Particles explained using Gifs!!

Over the past few months, I have been reading, understanding and implementing a number of existing algorithms in Computer Vision domain. Implementing particles and particle based algorithms have really had me excited and almost on the edge of my seat. One may ask what makes particles so interesting?? Let me try to get the concept through.

Particles, just like most existing algorithms in computer science, are inspired by nature. Have you ever seen a beam of sunlight coming through a window and illuminate a bunch of floating particles (impossible in London though I have seen it before)? When you see these tiny particles, you notice that they are suspended in air and that it's very difficult to predict their motion unless you disturb the surrounding air. This simple concept is vital for many computer algorithms that model motion/dynamics of an object.

Particles, along with their randomness, can be simulated inside a computer program. The simplest of such algorithm is called Random Walk, where a particle is modelled with its current position/state alone and a random displacement/jump determines its next position in time. Here I have shown one Random Walk particle:

A Single Random Walk Particle

Particle Filtering - Survival of the fittest

I recently studied dynamic system models such as Kalman and Particle Filters.
For Kalman Filter I followed a Matlab demo that can be found here.

In this demo, the simple problem of tracking a ball is addressed using a Kalman Filter. The input sequence is of a ball, which is travelling at varying velocity and which is occluded in some frames by a box. I think this is a great example to demonstrate the power of dynamic system  models, especially the occluded frames can be used to test how good a dynamic model is. Here is the actual sequence:

As you can see the ball goes underneath the box and comes out of the other end. If our dynamic model is accurate it will be able to predict the state of the ball even when it is not visible, and should match the position when the ball comes out.

One Image hiding over eight thousand different stories...

Working with large datasets has its own pros and cons. Whatever the implementation or field might be, there is always a need for training a machine learning algorithm to recognize the pattern in that data. We often discuss this "Pattern" in many different instants and a big chunk of literature addresses this recognition problem. However it is often not considered important to get to know how this pattern looks like? why is it even called "Pattern" in the first place??

Interestingly the answer lies in the above image which shows a collection of 8000 different samples, arranged in columns. Here the first thing to notice is that there actually is a repeating pattern in the data. This is the exact pattern which we are trying to learn. It may not make sense when looking at it, however with correct label representation, each sample can be used to build a model which is able to identify each class with high accuracy.

Mind == Blown!

 So sometime back I saw this video presentation of a new and, what I like to call it, novel method for extracting 3D structures from a single image. Part of the reason why this blows my mind, is that this approach is well defined for a specific scenario and it utilizes the best of both human brain and computer's processing power.

We have a great sense of depth perception of objects. Our brains are well trained to construct an object's three dimensional model, by just looking at pictures. This, however, is a trivial and a highly challenging task for computer algorithms. On the other hand, computers are capable of computing and interpolating data at a much faster rate than humans, given that the task is simple and fairly straightforward.

OUT-A-TIME: What is the fourth dimension?

I have been doing my research using three dimensional datasets acquired from both real and synthetic methods. During my past research I utilized Microsoft Kinect to acquire real-world objects in their three dimensional space. On the contrary I have also used computer graphics to generate such three dimensional datasets. Some other projects I have worked on have also revolved around concepts which were vaguely related to different multi-dimensions.

Working with these multi-dimensional datasets, I have always been interested in finding out how these multi-dimensions would exist in reality (if they ever did). Here I was more interested in the question about physical space we live in. Annoyingly this has always confused me. I simple could not comprehend more than three dimensions.

For those of you who are familiar with the picture below, this post is going to be as interesting for you to read as it was for me to write.