# Questions tagged [computer-vision]

Mathematical methods used in widely understood computer vision.

125 questions
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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 $g$ ...
1answer
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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 ...
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### Fast Marching Method - How does the procedure start?

I've read about the Fast Marching Method described by Sethian in his book "Level Set Methods and Fast Marching Methods" and also in the paper "Fast Marching Methods", which can be found for free here: ...
0answers
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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 ...
1answer
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### How to discretize and normalize an $n*n$ Gaussian kernel?

A 3x3 Gaussian kernel is usually shown as $$\frac{1}{16} \begin{bmatrix}1 & 2 & 1\\ 2 & 4 & 2\\ 1 & 2 & 1\end{bmatrix}$$ But where does that actually come from?
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### Discrete derivative of array

In relation to computational photography, let's say we have a 1 dimensional mean filter defined as $h =\begin{bmatrix} \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \end{bmatrix}$ Where $u$ is ...
3answers
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### Is it possible to point one camera to the location of some coordinates on the picture taken by another camera?

Let's say we have a scenario like this: There is the pink camera and the blue camera. Both cameras have different fields of view and orientations. The pink camera takes a picture like this one: On ...
1answer
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### There cannot be a concept of parallelism in a homogeneous projective space?

Page 4 of my computer vision textbook, Multiple View Geometry in Computer Vision (Second Edition), by Hartley and Zisserman, states the following: Affine geometry. We will take the point of view ...
0answers
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### Matching shapes between two images

I am working on a computer vision application for Arduino using a very low resolution camera (80x80 pixels). I want to detect moving shapes. The segmentation part works fine as i managed to detect ...
1answer
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### What is the resulting $\sigma$ after applying successive gaussian blur?

From Wikipedia Gaussian Blur it said that Applying multiple, successive Gaussian blurs to an image has the same effect as applying a single, larger Gaussian blur, whose radius is the square root of ...
1answer
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### Is the homogeneous point $(0,4,0,0)$ a point at infinity?

Can you please explain the geometric euclidean interpretation of homogeneous point $x= (0, 4, 0, 0) \in P$. Does it means a point at infinity?
1answer
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### Finding the linear mapping between homogeneous coordinates of affine camera

If I have an affine camera with a projection relationship governed by: \begin{equation} \begin{bmatrix} x & y \end{bmatrix}^T = A \begin{bmatrix} X & Y & Z \end{bmatrix}^T + b \end{...
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### Camera Location ( Projective Geometry - Computer Vision)

I want to find the location of a camera in 'world coordinates' based on projective geometry. My source of theory is the book Multiple View geometry in Computer Vision, as well as A Flexible New ...
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### “Eigen images” for categorical data

I have a sequence of categorical images. For a two category image, each image pixel can have one of two values. I would like to analyze these images using a technique like eigen images. The goal is to ...
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37 views

### A confusion on the variance of weight matrix of Kaiming He's initialization

When trainning neural networks with ReLU function, Kaiming He's initialization is a good way to initialize parameters. In the paper "Delving Deep into Rectifiers", the author gave detailed derivation ...
2answers
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### How to complete a noisy perspective rectangle?

I have an image of a rectangle that is noisy (perspective image). I know the value of $x$, $y$, and angle $3$. Angles "$2$" and "$4$" are not accurate. Also, I know the real rectangle size. The angle ...
2answers
41 views

### Top Base Fractional Number

For example: $2^3 = 2 \cdot 2 \cdot2$ But what about a fractional power such as: $$2^{2/3} = ?$$ 1) How would I explain this? 2) How would I find value? 3) How would computers calculate ...
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### Cross correlation coefficient for 2 matrices (two 2d arrays)

I'm trying to manually calculate cross correlation coefficient for 2 matrices. But I'm not sure how to apply the formula and how it works. Here are my example matrices: Matrix 1 Matrix 2 Any help ...
0answers
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### What is a Visual Sphere and where can I learn more about it?

I am reading a research paper by "Andrea Censi" and "Davide Scaramuzza" on Low Latency Event Based Visual Odometry. In the paper it is mentioned: "Let the data from the camera be a sequence of ...
0answers
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### Affine rectification via vanishing line

I'm trying to understand how to rectify an image given some lines that should actually be parallel in the final image. For example: from the book Multiple View Geometry. I know that the idea is to ...
0answers
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### how to find an angle between the person's body and camera?

I am working on project which requires me to find the angle between the person's body and the camera. I already have the pose coordinates of the person but I am not sure how to find the angle. Do you ...
0answers
50 views

### Unknown mathematical symbol in context of computer vision

I'm currently reading the paper "A Template Matching Method for Multi-Scale and Rotated Images Using Ring Projection Vector Conversion" and in one formula there is a mathematical symbol I don't know. ...
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### Obtaining depth to an object of known dimensions from a monocular calibrated camera

I am using notation defined in this page: Camera Calibration In summary: The standard frame is the frame that has the origin at the projection center and z axis pointed "out" from the lens. The ...
1answer
172 views

### 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 ...
0answers
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### Partial derivatives of surface curvature relative to a tangent plane

If we take the tangent plane (say, $\mathsf{T}$) to a convex surface $\mathcal{S}$ associated with a given surface normal vector $\mathtt{n}$, I assume the surface will have a fixed rate of change ...
2answers
273 views

### Identifying the Plane at Infinity in the World Necessitates Determining the Affine Geometry of the World?

Page 18 of my computer vision textbook, Multiple View Geometry in Computer Vision (Second Edition), by Hartley and Zisserman, states the following: 1.8 Auto Calibration $\vdots$ Generally ...
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### Displacement and rotation of the template pattern relative to the camera in 3D space

I have the template pattern (for example, rectangle), so I know it's size in mm. Also I have several frames with this pattern. So I know the intrinsic matrix $K$ of camera with which these frames were ...
1answer
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### Calculation of angle of rear wing of race car above x axis from an image

I am planning an application measuring the angle of rear wing of race car from image or realtime video (from lateral perspective target angle from this kind of image). This is the equation I am ...
1answer
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### Boundary conditions in minimizing Dirichlet energy for an image processing problem.

Suppose $$\mathcal{L} =\mathcal{L}(x,y,u,u_x,u_y) = \frac{1}{2} \lVert \nabla u \rVert^2$$ and I want to find $u$ such that the functional $$E(u)=\int_{\Omega} \mathcal{L}dxdy$$ is minimized, ...
1answer
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### What is the meaning of “linear projections onto rows of some matrix”?

I was reading through a research paper on compressive particle filtering for target tracking, and I came across the following: Let $z \in d_{z}$ denote a vectorized image with $d_{z}$ pixels. Assume ...
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199 views

### Substitute a Fully-Connected layer with 1x1 Conv Layer

I am following Andrew Ng's class on ConvNets and I don't get the part where we try to replace a FC layer with a Conv layer and say that both are mathematically equivalent. Here is a picture from the ...
0answers
23 views

### Comparison of 3 Computer Vision Metrics

right now i do a comparison of 2 Algorithms, with the help of 3 metrics. The problem is that in one paper the metrics are differently described than in the other so i have to "proof" that they are the ...
0answers
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### Calculating depth image from surface normal images, confused about integration/summation algorithm

(Originally posted in Stack Overflow, re-posting here since my question's probably a better fit here) I'm going through Forsyth/Ponce and working through their reading on recreating a depth map from ...
0answers
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### Is it reasonable to use a log-concave density to model the joint density of natural images?

That is, something like $$p(x) \propto \exp(-V(x) - \phi(x)),$$ where $V: \mathbb R^p \rightarrow \mathbb R$ is a convex function on the image manifold (here assumed to be $\mathbb R^p$, where $p$ ...
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### Getting mean curvature using the normal vector map $N(x,y,3)$

To be honest, it is a question for computer vision. There is a normal vector map $N(x,y,3)$ represents the normal vector $(nx,ny,nz)$ on the point $P(x,y)$. If the resolution is high enough (...
1answer
181 views

### How to get interpolated normal of triangle?

I have this 3D Triangle of which I want to get the interpolated normal of V3. I know how to get the normal per triangle face, but I don't know how to get to interpolated normal. I would calculate ...
3answers
39 views

### How to mathematically write: last matrix position that equals one?

Consider the following (4 x 5) 2D matrix: 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 I need to write in a mathematical language "The last column at row 3 that ...
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### Euler lagrange equations for a curve integral

I'm reading through this paper, where a variational framework to some computer vision feature detection techniques is given. I'm familiar with variational techniques, though I'm not an expert. There's ...
0answers
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### Cannot get laplacian operator from leads given by a computer vision book

This a follow up question to this one. I've tried to follow the explanation given that should allow me to derive a laplacian operator, But what I got isn't correct. The quote is from "Computer Vision ...
0answers
45 views

### Parabola Equation from its trajectory points in a Video

I have a video of an object describing a ballistic trajectory (i.e. A ball being thrown) The video is filmed with an angle and not orthogonally to the moving object, the camera is calibrated. I am ...
1answer
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### I don't know how to find coordinate systems for a question. [closed]

MST is $3 \times 3$ homogeneous matrix that transform points from coordinate system $S$ to coordinate system $T$. 1- What are the coordinates of $P$ in coordinate system $O$? 2- What are the ...
3answers
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### How to get the transform the coordinates of a 3D point from the standard basis to another basis?

Suppose I have the coordinates of a point in the standard $\mathbb{R}^3$ basis $B_0 = (\vec{e_0}, \vec{e_1}, \vec{e_2})$, with $\vec{e_0} = (1,0,0)$, $\vec{e_1} = (0,1,0)$ and $\vec{e_2} = (0,0,1)$. ...
1answer
59 views

### Instrinsic Camera Parameters

I am trying to understand intrinsic camera parameters. Specifically I not able to understand the skew factor and pixel scaling derivation in it. Example: Most of the literature explanation starts ...