Archive for the ‘Math’ category

Hough transform

16 January 2010

Hough transform of black image with broken lines

As part of an image recognition project I was working on today I was introduced to the Hough transform.  This transform is useful for finding lines and other regular shapes (circles, ellipses) in an image.  Every pixel on the image is sampled, and an accumulator array (whose dimension is equal to the number of parameters in the shape: line=2, circle=3, ellipse=5) is used to tabulate votes based on edges in that pixels neighborhood.  This description shows several nice image pairs.

The similar Radon transform is in some sense a continuous version of the Hough transform, and used in tomography.   The complex form of the Radon transform is the Penrose transform, which is somehow important in twistor theory.

SAGE history and ODE solvers

12 December 2009

William Stein recently wrote up an interesting history of his trajectory in mathematics and creation of SAGE (which I’m a big fan of).   This document lead me to discover (Pyrex and) Cython, which looks very useful for my work.

Also, after reviewing and debugging my RKF method, I’m ready to use the scipy solution, scipy.integrate.odeint, which provides and interface to LSODA in the ODEPACK.   Getting to know ODEPACK intimately will be the key for implementing my ode.

Kinematic closure applied to protein folding

10 December 2009

Introduced to the work of Dr. Evangelos Coutsias at UNM, an read through a couple of his papers

CUDA articles

30 November 2009

Read several interesting articles on the parallel programming architecture CUDA, some of which emerged from the SC 2009 conference, and some from the nVidia website.

Oblate spherical coordinates

29 October 2009

Elliptical coordinates are defined in 2D and can be rotated around the x or y axis to yield 3D oblate spherical coordinates or prolate spherical coordinates.

Project Euler #254

12 September 2009

This week worked intently on Problem 254 on Project Euler, which is very interesting.  Didn’t solve it, but did type up my notes here – ProjectEuler254.

Math Proofs Demystified

18 July 2009

MathProofsDemystifiedI borrowed Math Proofs Demystified from the library and worked through about half of it in May and in July.  As with the other demystified books it provides an opening to self teaching, and does a good job.  Working through the examples rather than just reading through them is the key with this book, however, since all the chapter tests are multiple choice.