# Questions tagged [computer-vision]

Mathematical methods used in widely understood computer vision.

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### Finding Rotation and Translation from 2 known sets of data

As illustrated in the Figure above, I have 2 point clouds $X$ and $X'$ which initially lie on the same plane $\mathcal{P}$. The orientation of $\mathcal{P}$ - i.e. both Rotation $\mathbf{R}_0$ and ...
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### Why the epipoles are the Fundamental matrix right and left null space in Computer Vision?

I have known that the Fundamental matrix is $\operatorname{rank}(2)$,and all the epipolar lines meet at the epipoles. Given this identity $(e')^T\cdot (Fx)= \mathbf 0$, in order to make this equation ...
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### Deriving the essential matrix using the scalar triple product

I'm trying to test my understanding by deriving famous results from computer vision. This one: the essential matrix. I'm using the scalar triple product to encode the co-planarity constraint. I'm ...
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### Object detection uncertainty due to camera limitations

I have a 2-D image of an object, and am using this to detect an object and estimate the object's position relative to the camera's pose (say, as a vector between the origin of the camera's coordinate ...
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### Why are these matrices oddly sized?

With regards to the above image which was delivered as a slide in a Computer Vision course, I can't understand why this matrix multiplication is represented as a $4\times4$ * $4\times1$ where I feel ...
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### How can I turn a mirrored image of an object into a natural perspective of itself?

I am trying to get the 3D mapping of a fast moving object and only have 1 high fps camera on-hand. Thus I am opting for a setup using a mirror to reflect the 2nd perspective to my camera. The software ...
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### Constants in the mathematics of sRGB [closed]

I am learning about color spaces in digital images, and while researching the precise definition of the sRGB space on wikipedia, found what seemed to me as an unnecessarily complex, full of (to me) ...
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### Calculating whitespace given list of rectangles?

It's part of a software application, but should be irrelevant for this. The main thing is the code generates a set of rectangles (with each having x, y position and width, height). Some rectangles ...
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### Extracting vanishing points from the camera projection matrix

I’m struggling with the following paragraph from the book Multiple View Geometry: The columns of the projective camera are 3-vectors which have a geometric meaning as particular image points. ...
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### Using trigonometry to find projection of a point at $(x, y, z)$

The following slide is part of a lecture on computer graphics, where the author is explaining the pinhole camera model: I don't understand what "trigonometry" the author is referring to here. It ...
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### Understanding the formula of anisotropic filtering (Barcelos et al. (2003))

I am currently trying to understand a paper about shadow removal (DESHADOWING OF HIGH SPATIAL RESOLUTION IMAGERY APPLIED TO URBAN AREA DETECTION, Samara Azevedo et al.), but I am currently stuck at ...
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### Radius of the paraxial impulse response of a pinhole camera

I have the following pinhole camera: The cone of rays that would enter the pinhole from the object would resemble the following: (Image from https://www.optilayer.com/products-and-services/tools/...
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### Calculating half-angle of cone of rays entering pinhole camera

I have the following pinhole camera: The cone of rays that would enter the pinhole from the object would resemble the following: (Image from https://www.optilayer.com/products-and-services/tools/...
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### Why is the null-space of A 2-dimensional if 7 point correspondences are used to estimate the fundamental matrix?

Just have a bit of confusion with understanding the 7-point algorithm for calculating the Fundamental Matrix. When reading notes, I see that the 7-point algorithm uses 7 point correspondences in the ...
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### Hi, non-mathematician here, looking for any proof regarding gimbal lock being unavoidable for 3-value rotation representations

So while there are many CG-oriented guides explaining gimbal-lock, they always jump into quaternions without first stating the necessity for doing so in that it's a dead end for deriving rotations ...
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### 8 degrees of freedom in homography

I am working through the math behind homographies, but my math skills are a bit rusty. A homography can be calculated with 8 corresponding points (4-4) because the homography matrix has 8 degrees of ...
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### Finding side length from two scalene triangles with common angle and side and ratio between sides. Trigonometry

I have two scalene triangles with a common angle and side. I would like to find the length of $x_2$. I have all variables in green: the angles $\angle$ B,$\angle$ C,$\angle$ D,$\angle$ E and side "...
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### Calculating FPIR/FNIR the way NIST does

My question is about the metrics NIST uses to calculate FPIR (false positive identification rate) and FNIR (false negative identification rate). Their official report on testing biometric vendors (...
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### Is it possible to constrain an ellipsoid knowing projected points coordinates on image plane?

Simple Case If we know the 3D position of the points and know they are on an ellipsoid Q, we could directly use the equation: $X^TQX=0$, where Q is the 4x4 matrix. Question I'm wondering is it ...
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### Minimizing the Frobenius norm for projecting on the essential space

In order to understand the eight-point algorithm I have some trouble with the proof of theorem 0.3 from https://cs.gmu.edu/~kosecka/it835/lect4.pdf in the first step. The idea is to show that for a ...
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### Identifying that two planes touch and “merging” them

I have a series of finite planes defined by 4 corner points. Some of the planes are "touching" (to a certain small tolerance), and I would like to identify these touching planes and "merge" them into ...
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### Solving PDE produced for $C^1$ isometric embedding and its complexity analysis

I am a beginner in differential geometry and I am investigating $C^1$ isometric embedding of Riemannian manifolds to Euclidean space for computer vision. I know that the PDE produced for a metric $g$ ...
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### What's the meaning of a derivative of a parametric curve?

A parametric curve $C$ can be defined as follows $$C(p) = \{x(p), y(p) \}, \; p \in [0, 1]$$ where $p$ is the parameter. We can define the unnormalised tangent to the point of the curve ...