Questions tagged [computer-vision]

Mathematical methods used in widely understood computer vision.

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Curve Fitting and continuous identification of parameterized matrix eigenvector from unconnected data points

I need some help potentially applying machine learning or curve fitting techniques to a numerical linear algebra problem I am working on. I have a parameterized symmetric matrix $M(s)$ whose ...
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Book Recommendation on Edge or Boundary Detection

I have recently being interested in the estimation of discontinuities or jumps from noisy signals or densities and spend some time reading "Image Processing and Jump Regression Analysis" by ...
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Confused about notations used in a Computer Vision paper

I was reading a computer vision paper for 3D reconstruction and was a bit confused by two notations: https://www.researchgate.net/publication/327805907_3D_Image_Reconstruction_from_Multi-...
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Computer Vison geometry: distance estimation of moving object from single fixed camera

I have a problem that I am still not sure if it's solvable. I have a system with a single fixed camera pointing to a fixed background (i.e., a wall). the distance between lens and background (at the ...
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"Histogram Equalization" Problem

Here we deal with the problem of Histogram Equalization. Let $\Omega$ be the set of all pixels in an image, but you can just treat it as some arbitrary set in this case. Let $f: \Omega \rightarrow \{0,...
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Fundamental matrix from camera matrices satisfying transpose property

Assume we are given a pair of calibrated cameras with projection matrices $\mathbf \Pi_0$ and $\mathbf \Pi_1$. From Hartley and Zisserman (pg 246), the fundamental matrix is \begin{align} \mathbf F &...
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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 ...
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Need help in comparing two 3D point clouds

I am supposed to take 2 input point clouds and compare them to figure out if there are any differences in them in terms of lets say the location of the components, etc. I thought of doing the feature ...
Ayush Singh's user avatar
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Moving Eyespace/Camera around Globalspace

Im having a hard time understanding the concept of moving the eyespace/camera around the globalspace mathematically. Ive checked out a lot of videos/articles etc., but tbh at this point Im just ...
xhera83's user avatar
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How do projective transformation matrices work?

I've been working on a tool to turn photos of graphs into digital data (I know there are already tools out there, I wanted to understand the mechanism and I find learning by doing the easiest), but I ...
Laurengineer's user avatar
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calculating relative focal length based on a cylinder

I am trying to camera match a photo of a cylinder. The photo is taken relatively straight, and I can get a rotation matrix for the camera based on the elipsis created by projecting the top circle. ...
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finding the radius of a cylinder based on camera position

Not entirely sure this is the right forum, but I'll give it a go. I have a cylinder that is projected onto a 2d plane (3d world with a virtual camera). What I want to figure out is, given a point on ...
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Pinhole camera, rectangle projected to one parallel to axes in image.

I have a situation where I want to take a rectangle in a pin hole camera view and find which the possible corresponding rectangles in 3D space are. Own work: My intuition tells me that the set of ...
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Confused with understanding an equation written with inverse compositional operators

In the paper "Are we ready for Autonomous Driving? The KITTI Vision Benchmark suite" by Lenz and Urtasun (https://www.cvlibs.net/publications/Geiger2012CVPR.pdf) \ The translation error ...
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Transformation/Pose of a sphere using a spherical camera model

I stumpled upon a problem that is related to the Perspective-n-Point problem (https://en.wikipedia.org/wiki/Perspective-n-Point) in Computer Vision and the Orthogonal Procrustes problem (https://en....
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How was the formulas for x,y,z derived from Perspective Projection Formula (stereo vision)

Perspective Projection Formula Reference Hello, I'm learning some formula in relation to computer vision and came across this. How was the formula for x, y, and z formed? Here's the referenced video (...
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Homogeneous coordinates in projective geometry

I am studying Projective Geometry in 3D for Computer Vision. I am confused on the high-level rationale behind our need to map from heterogeneous to homogeneous coordinates, and I would like to confirm ...
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Transforming 2D Laser Profile Data to 3D Coordinates with Angle Considerations: Resolving Discrepancies

General Understanding of what the project does: I'm building a system where I take image(s) of an object at Various positions with a Line-Lazer being projected onto the object Vertically (...
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Velocity field and deformation flow in diffeomorphic registration

I am trying to implement a diffeomorphic registration of two images using an unsupervised algorithm$^\color{magenta}{\star}$ and one of the steps is a generation of velocity field $\bf z$ which is ...
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Choosing number of subdivisions for approximating double integrals in context of image processing

I have a few double integrals that I have to approximate that are based on getting motion parameters from a sequence of images, and I have chosen to use Riemann sums for that purpose. These integrals ...
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how erosion works in mathematical morphology?

I have these definitions: Let $A \subset E^N$ and $b \in E^N$. The translation of $A$ by $b$, denoted by $(A)_{b r}$ is defined as $$ (A)_b=\left\{c \in E^N \mid c=a+b \quad \text { for some } a \in A\...
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Pinhole camera model definitions

As I were implementing the pinhole camera model based on Tsai, I noticed that there were two conventions used. For opencv and others, the following is used: $$ \begin{pmatrix} u_{c} \\\ v_{c} \\\ h_{...
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Deriving equations for estimating the motion parameters of a rigid body [closed]

I am referencing the book "Robot Vision" by Dr Horn. There, he provides the following equations for estimating the general motion parameters of a rigid body:- ∫∫((u-ur)β - (v - vr)α)(-xyβ + (...
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Need help with deriving equations for estimating the motion parameters of a rigid body

I am referencing the book "Robot Vision" by Dr Horn. There, he provides the following equations for estimating the general motion parameters of a rigid body:- $∫∫((u-u_r)β - (v - v_r)α)(-xyβ ...
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Reversing perspective projection of cricles

I have a set of real-world images containing circles, but due to the images not being taken parallel to the circle plane, the circles appear as ellipses in the images. I need to crop out the inside of ...
spam junk's user avatar
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Vanishing points are collinear

I am studying projective geometry where I came across a definition of vanishing line, "The line containing the vanishing point of 2 or more sets of parallel lines on a plane form the vanishing ...
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Min-Sum Belief Propagation not working on a chain model with equal unary potentials

Given is a chain factor graph as presented in the image below with the following properties: Each node can take values 0 or 1 All unary potentials are equal (e.g. $U(a) = 0$ for every node) All ...
Uros Isakovic's user avatar
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Neural Networks Miscalibration Measure

I have read two papers related on a neural networks miscalibration problem (first: "On Calibration of Modern Neural Networks", link: https://arxiv.org/abs/1706.04599 ; second: "...
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Self-Calibration in Aerial Computer Vision

I have read that there are 4 common procedures for auto-calibration in Computer Vision: Mendonca & Cipolla's Method Classical Kruppa's Method Simplified Kruppa's Method Dual Absolute Quadric ...
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Coordinate transform with known camera pose pairs

Let's say that we have two $3D$ coordinate systems, $A$ and $B$. Now I want to get the coordinate transform matrix $T_{AB}$ such that for any points $p_A$ in $A$, we can get its coordinate in $B$ by $...
WButter's user avatar
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1 answer
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Connection between image space and Hough space? [closed]

The other day I got very interested in learning about Hough Transform that is used to detect edges in images. After going through OpenCV documentation, I still couldn't piece together an understanding ...
kiyanuDevs's user avatar
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Question about 3D homogenous line segments from a textbook

I'm reading about homogeneous coordinates from a computer vision textbook. I'm not sure what the author means by "instead of the four degrees that a 3D line truly has." I think in the first ...
codingcultivator445's user avatar
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For two square matrices $A$ and $B$, if $\left | A - B \right |^2_F$ is a small scalar number then can we assume $A \approx B$?

When researching a way to evaluate if two square matrices are equal or (very close to being equal) for a computer vision localization problem, I came across this Math Exchange post Minimize the ...
Azmyin Md. Kamal's user avatar
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Prerequisits on eulerian video magnification

From this article http://people.csail.mit.edu/mrub/papers/vidmag.pdf I became extremely interested in the subject, but I couldn't find too much content that starts from the "basics". This ...
underfilho's user avatar
1 vote
1 answer
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Understanding distance from point to line in homogeneous coordinates

I would like to find the distance between A 2d point given as the homogeneous $P=(x, y, z)$, and a 2d line given as $L=(a, b, c)$. I found an algorithm that does this, I can't figure out why it is ...
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How to calculate the projective transformation matrix given two planes?

When projecting an image from one plane $\left\{ A \right\}$ to another plane $\left\{ B \right\}$, we have $X' = \mathbf{H} \cdot X$ Namely, $\begin{bmatrix}x'\\ y'\\ 1\end{bmatrix} = \begin{bmatrix}...
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Place the camera to match a given camera - object transformation

I know the pose (in camera frame) of an object related to a camera in real world (results are coming from a 6d-pose estimator). In the simulation I want to replicate the same view and same position (...
hosh0425's user avatar
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Small doubt about Constrained Least Squares solution

I was watching this video about Camera Calibration and I have a doubt regarding the solution of the following Constrained Least Squares problem $$ \underset{\mathbf{p}}{\operatorname{min}}\Vert A\...
ИванКарамазов's user avatar
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How to determine if an object is within a camera's frame and its position within said frame knowing the camera properties and distance?

I will list camera and lens properties that may be of use. Camera resolution: 1280×1024 ((0,0) top left and (1279, 1023) bottom right) Lens Focal Length: 3.5 mm Sensor size and lens format: 1/2&...
Johnie Dowe's user avatar
1 vote
1 answer
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Does there exist a structuring element B such that $X \oplus B \supseteq X \ominus B$ isn't true?

In general, if B contains the origin of $\mathbb{E}$ then, the set erosion and dilation by $B$ become, respectively, anti-extensive and extensive; i.e., for all $X$: $ \begin{equation} X \ominus B \...
Nyquist-er's user avatar
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SVD and identifying a projectivity upto similarity

This is from Hartley-Zisserman's Multiple View Geometry in Computer Vision pg 55-56. We are given a conic $$C_\infty^* = \begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0& 0 & 0 \end{...
matpiliya's user avatar
1 vote
1 answer
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Decomposition of a projective transformation of $\mathbb{P}^2$

On page 42 of Hartley-Zisserman's Multiple View geometry in Computer Vision, it states that a projective transformation of the plane (which can be represented by a nonsingular matrix $H$) can be ...
matpiliya's user avatar
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Trouble with chessboard set definition

The following equation is supposed to define a set of points that produces a square grid (like a chessboard). s is the distance between each square in the grid w and h are the dimensions of the board ...
Bradley's user avatar
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Combining two fundamental matrices

Let $\mathcal{F_{ab}}$ be the fundamental matrix obtained from images $A$ and $B$ $$ \mathcal{F_{ab}} = \begin{bmatrix} ab_{11} & ab_{12} & ab_{13} \\ ab_{21} & ab_{22} & ab_{23} \\ ...
user1057053's user avatar
1 vote
1 answer
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How to determine the pose of a 3D ellipse given two projections to 2D of the ellipse?

This question is about whether I'm doing an optimization problem the right way, or if it can be done in a simpler way. I'll start with my problem scenario and then move into my proposed solution. I ...
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Prove: affine transformation maps "line at infinity" to "line at infinity"

I'm studying Computer Vision and my lecturer stated that: The affine transformation maps "line at infinity" to "line at infinity". I'm trying to prove it as part of my ...
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Minimization of residual in Shi-Tomasi feature extraction

I don't understand how in the following paper https://users.cs.duke.edu/~tomasi/papers/shi/TR_93-1399_Cornell.pdf (Good features to track) the residual (Eq. 3.1) is differentiated so that Equations 3....
Knowledge seeker's user avatar
2 votes
0 answers
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Transform matrix calculation for image registration known the relative camera poses

I'm working on a problem where I define some positions of a chaser around an target object and take pictures of the same target with 2 cameras separated by a baseline. Example of the described problem ...
AlessandroColombo's user avatar
1 vote
1 answer
209 views

Why can't I estimate the Fundamental Matrix from a coplanar set of points?

I am learning how to estimate the Fundamental Matrix via the 8-point algorithm: From N > 8 corresponding points that satisfy $xFx' = 0$, we need to solve the LS problem: $kron(x,x')f = 0$ Where $...
Elad Maimoni's user avatar
1 vote
1 answer
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Back projecting a 2D pixel from an image to its corresponding 3D point.

I have been trying to understand how to project a 3D point to 2D image and vice versa. I had images of a building taken by a drone, I reconstructed the building using COLMAP(an SFM tool). For those ...
Sarvesh Thakur's user avatar

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