Browsing All Posts filed under »Research«

Simulating a Mechanical System with Differential Equations

June 30, 2018

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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 […]

Vector Differentiation

April 24, 2018

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Just a quick cheatsheet on derivatives (of scalars and vectors) wrt of a vector. This is borrowed from the wiki page : Matrix Calculus. Usually, in print following notations are in use: A : Matrix (capital and bold) b : Vector (small and bold) c : scalar (small and not bold) The rules for derivatives […]

Why should I study differential equations?

January 18, 2018

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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 […]

Optimal Triangulation for Tuning Keypoint Co-ordinates

October 11, 2017

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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 […]

Image Keypoint Descriptors and Matching

August 17, 2017

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[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 […]

HowTo – Pose Graph Bundle Adjustment

April 29, 2017

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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 […]

Generating randoms from a specified CDF

March 9, 2017

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This post deals with generating random numbers given a CDF (Cumulative distribution function). CDF may be specified as an analytical function or as a table of values. We also assume that we have a source of pseudo-random uniformly distributed numbers. Probability Integral Transform At the core of this issue is the ‘Probability Integral Transform’.  It states that, […]