Questions tagged [computer-vision]

Mathematical methods used in widely understood computer vision.

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uniform random point in triangle in 3D

Suppose you have an arbitrary triangle with vertices $A$, $B$, and $C$. This paper (section 4.2) says that you can generate a random point, $P$, uniformly from within triangle $ABC$ by the following convex combination of the vertices: $P = (1 -…
dsg
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How to find camera position and rotation from a 4x4 matrix?

To find the intrinsic and extrinsic parameters I calibrated it and the software gave me the extrinsic parameters as a 4 x 4 matrix. This seems to be a 4x4 homogeneous transformation matrix. The values are as follows $$ \left( \begin{array} 0.211…
Kevin Boyd
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Inverse of Perspective Matrix

I am trying to calculate Image to World model for my thesis dealing with road lanes. As a disclaimer I have to say that linear algebra is not my strong suite. The idea is - given that I know yield, pitch, and position of the camera - I can translate…
Tomáš Kohout
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Finding Transformation matrix between two $2D$ coordinate frames [Pixel Plane to World Coordinate Plane]

The question I'm trying to figure out states that I have $N$ points $$(P_{a1x},P_{a1y}) , (P_{a2x},P_{a2y}),\dots,(P_{aNx},P_{aNx})$$ which correspond to a Pixel plane $xy$ of a camera, and other $N$ points $$(P_{b1w},P_{b1z}),…
John
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What are the use cases of the Dirichlet energy in computer vision?

I am reading a paper, in the context of computer vision, that mentions the "famous" Dirichlet energy. I am not familiar with this Dirichlet energy, but apparently we can minimise it. What are specific use cases of the Dirichlet energy in computer…
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Solving the matrix equation $X^tA+A^tX=0$ for $X$ in terms of $A$

Suppose that I know $A$. And all matrices in the equation are square matrices. I want to solve for $X$ given that $$X^tA + A^tX = 0$$ I'm not really good at matrix calculus. Is it possible to solve this problem in the sense that we find a closed…
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Approximation of Hessian=$J^TJ$ for general non-linear optimization problems

My question is: when is the aprroximation of Hessian matrix $H=J^TJ$ reasonable? One truth is that it is reasonable to approximate Hessian with first order derivatives (jacobian), i.e., $H=J^TJ$ when we are solving a non-linear least square problem…
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How to solve a distance problem inside of a picture?

sorry for my bad english. I have the following problem: In the picture you can see 4 different positions. Every position is known to me (longitude, latitude with screen-x and screen-y). Now i want to know, where in the picture a specific position…
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2 answers

Curvature Blindness Illusion: Any mathematical explanation?

Takahashi, Kohske. "Curvature Blindness Illusion." i-Perception 8.6 (2017): 2041669517742178. (Journal link)                     "All lines are identical sine waves. [...] A wavy line is perceived as a zigzag line." Q. I wonder if there is…
Joseph O'Rourke
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Differences between homography and transformation matrix

I'm wondering whats the differences between a homography and a transformation matrix? For me it's kinda look like the same? Or is homography just the more precise word in the area of computer vision and transformation of image plane?
flor1an
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How does one generate recognizable point-patterns on a plane?

I've recently learned that some smartpens (e.g. Livescribe) have a camera in their front part. They film the paper. You have to use special paper which looks as if somebody made a lot of tiny holes with a needle in that paper. Those holes are not in…
Martin Thoma
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How to calculate the inverse of a known optical distortion function?

Assume I have the following lens distortion function: $$ x' = x (1 + k_1 r^2 + k_2 r^4) \\ y' = y (1 + k_1 r^2 + k_2 r^4) $$ where $r^2 = x^2 + y^2$. Given coefficients $k_1$ and $k_2$, I need to calculate the inverse function: $$ x = f(x') = \,…
Pal Szasz
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How to derive the formula for line correspondences to estimate a homography?

When calculating a homography with line correspondences instead of point correspondences, what is the derivation of the formula: $$ l_i = H^T\cdot l^{'}_i $$ I know that: $$ l^T\cdot x = 0 \quad\text{and}\quad l^{'T}\cdot x^{'} =…
4
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Relative camera matrix (pose) from global camera matrixes

I have a list of camera poses from a given ground truth. Each pose is given in the form of a quaternion and a translation, from some arbitrary world origin. Each pose can be assembled into a 4x4 camera matrix of the form : $ P = \begin{bmatrix} R &…
mtourne
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Calculate Camera Pitch & Yaw To Face Point

How do you calculate pitch & yaw for a camera so that it faces a certain 3D point? Variables Camera X, Y, Z Point X, Y, Z Current Half Solution Currently I know how to calculate the pitch, and I do that using the…
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