Mathematical methods used in widely understood computer vision.
Questions tagged [computer-vision]
242 questions
99
votes
4 answers
Finding the transform matrix from 4 projected points (with JavaScript)
I'm working on a project using Chrome - JS and WebKit 3D CSS3 transform matrix. The final goal is to create a tool for artistic projects using projectors and animation - somewhat far away from using maths...
I'm using a projector to project several…
mika
- 1,013
37
votes
4 answers
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
- 1,471
33
votes
2 answers
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:
$$ \left(
\begin{array}
…
Kevin Boyd
- 355
18
votes
1 answer
What are the use cases of the Dirichlet energy in computer vision?
I am reading a paper, in the context of computer vision, that mentions the "famous" Dirichlet energy. I am not familiar with this Dirichlet energy, but apparently we can minimise it. What are specific use cases of the Dirichlet energy in computer…
user168764
18
votes
1 answer
Inverse of Perspective Matrix
I am trying to calculate Image to World model for my thesis dealing with road lanes. As a disclaimer I have to say that linear algebra is not my strong suite.
The idea is - given that I know yield, pitch, and position of the camera - I can translate…
Tomáš Kohout
- 283
10
votes
2 answers
Finding Transformation matrix between two $2D$ coordinate frames [Pixel Plane to World Coordinate Plane]
The question I'm trying to figure out states that I have $N$ points $$(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
- 101
9
votes
5 answers
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:
$$
x = f(x') = \,…
Pal Szasz
- 191
9
votes
0 answers
Are convex objects determined by their silhouettes?
Informally, the silhouette of a 3D shape is a viewpoint-dependent 2D projection of it. You might imagine looking at several silhouettes and attempting to construct the overall shape. My question is theoretical: if you have access to the set of all…
user326210
- 19,274
8
votes
2 answers
Solving the matrix equation $X^tA+A^tX=0$ for $X$ in terms of $A$
Suppose that I know $A$. And all matrices in the equation are square matrices. I want to solve for $X$ given that
$$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…
stressed out
- 8,330
8
votes
2 answers
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…
MapleWings
- 81
8
votes
2 answers
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
- 211
6
votes
2 answers
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
- 163
6
votes
0 answers
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…
Frame91
- 155
- 1
- 7
6
votes
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
- 31,079
6
votes
2 answers
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^{'} =…
Matthias Preu
- 307