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How Can Convolution and Deconvolution be Defined for 3D Images?

For one variable, we have $$ y(i) = \sum_m x(i-m) \cdot h(m). $$ For two variables it's $$ y(i,j) = \sum_m \sum_n x(m,n) \cdot h(i-m,j-n). $$ For three: $$ y(i,j,k) = \sum_m \sum_n \sum_p x(m,n,p)...
AnonSubmitter85's user avatar
5 votes
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How to understand the basis sinusoids of 3D FFT?

To understand the Fourier Transform (and FFT) in 3 or more dimensions, you first have to get what it "operates over". The 1D FFT operates over a time series. That is, discrete measurements ...
A_A's user avatar
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4 votes

Analytical expression for the eigenvectors of a 3x3 real, symmetric matrix?

There's a newer (2017) closed-form formulation for the eigendecomposition of 2x2 and 3x3 Hermitian matrices here: Charles-Alban Deledalle, Loic Denis, Sonia Tabti, Florence Tupin. Closed-form ...
Luke Hutchison's user avatar
3 votes
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Multiple-image dense point cloud reconstruction with camera extrinsics/intrinsics

First, a warm welcome to SE! Basically, you have a calibrated 3D reconstruction problem. The typical approach follows a 5-stage pipeline: Identify 2D features in each image along with the associated ...
Tolga Birdal's user avatar
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3 votes
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why is it so hard to simulate up and down position on headphones?

Front/back is actually very hard too, at least for stationary simulation without head tracking. The main reason is simple: Left/Right is done by looking at the differences between the two ear signals,...
Hilmar's user avatar
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3 votes

What algorithms can automatically determine a 3D scene from one or a few 2D images?

SLAM(Simultaneous Localization and Mapping) algorithms can be used to for 3D reconstruction. They offer solutions for both monocular as well as stereo cameras. With single camera they estimate depth ...
Navin Prashath's user avatar
3 votes
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How does google automatically create 3D cityscapes?

They basically use 3D reconstruction based on ground and sometimes aerial footage of places, generally using stereo cameras. With this footage, they build a 3D point cloud based on the images to do ...
spektr's user avatar
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2 votes

Essential Matrix from line correspondences

When I think of lines in correspondence, my mind immediately goes for Pluecker representations, which are very suitable for such estimation tasks. In fact this work exists for camera pose estimation ...
Tolga Birdal's user avatar
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2 votes

Extending 1D window functions to 3D (or higher)

this question is old, but I needed same function. I wrote a function that receive one-dimensional window as parameter and transformed into a cube window ...
Angel's user avatar
  • 121
2 votes

Point cloud comparison

This is termed 3D object retrieval. There are many possible approaches to follow. First, if your meshes are nice, clean and descriptive, you could then consult the academic literature of computer ...
Tolga Birdal's user avatar
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2 votes
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Triaxial accelerometer to single signal

Your expression $A=\sqrt{a_x^2+a_y^2+a_z^2}$ calculates the length of the 3-dimensional vector with coordinates $(a_x, a_y, a_z)$. So, it is the magnitude of the acceleration. Your expression $a=\...
Maximilian Matthé's user avatar
2 votes
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A PID that can handle 2 inputs for my application

If you require two outputs, which belong to a movement in x and the other in y direction, you could start with the assumption, that both movements are independent an simply implement two PID ...
user6522399's user avatar
2 votes

Is there any simple algorithm to convert a sound source in 3d to volume and panning

inverse-square law for distance. and Blumlein stereo for pan.
robert bristow-johnson's user avatar
2 votes

What algorithms can automatically determine a 3D scene from one or a few 2D images?

Let us first assume you can produce estimates of the camera state (position and attitude) via sensors, a filter like a Kalman Filter, and a (simple) model for the camera itself. Using this information,...
spektr's user avatar
  • 263
2 votes

3D reconstruction of moving object

This problem is also known as "4D reconstruction" or "spatio-temporal reconstruction." Several methods have recently been developed to solve this problem, such as "occupancy ...
Anderson Green's user avatar
2 votes

2D to 3D view conversion

It seems to be at a stadium which uses 12 cameras and Replay-Technologies special signal processing called FreeD: https://www.youtube.com/watch?v=N1kgt2VDjdM The image you show seems to use 2-3 ...
bandybabboon's user avatar
1 vote

Is there any simple algorithm to convert a sound source in 3d to volume and panning

If you want simple, you have to get rid of elevation (z-axis). If you want dead simple with two channels with a fixed range of motion, you can just take the square root of the panning width, ...
Jacob Sundstrom's user avatar
1 vote

Is there any way to do 3D (Voxel Data) feature detection?

I never personally tried it but using image registration algorithm on Voxel Data you may have some results by trying registration on sub-cluster of voxel. I would be interested in any feedback about ...
NRVL's user avatar
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1 vote
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Isosurfaces from three dimensional column data: methods

You are given a series of $N$ triplets of values ($P_1$, $P_2$, $P_3$), pertaining to physical measurements. $N$ is in the order of $100$ to several thousands. My colleague would like to draw ...
A_A's user avatar
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1 vote

Is it possible to generate depth map from graycode sequence without using printed calibration patterns?

... if the camera's intrinsics are known and calibrated, is it possible to generate the depthmap fully automatically through a graycode sequence without any manual calibration process ? Yes, provided ...
A_A's user avatar
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1 vote

1D as a 3D FFT - what’s wrong here?

OK, I need to answer my own question. The math transform I described is GOOD, the problem was like always, stupid mistake in the code. But Stanleys answer helped me much. Thanks a lot.
pajczur's user avatar
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1 vote
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Camera calibration and extrinsic parameters for perspective transformation

You can bypass all the OpenCV stuff, and create a custom mapping from pixel location to real world location of the form: $$ x = A_x m^2 + B_x mn + C_x n^2 + D_x m + E_x n + F_x $$ $$ y = A_y m^2 + ...
Cedron Dawg's user avatar
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1 vote

Camera calibration and extrinsic parameters for perspective transformation

For your application, here are the steps I would follow: Calibrate the camera and obtain the intrinsics - You have obviously done that and corrected for the distortion already. ...
Tolga Birdal's user avatar
  • 5,465
1 vote

Why are two cameras mounted in paralle in stereo application?

When you say cameras are parallel it only means that the center pixels are parallel. Every pixel has a different angle, and that refers to the overlapping regions you were talking about. Actually ...
Cherny's user avatar
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1 vote
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Sensor fusion with accelerometer and gyroscope only

Actually, the plots for the components of gravity look good. What you miss is the fact, that your overall gravity (i.e. gravity sum) is the length of the vector, that is spanned by the three ...
Maximilian Matthé's user avatar
1 vote

the position of image plane in optical imaging

I agree with user lxg that it is a notational difference, as for the pinhole camera we always have: $$S_2 = f$$ That is not necessarily true for a camera with a lens. A pinhole camera is not the ...
Olli Niemitalo's user avatar
1 vote
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Backprojection of 2D image on 3D model

In section 2 of the paper it is mentioned that "Our image formation model assumes weak perspective projection, relatively distant illumination, and Lambertian reflectance" (emphasis is mine). All ...
A_A's user avatar
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1 vote

How can we combine 2D image with 3D image for the same sense?

Formally speaking, you would like to extrinsically calibrate the laser scanner to the 2D image. I have taken the liberty to edit your question to reflect that. Here is how my initial approach would ...
Tolga Birdal's user avatar
  • 5,465
1 vote

Generate 3D image from Multiple 2D Images

If you want to do this seriously, you should have a look into photogrammetry techniques - or rethink you problem and find out if you really need a full 3D model. For photogrammetry, I assume you would ...
M529's user avatar
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1 vote

Generate 3D image from Multiple 2D Images

You can make a 3D model of the scene (<=> the depth) if the two cameras are looking to the same scene. After that you detect/extract the commun points between the two images and do some ...
ROS_OPENCV's user avatar

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