Category: Research Blog

Blog articles to discuss about a specific technical topic.

List of Significant Probability Puzzles

I am collecting a list of probability/statistics/random processes puzzle problems. Click on the links for the description and solutions of the problem. It is well worth the effort to study, understand and derive the solutions to these. Helps sharpen the mind and increase your analysis skill. Please feel free to add your suggestion if I … Continue reading List of Significant Probability Puzzles →

Part-3 : Controlling a Mechanical System

This is the third post in my series on control systems. In part-1 we explored what the differential equations can do for you and how to make use of a differential equation, particular the Euler-Lagrange equations to describe a mechanical system. In part-2, we derived these differential equations for our 'pendulum on a cart' system. … Continue reading Part-3 : Controlling a Mechanical System →

Part-2 : Simulating a Mechanical System with Differential Equations

This is my second part in a built-up towards understanding and implementing a real world control system. In my past post, I talked about differential equations.  The take home message from my last post was that, given a mechanical system and solving the free body diagram of it, we can get the differential equations describing … Continue reading Part-2 : Simulating a Mechanical System with Differential Equations →

Vector Differentiation

Just a quick cheatsheet on derivatives (of scalars and vectors) wrt of a vector. This is borrowed from the wiki page : Matrix Calculus. Vector Calculus CAS Tricks The following document is borrowed from here. Vector Calculus with Maxima (Computer Algebra System)Download Oftentimes, we need to get linear approximation of a complicated function. This is … Continue reading Vector Differentiation →

Part-1 : Why should I study differential equations?

What's the point of studying differential equations? Can we not do away with them? I almost never see an application of those as a computer science or an ECE systems student. Is it like the analog systems, we study for the legacy reason. Can we not do away from differential equations. I used to side … Continue reading Part-1 : Why should I study differential equations? →

Optimal Triangulation for Tuning Keypoint Co-ordinates

Given a set of correct keypoint matches and a fundamental matrix, to optimize the coordinates of these key points such that they satisfy the epipolar constraint. A point (x,y) on the left image (pose: [I|0]) and (x',y') on the right image (pose: [R|t]). These points are undistorted and in normalized image coordinates. Having known the pose … Continue reading Optimal Triangulation for Tuning Keypoint Co-ordinates →

Image Keypoint Descriptors and Matching

[GitHub] Extracting keypoints from images, usually, corner points etc is usually the first step for geometric methods in computer vision. A typical workflow is: keypoints are extracted from images (SIFT, SURF, ORB etc.). At these keypoints descriptors are extracted (SURF, ORB etc). Usually a 32D vector at each keypoint. The nearest neighbor search is performed to … Continue reading Image Keypoint Descriptors and Matching →

HowTo – Pose Graph Bundle Adjustment

SLAM (Simultaneous Localization and Mapping) is one of the important practical areas in computer vision / robotics / image based modelling community. A SLAM system typically consists of a) odometry estimator (relative pose estimator), b) Bundle adjustment module, c) sensor fusion module (for visual-inertial system), d) mapping module. While there are several excellent resources, refer … Continue reading HowTo – Pose Graph Bundle Adjustment →