
Roberto Iacono
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