Mathematical methods used in widely understood computer vision.
Questions tagged [computer-vision]
244 questions
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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 \subseteq X \subseteq X \oplus B…
Nyquist-er
- 143
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Understanding a set of equalities to derive the intrinsic/extrinsic camera parameters during camera calibration
I am trying to understand Section $1.3$ of Forsyth and Ponce's Computer Vision: A Modern Approach,
Supposing we have an intrinsic camera matrix
$$K = \begin{bmatrix} \alpha & - \alpha cot(\theta) & x_0 \\ 0 & \beta sin(\theta) & y_0 \\
0 & 0 & 1…
IntegrateThis
- 3,778
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How to calculate the coefficients of lens distortion (radial distortion)?
How to calculate the coefficient k for the lens in the picture below?
https://i.stack.imgur.com/QDhW8.png
The lens needs to be described by a simplified Quartic model (the fourth-order coefficient is equal to…
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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 this formula:
Equation about anisotropic…
KalvinB
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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. I tried to search it and looked over several…
tobyblack
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What does this Gaussian window size equation mean?
Gaussian Window size W Equation
I came across this from a paper in Computer Vision. What exactly is an average operator? What I understood at the very least from this equation is that the loci r1 and r2 are from the images f and g's pixels which are…
Paolo
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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-ur)β - (v - vr)α)(-xyβ + (y^2 + 1)α)dxdy = 0,
∫∫((u-ur)β - (v - vr)α)((x^2+1)β -…
Harkais
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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:-
$∫∫((u-u_r)β - (v - v_r)α)(-xyβ + (y^2 + 1)α)dxdy = 0$,
$∫∫((u-u_r)β - (v -…
Harkais
- 21
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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 Method
I also understand that one can use the Bundle…
Gary Allen
- 408
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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 part, when the author writes, "A disadvantage of the…
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Understanding focal length (Camera intrinsics)
I'd like to know if my understanding is correct regarding camera focal length.
The intrinsics of the camera consists the focal length (and of course other parameters, not focusing on them here..) which is really derived from the two parameters Fx…
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Hand Selected Points and Homography precision.
I have two calibrated cameras, so I know the essential an intrinsic matrices and I have computed the homography between a set of hand selected points. They are hand selected because the selection of the points requires domain knowledge beyond which…
RickF
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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?
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Estimation of multiple motions from two views, understanding an example.
From my reference on the subject there's this simple example of which I can't understand the notation. In summary it is my understanding the goal here would be given two views of a scene where we have many objects moving can we estimate the…
user8469759
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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"
Angle of view (1/2"): 77.8° x 105.9° (Diagonal:…
