Mathematics behind Motion Blur

Recently I understood how the Gaussian Filter works and I was awed by the beauty of the mathematics behind it. Now while doing some coding stuffs in Octave I came across another type of blur, which is mentioned as $ image$ $ blur$ , and it gave me an output like this, enter image description here

It is beautiful, but i cannot find on the internet any explanation on the mathematics behind it?

Everywhere I searched $ Gaussian$ $ Filter$ is popping up, but i believe that this 2 are different to some extent as $ Gaussian$ $ Filter$ gave me this output–>

enter image description here

Which u can clearly see is $ different$ in appearance than the $ motion$ $ blur$ .

So, my question is, how is motion blur implemented?

Algorithm for coherent motion. Which bus is app user on?

I am currently working on an app with a map of the city, with markers for each bus. As a feature, the phone should show which bus the user is on.

To achieve this I am working on building a function that consumes a stream of a set of buses and their positions (Stream<Set<Tuple2<BusId, Location>>>), and a stream of phone location, to produce a Stream of bus predictions. The prediction should contain a confidence level.

The function should return the current prediction in real-time, and handle scenarios where the user changes the bus.

How could this be accomplished?

Both streams contain very precise locations at a rate of once every second.

$O(1)$ time, $O(1)$ state random access Brownian motion?

I would like to generate discrete samples $ 0 = B(0), B(1), \ldots, B(T)$ of a Brownian motion $ B : [0,T] \to \mathbb{R}^d$ . It is possible to get $ O(\log T)$ time random access into a consistent sequence of samples $ B(k)$ by constructing the path in tree fashion. We choose $ B(T) = \sqrt{T} Z_0$ where $ Z_0$ is a standard Gaussian, then let $ B(T/2) = B(T)/2 + \frac{\sqrt{T}}{2}Z_1$ where $ Z_1$ is an independent standard Gaussian, construct $ B$ for the intervals $ [0,T/2]$ and $ [T/2,T]$ independently conditional on $ B(0), B(T/2), B(T)$ , and so on recursively.

Since any particular $ B(k)$ constructed in this fashion only depends on $ O(\log T)$ Gaussian random values, this gives us $ O(\log T)$ time random access into a consistently sampled sequence of Brownian motion as long as we have random access random numbers. The only state we need is the random seed. As long as we use the same seed, evaluations of $ B(k)$ for different $ k$ will be consistent, in that their joint statistics will be the same as if we had sampled Brownian motion in sequential fashion.

Question: Is it possible to do better than $ O(\log T)$ , while preserving the $ O(1)$ state requirement (only the seed must be stored)?

My sense is no, and that it would easy to prove if I found the right formalization of the question, but I don’t know how to do that.

Can I measure time by counting frames and trusting on the ‘240 FPS’ that my iPhone 7+ slow motion camera is capable of record?

I’m using a slow motion video recorded using an iPhone 7+ to track something but would like to avoid recording a chronometer to know the time the process is taking. I need to measure about 10 seconds with an uncertainty of at most 0.1 s… Is this possible by just counting 2400 frames of my homemade video?

Leap Motion : Leap service running, “Leap Service not connected” in Unity3D, connected in SteamVR

I’m having trouble to use Leap Motion with Unity3D on one of my machines.

Unity doesn’t see Leap Service running : Leap Service not connected

Both computers run the same version of the software: Unity 2018.2.15.f1 and Orion 3.2.1

  • The Leap Service is running fine on the PC – I tried also to start and stop it manually, it didn’t affect the results

  • I installed and re-installed the drivers below – in the SteamVR window, I see the controllers, and they do stop blinking when the hands are in front of the sensor

    • https://github.com/cbuchner1/driver_leap (original one)
    • https://github.com/SDraw/driver_leap (updated one)
  • When opening the Diagnostic Visualiser, the hands show just fine

  • I tried connecting the Leap to the headset and to different USB ports, didn’t change anything

  • When running the same project on the other PC, leap motion hands are displayed in Unity normally

Any leads?

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Projectile motion function [on hold]

An artillery crew is trying to hit multiple different targets over the course of a battle. Where and when these targets show up is initially unknown but they all appear at different ranges (x) and different heights (h). The crew needs to calculate the angle ( Θ ) to aim the gun at to hit a target. Assume the velocity (v) is 100m/s and gravity (g) is 7.5.

Find the equation for Θ where x and h can remain variables so that the gun crew can use them to deduce the angle they need to aim their gun at.

I really need this to be cookie cutter, plug in the x and h and it rolls out theta if you crunch the numbers.