Let's take the example of trying to track an object in an image. So you do not know where it is at the start to you make a load of guesses. So let's say a particle has an x and y position and let's say it has a constant velocity (or that is how we are going to model it in our particle - but the beauty of the particle filter is that this simple model works pretty well for an object moving with any sort of motion). So how do we generate these first guesses ie a set of particles? Well for each particle assign it a random position (eg using an even distribution over that image), and we assign random velocities. The only other thing the particle needs is a weight. This is the same for all these first particles. So what next? We get a measurement. This measurement is used to recalculate the weights of each particle. So in the context of an image if we say that the object is more likely to be at a pixel position the brighter the pixel is, then we can update the weights of each pixel. This is done by multiplying the previous weight by the pixel intensity for the particles position in the image. So now we have updated the particles given an observation. Next for all the particles predict into the future. So for each particle take its x,y position and move it according to that particles velocity AND we add a bit of noise too to each of these componts. Now we have predicted the furture! Now we get another observation so now we do not do the same thing to our set of particles. If we have 100 particles we 'pick' 100 new particles. We do this at random - well not actually random - it is random but a weigted random were this likelyhood of picking a particle is proportional to that particles weight. So now you have this next set of particles that you are using. So you are now in the looping. You update the particles based on the observation, you predict the future, you resample the particles, you update based on the observation, you predict the future, you resample the particles, you update based on the observation, you predict the future, you resample the particles, you update based on the observation, you predict the future, you resample the particles, you update based on the observation, you predict the future, you resample the particles, you update based on the observation, you predict the future, you resample the particles, you update based on the observation, you predict the future. Don't forget you need to be adding the noise - this gives the particle filter it's power. The result is actually a set of particles. The particle filter does not define how you interpret these particles as a result. For this scenario of an image, you can simply visualise the particles and the human brain is great at understanding images. A crude way is to 'average' the particles or find a maxima. This step is up to you.
I just came across this video to understand the Particle Filter better and surely it helped a lot, so thank you! However, I have a question regarding the algorithm. Isn't the normalization factor eta supposed to be inside the for loop to set back to 0 after normalizing all the resampled weights? Because otherwise it would carry on the normalization of the previous step weights and the probability distribution wouldn't sum one, right?
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The explanation is very clear and provides a very good intuition behind the particle filter.
the explanation is not clear at all! You are just reading the algorithm !!
Let's take the example of trying to track an object in an image. So you do not know where it is at the start to you make a load of guesses. So let's say a particle has an x and y position and let's say it has a constant velocity (or that is how we are going to model it in our particle - but the beauty of the particle filter is that this simple model works pretty well for an object moving with any sort of motion). So how do we generate these first guesses ie a set of particles? Well for each particle assign it a random position (eg using an even distribution over that image), and we assign random velocities. The only other thing the particle needs is a weight. This is the same for all these first particles. So what next? We get a measurement. This measurement is used to recalculate the weights of each particle. So in the context of an image if we say that the object is more likely to be at a pixel position the brighter the pixel is, then we can update the weights of each pixel. This is done by multiplying the previous weight by the pixel intensity for the particles position in the image. So now we have updated the particles given an observation. Next for all the particles predict into the future. So for each particle take its x,y position and move it according to that particles velocity AND we add a bit of noise too to each of these componts. Now we have predicted the furture! Now we get another observation so now we do not do the same thing to our set of particles. If we have 100 particles we 'pick' 100 new particles. We do this at random - well not actually random - it is random but a weigted random were this likelyhood of picking a particle is proportional to that particles weight. So now you have this next set of particles that you are using. So you are now in the looping. You update the particles based on the observation, you predict the future, you resample the particles, you update based on the observation, you predict the future, you resample the particles, you update based on the observation, you predict the future, you resample the particles, you update based on the observation, you predict the future, you resample the particles, you update based on the observation, you predict the future, you resample the particles, you update based on the observation, you predict the future, you resample the particles, you update based on the observation, you predict the future. Don't forget you need to be adding the noise - this gives the particle filter it's power. The result is actually a set of particles. The particle filter does not define how you interpret these particles as a result. For this scenario of an image, you can simply visualise the particles and the human brain is great at understanding images. A crude way is to 'average' the particles or find a maxima. This step is up to you.
Easy explanation.. thank you!
I just came across this video to understand the Particle Filter better and surely it helped a lot, so thank you!
However, I have a question regarding the algorithm. Isn't the normalization factor eta supposed to be inside the for loop to set back to 0 after normalizing all the resampled weights? Because otherwise it would carry on the normalization of the previous step weights and the probability distribution wouldn't sum one, right?
Good explanation.
What class is this from on udacity?
Intro to computer vision