MuJoCo (Multi-Joint dynamics with Contact) is a physics engine mainly developed by Emo Todorov and maintained by Google DeepMind. It is widely used in robotics, reinforcement learning research, and biomechanics. This post covers installation on macOS, importing model, and running simulations i...
The Particle Filter is a sequential Monte Carlo implementation of the Bayesian Filter. Unlike the Kalman Filter, it does not require linearity or Gaussian assumptions, making it suitable for highly nonlinear systems and non-Gaussian distributions. Instead of representing the belief with a mean...
The Kalman Filter is a specialized implementation of the Bayesian Filter. It is widely used in various engineering fields due to its optimality and computational efficiency when applied to linear systems with Gaussian noise. Below is a step-by-step mathematical derivation of its update equatio...
Image denoising is a fundamental task in computer vision, aiming to recover a clean image from a noisy observation. Total variation minimization, introduced by Rudin, Osher, and Fatemi (ROF), addresses this by penalizing the image gradient and data fidelity. This post explores the mathematical...
This article explains how to solve roots of a quartic polynomial in the complex plane. I use the depressed form of the quartic polynomial and Descartes’ method. Additionally, I demonstrate an interactive demo which visualizes the roots of a quartic polynomial.